Analysis report

Engine Horsepower (refined)

Automatically produced by Diafunc

Target: Class
Analyzed: 2026-10-24 17:42 UTC

Summary

The model describes how Class moves with three inputs, above all City-mpg, with which the model's output falls: moving City-mpg from 19.0 to 30.0 lowers the model's output by about 35.8 on average, with all other inputs as observed. Engine-size is the next strongest input and raises the model's output as it increases. While the model surpassed a straight line through the data by a slight margin, most of what it learned comes from City-mpg.

The margin over the baseline was small, so much of the model's answer can be reached with a simple regression. Residual variance grows sharply with the predicted value: the model becomes much less accurate for larger predicted values, and the analysis checked its accuracy on only 40 held-out rows, so every figure rests on a small sample. Validate on a fresh sample before relying on the model for decisions about high-magnitude cases.

Formula

Class = 0.3 × (Engine-size − 0.26 × Length) + 0.7419 × csch(atan2(City-mpg, 50^2))

3 terms · additively decomposable

Held-out diagnostics

Target	Quality	Error	R²	MAE	N without target	Generalization	Rows
Class	82.79 %	13.66 %	0.8419	9.598	1	generalizing	40

Class · Quality 95 % CI 72.18 % – 89.37 %
Class · Error 95 % CI 8.43 % – 22.07 %
Class · R² 95 % CI 0.7501 – 0.9012
Class · MAE 95 % CI 7.261 – 12.44

Concerns

CRITICAL model

Residual variance grows sharply with predicted value: the model is systematically less accurate on high-magnitude predictions

Across 40 held-out rows split into thirds by predicted value, the residual standard deviation in the top third is 20.7, against 5.97 in the bottom third, 3.47 times as large. The bottom third holds predictions up to 80.2 and the top third predictions from 119. The model is accurate at the low end and misses systematically at the high end, where the residual spread is 3.47 times as large. A log transform of the target, or an input that captures the magnitude, may help. The Regression Diagnostics chapter plots the residuals against the predicted values.

INFO implications

2 inputs could stand in for a column, if that column must not steer predictions

This matters only for a column that is a characteristic the predictions must not follow, such as a person's age, sex or origin; for ordinary properties of the data it needs no action. For 2 pairs an input a model reads and a column the Fairness chapter compares go together with an association of at least 0.5 on a scale from 0 to 1. The closest: City-mpg with Fuel-system (0.748); Engine-size with Engine-type (0.644). A model that reads such an input can tell the column's groups apart, so leaving the column out of the inputs would not keep it out of the predictions. The Fairness chapter compares the model across its groups. An association, not a cause.

Complete list (2)
Column	Detail
fuel_system	City-mpg goes with it, an association of 0.748 on a scale from 0 to 1
engine_type	Engine-size goes with it, an association of 0.644 on a scale from 0 to 1

Analysis

The report opens with the Headline and the Concerns, followed by the Discovered Relations when the analysis has targets and by Questions & Answers when questions were asked. Three sections carry the detail: Model presents one model per target, Implications states where the models hold and what to weigh before relying on them, and Data describes the table as supplied, column by column, for reference.

Generated 2026-10-24 17:43 UTC, analysis 27b5ec60-c685-11f1-b558-07fc56137a66, 1 target, time budget 1 h 0 min, compute budget 500 credits, 205 rows. The Provenance & Audit chapter holds the full record.

Validity

Validity: valid. Nothing in the data or the formula speaks against relying on this result.

How to read this

Whether this result is one to rely on. Quality says how closely the formula follows the data; validity says whether that closeness means anything. A formula that only restates its target, or that reads a column which already holds the answer, can reach a very high quality and still tell you nothing new.

What it found

Class rises with Engine-size and falls with City-mpg.

City-mpg carries most of the model for Class. City-mpg accounts for 80% of what the formula explains, and Engine-size for 19%. Length adds 0.7%.
The model's output for Class rises with Engine-size. For each additional 10 units of Engine-size, the model's output for Class is higher by 3. This holds with the other inputs at typical values.
Highway-mpg is not in the formula for Class. It has the second-strongest correlation with Class in the table (-0.77). Rows with more of it have more City-mpg (correlation 0.97), and City-mpg is in the formula.
The formula's lead over a straight line is within chance. The formula explains 84% of Class; a straight line explains 77%, but on 40 unseen rows that gap is within chance, so treat them as level. The formula typically misses Class by 9.6.

Summary

What to do next: 6 columns compared, 6 flagged: Aspiration (a group is systematically over- or under-predicted), Body-style (a group receives systematically smaller predictions), Drive-wheels (a group receives systematically smaller predictions), Engine-type (a group both receives smaller predictions and is systematically mis-predicted), Fuel-system (a group both receives smaller predictions and is systematically mis-predicted), Fuel-type (a group is systematically over- or under-predicted).

5 chapters, each headed by what it found.

City-mpg carries most of the formula

What the formula relies on. Shares of the formula: City-mpg 80%, Engine-size 19%, Length 0.7%.

The model's output falls with City-mpg on every one of the 3,036 steps between observed values. The model's output rises with Engine-size on every one of the 4,692 steps between observed values. The model's output falls with Length on every one of the 138 measured rows (exact derivative). Moving City-mpg from 19.0 to 30.0, its first and third quartile, with every other input as observed lowers the model's output by 35.8 on average. These are measurements on the rows the search trained on, inside the observed ranges; outside them nothing is claimed.

Input	Share of importance	Permutation importance	Sensitivity	Residual correlation	Occurrences	Model's output as the input rises	Change, first to third quartile
City-mpg	80.05 %	4.767	3.542	0.1992	1	Falls (3036 of 3036 steps)	-35.8 (19 to 30)
Engine-size	19.27 %	1.148	0.3	0.06586	1	Rises (4692 of 4692 steps)	+14.4 (98 to 146)
Length	0.68 %	0.040	0.078	0.1341	1	Falls (138 of 138 rows)	-1.232 (167.3 to 183.1)

Rows the search trained on, measured: 138
Inputs the formula does not read: Aspiration, Body-style, Bore, Compression-ratio, Curb-weight, Drive-wheels, Engine-location, Engine-type, Fuel-system, Fuel-type, Height, Highway-mpg, Make, Num-of-cylinders, Num-of-doors, Peak-rpm, Price, Stroke, Symboling, Wheel-base, Width

Read as a sum, the formula has 3 additive terms. Two of them carry 102% of the variation of the model's output on the 138 rows the search trained on: 0.7419 × csch(atan2(City-mpg, 50^2)) (63%) and 0.3 × Engine-size (39%). A share describes the model's output, not the target. Each curve below shows one term's response to its free inputs, with the other inputs held at the training median.

Additive: Yes
Rows the search trained on, measured: 138
Terms in the formula: 3
Notation: 0.3 × (Engine-size − 0.26 × Length) + 0.7419 × csch(atan2(City-mpg, 50^2))
Target: Class

It holds on new rows: R² 0.84 held out, 0.79 on the training rows

How well it holds. The formula explains 84% of Class; a straight line explains 77%, but on 40 unseen rows that gap is within chance, so treat them as level.

R² of 0.842: good. The model captures most of the variation; individual predictions still carry uncertainty; the Prediction Interval Coverage chapter shows how wide it is. Mean absolute error is 9.60 on the target's scale.

Error: 13.66 % (95 % CI 8.43 % – 22.07 %)
MAE: 9.598 (95 % CI 7.261 – 12.44)
N: 40
Held-out rows offered: 41
Training rows: 153
Held-out rows scored: 4000 %
N without target: 1
Quality: 82.79 % (95 % CI 72.18 % – 89.37 %)
R²: 0.8419 (95 % CI 0.7501 – 0.9012)
Target: Class

The model beats the strongest simple yardstick, a straight line through the data, by 6.8 points of variance explained on the held-out rows. Row by row the margin is small: on many individual rows the yardstick does about as well, and whether the complexity is justified depends on the use. Of the 40 held-out rows where the two differ, the model is closer on 53% (95% interval 37% to 67%). The interval of the margin includes zero: on this many held-out rows the lead is not settled.

Best yardstick's score: 0.774 (95 % CI 0.6746 – 0.8477)
Best baseline R²: 0.774
Effect size d: 0.2404 (95 % CI -0.06743 – 0.5061)
Effect size d magnitude: small
Margin over the best yardstick: 0.06793 (95 % CI -0.0106 – 0.1594)
Margin's interval stays above zero: No
Model MAE: 9.598 (95 % CI 7.261 – 12.44)
Model: 0.8419 (95 % CI 0.7501 – 0.9012)
Model R²: 0.8419 (95 % CI 0.7501 – 0.9012)
Held-out rows: 40
Held-out rows without an answer: 0
Target: Class
Rows where the model is closer: 52.5 % (95 % CI 37.5 % – 67.06 %)
Rows compared: 40
Rows level: 0
Regression yardstick trained with gaps filled (too few complete rows): No
Training rows of the regression yardstick: 153

The model explains held-out rows about as well as training rows (held-out R² 0.842, gap between training and held-out R² -0.0482): it generalizes. The structure the formula encodes carries from the training rows to the held-out rows.

Generalization gap: -0.04822
N test: 40
Target: Class
Test error: 9.598 (95 % CI 7.261 – 12.44)
Test R²: 0.8419 (95 % CI 0.7501 – 0.9012)
Train error: 0.1441
Train R²: 0.7937
Verdict: Generalizing

No range of its inputs where it is markedly weaker

Where it is weak. The largest miss on a held-out row is 40.6 (recorded 160, predicted 119). 9.8% of the held-out rows are unlike the rows it learned from.

Segment num_of_doors in the highest quarter (4) performs in line with the aggregate (24 held-out rows): segment R² 0.758 against aggregate R² 0.842 (gap -0.0841). No quality drift detected.

Segment	Rows	R²	Gap to all rows	Verdict
Num-of-doors = q4	24	0.7578	-0.0841	In line with all rows
Body-style = sedan	21	0.8086	-0.0333	In line with all rows
Drive-wheels = fwd	26	0.8177	-0.0242	In line with all rows
Num-of-cylinders = q4	39	0.8313	-0.0106	In line with all rows
Fuel-type = gas	36	0.8345	-0.0074	In line with all rows
Engine-location = front	40	0.8419	+0.0000	In line with all rows
Engine-type = ohc	29	0.8611	+0.0192	In line with all rows
Aspiration = std	30	0.8838	+0.0419	In line with all rows
Engine-type = dohc	3	-14.1684	-15.0103	Too few rows to judge
Highway-mpg = q3	9	-0.2062	-1.0481	Too few rows to judge

The first 10 rows of 24. The other 14 are in the notebook.

Aggregate R²: 0.8419
Measure: r2
Target: Class

The worst held-out row was missed by 40.6 (target's scale). The 10 rows with the largest absolute residuals out of 40 held-out rows are shown. Each card breaks the failure down into per-term contributions and input values, so the failure mode is inspectable. A large residual with one concentrated term contribution means one term got this row wrong; a large residual with balanced contributions means a structural mismatch.

Actual	Predicted	Residual	City-mpg	Engine-size	Length
160.0	119.4	+40.6	19	121	186.6
162.0	133.4	+28.6	17	130	188.8
162.0	133.4	+28.6	17	130	188.8
161.0	134.6	+26.4	19	171	183.5
97.0	119.1	-22.1	19	120	186.7
115.0	130.1	-15.1	18	136	176.6
110.0	124.4	-14.4	19	136	180.2
110.0	123.4	-13.4	19	136	192.7
143.0	129.8	+13.2	19	151	168.9
62.0	75.1	-13.1	31	92	158.7

Additive: Yes
N extrapolated: 0
Held-out rows: 40
Held-out rows for the interval: 40
Residual P5: -14.41
Residual P95: 28.62
Residual std: 13.14

4 of 41 held-out rows (9.8%) lie further from the training rows than 99 in 100 rows like them would, measured on the 3 inputs the model reads (city_mpg, engine_size, length). That is a small minority; the held-out figures describe the model on rows like the ones it was trained on.

Target	Inputs measured	Line	Held-out rows	Beyond the line	Share
Class	City-mpg, Engine-size, Length	3.368	41	4	9.76 %

Score bins · 24 of 30 rows shown
Count	From	To
0	0	0.16
2	0.16	0.32
2	0.32	0.481
5	0.481	0.641
0	0.641	0.801
0	0.801	0.961
3	0.961	1.121
4	1.121	1.281
4	1.281	1.442
3	1.442	1.602

The first 10 rows of 24. The other 14 are in the notebook.

Not ready to use yet: 1 critical concern

What to watch. First: Residual variance grows sharply with predicted value: the model is systematically less accurate on high-magnitude predictions.

Severity	Section	Concern	Detail
Critical	Model	Residual variance grows sharply with predicted value: the model is systematically less accurate on high-magnitude predictions	Across 40 held-out rows split into thirds by predicted value, the residual standard deviation in the top third is 20.7, against 5.97 in the bottom third, 3.47 times as large. The bottom third holds predictions up to 80.2 and the top third predictions from 119. The model is accurate at the low end and misses systematically at the high end, where the residual spread is 3.47 times as large. A log transform of the target, or an input that captures the magnitude, may help. The Regression Diagnostics chapter plots the residuals against the predicted values.
Info	Implications	2 inputs could stand in for a column, if that column must not steer predictions	This matters only for a column that is a characteristic the predictions must not follow, such as a person's age, sex or origin; for ordinary properties of the data it needs no action. For 2 pairs an input a model reads and a column the Fairness chapter compares go together with an association of at least 0.5 on a scale from 0 to 1. The closest: City-mpg with Fuel-system (0.748); Engine-size with Engine-type (0.644). A model that reads such an input can tell the column's groups apart, so leaving the column out of the inputs would not keep it out of the predictions. The Fairness chapter compares the model across its groups. An association, not a cause.

The analysis ran with the configuration below. The checks and the verdict of this chapter are read against it.

Targets: 1 target: class
Rows: 205 rows
Per-Segment Predictions: not produced, because no segment column was chosen
Fairness: compared across 8 categorical columns (aspiration, body_style, drive_wheels, engine_location, engine_type, fuel_system, fuel_type, make); which of them are protected attributes is not decided here
Out-of-Distribution: held-out rows are scored against the training rows; predictions made outside this report are not scored
Provenance & Audit: recorded in the chapter of that name

Across 6 checks (4 pass, 1 warns, 1 fails, 1 critical concern), at least one check fails or a critical concern is open: Not ready. The failing checks need addressing first; they typically indicate data leakage, severe miscalibration, or a model that loses to its baseline.

Name	Status	Detail
Generalization	Pass	held-out quality holds up against training quality
Prediction Interval Coverage	Warn	intervals are wider than their level requires, largest gap 7.50 percentage points
Baseline Lift for Class	Pass	beats the best baseline, R² lift 0.0679
Model Constraints	Pass	every held-out prediction is finite and within the training range
Fairness	Fail	6 columns compared, 6 flagged: Aspiration (a group is systematically over- or under-predicted), Body-style (a group receives systematically smaller predictions), Drive-wheels (a group receives systematically smaller predictions), Engine-type (a group both receives smaller predictions and is systematically mis-predicted), Fuel-system (a group both receives smaller predictions and is systematically mis-predicted), Fuel-type (a group is systematically over- or under-predicted)
Out-of-Distribution	Pass	9.8% of held-out rows are out of distribution

N critical concerns: 1
N fail: 1
N pass: 4
N warn: 1
Overall verdict: Not ready

Column Engine-type splits the held-out rows into 4 groups. The prediction-parity ratio is 0.614 (smallest over largest mean prediction), the largest absolute group residual mean is 19.2 (1.46 times the overall residual standard deviation). Parity gap and residual bias: the model both predicts systematically lower for some groups and errs systematically against at least one group. This is the worst-case fairness signal on this column; review before deployment. num_of_cylinders goes closely with engine_type (association 0.778 on a scale from 0 to 1, and 4 more columns at 0.5 or above): a model that reads num_of_cylinders can tell the groups of engine_type apart, so leaving engine_type out of the inputs does not keep it out of the predictions.

Aggregate residual std: 13.14
Held-out rows offered: 41
N columns: 6
N proxies: 21
N without target: 1
Proxy threshold: 0.5

Columns
Bias max abs residual mean	Column	Groups	Interpretation	N groups	N proxies	Prediction parity ratio	Verdict
11.8	Aspiration	turbo, std	Column Aspiration splits the held-out rows into 2 groups. The prediction-parity ratio is 0.835 (smallest over largest mean prediction), the largest absolute group residual mean is 11.8 (0.898 times the overall residual standard deviation). Residual bias: at least one group is systematically over- or under-predicted. The model's errors are not zero-mean across groups; its predictions for the affected groups deserve caution. fuel_system goes closely with aspiration (association 0.61 on a scale from 0 to 1): a model that reads fuel_system can tell the groups of aspiration apart, so leaving aspiration out of the inputs does not keep it out of the predictions.	2	1	0.8353	Residual bias
3.899	Body-style	wagon, hatchback, sedan	Column Body-style splits the held-out rows into 3 groups. The prediction-parity ratio is 0.785 (smallest over largest mean prediction), the largest absolute group residual mean is 3.90 (0.297 times the overall residual standard deviation). Parity gap: at least one group receives systematically smaller predictions on average. Whether that is a property of the target itself or a model bias against the group needs checking. num_of_doors goes closely with body_style (association 0.759 on a scale from 0 to 1, and 2 more columns at 0.5 or above): a model that reads num_of_doors can tell the groups of body_style apart, so leaving body_style out of the inputs does not keep it out of the predictions.	3	3	0.7852	Prediction parity gap
2.129	Drive-wheels	rwd, fwd	Column Drive-wheels splits the held-out rows into 2 groups. The prediction-parity ratio is 0.731 (smallest over largest mean prediction), the largest absolute group residual mean is 2.13 (0.162 times the overall residual standard deviation). Parity gap: at least one group receives systematically smaller predictions on average. Whether that is a property of the target itself or a model bias against the group needs checking. curb_weight goes closely with drive_wheels (association 0.683 on a scale from 0 to 1, and 4 more columns at 0.5 or above): a model that reads curb_weight can tell the groups of drive_wheels apart, so leaving drive_wheels out of the inputs does not keep it out of the predictions.	2	5	0.7313	Prediction parity gap
19.18	Engine-type	dohc, ohcf, ohc, l	Column Engine-type splits the held-out rows into 4 groups. The prediction-parity ratio is 0.614 (smallest over largest mean prediction), the largest absolute group residual mean is 19.2 (1.46 times the overall residual standard deviation). Parity gap and residual bias: the model both predicts systematically lower for some groups and errs systematically against at least one group. This is the worst-case fairness signal on this column; review before deployment. num_of_cylinders goes closely with engine_type (association 0.778 on a scale from 0 to 1, and 4 more columns at 0.5 or above): a model that reads num_of_cylinders can tell the groups of engine_type apart, so leaving engine_type out of the inputs does not keep it out of the predictions.	4	5	0.6141	Parity and bias
6.087	Fuel-system	mpfi, 1bbl, idi, 2bbl	Column Fuel-system splits the held-out rows into 4 groups. The prediction-parity ratio is 0.635 (smallest over largest mean prediction), the largest absolute group residual mean is 6.09 (0.463 times the overall residual standard deviation). Parity gap and residual bias: the model both predicts systematically lower for some groups and errs systematically against at least one group. This is the worst-case fairness signal on this column; review before deployment. compression_ratio goes closely with fuel_system (association 0.989 on a scale from 0 to 1, and 4 more columns at 0.5 or above): a model that reads compression_ratio can tell the groups of fuel_system apart, so leaving fuel_system out of the inputs does not keep it out of the predictions.	4	5	0.6347	Parity and bias
4.346	Fuel-type	gas, diesel	Column Fuel-type splits the held-out rows into 2 groups. The prediction-parity ratio is 0.966 (smallest over largest mean prediction), the largest absolute group residual mean is 4.35 (0.331 times the overall residual standard deviation). Residual bias: at least one group is systematically over- or under-predicted. The model's errors are not zero-mean across groups; its predictions for the affected groups deserve caution. fuel_system goes closely with fuel_type (association 0.985 on a scale from 0 to 1, and 1 more column at 0.5 or above): a model that reads fuel_system can tell the groups of fuel_type apart, so leaving fuel_type out of the inputs does not keep it out of the predictions.	2	2	0.9661	Residual bias

A larger held-out set would firm up the figures

What to collect next. The figures rest on 40 held-out rows.

Collect more rows with high values of the model's output, especially where predictions are largest. Reason: the diagnostics warn that the model is systematically less accurate on high-magnitude predictions and that residual variance grows sharply with predicted value.
Collect more rows representing every group in the columns Aspiration, Body-style, Drive-wheels, Engine-type, Fuel-system, and Fuel-type. Reason: the diagnostics flag prediction parity gaps and group differences in model error for these columns, indicating the model's errors differ between groups or show bias.
Add columns that capture the factors behind variation in the model's output at higher predicted values. Reason: the model is less accurate as the prediction rises, so candidate inputs that explain the gap would make the model stronger in that range.

Evidence

Every chapter of the analysis in full: the figures the story rests on, and everything else the analysis measured.

Headline

Diafunc modeled Class from 24 columns, of which the model uses 3. The model explains 84% of the variation in Class and relies most on City-mpg, with which the model's output falls.

One target was modeled; 40 rows were held out for checking.
A straight line through the data explained 77%; the model added 6.8 points of variance explained, a slight but consistent margin compared with the straight line.
Residual variance grows sharply with predicted value: the model is systematically less accurate on high-magnitude predictions.

Best R²: 0.8419
Best quality: 82.79 %
Best target: class
Targets: 1

Concerns

Severity	Section	Concern	Detail
Critical	Model	Residual variance grows sharply with predicted value: the model is systematically less accurate on high-magnitude predictions	Across 40 held-out rows split into thirds by predicted value, the residual standard deviation in the top third is 20.7, against 5.97 in the bottom third, 3.47 times as large. The bottom third holds predictions up to 80.2 and the top third predictions from 119. The model is accurate at the low end and misses systematically at the high end, where the residual spread is 3.47 times as large. A log transform of the target, or an input that captures the magnitude, may help. The Regression Diagnostics chapter plots the residuals against the predicted values.
Info	Implications	2 inputs could stand in for a column, if that column must not steer predictions	This matters only for a column that is a characteristic the predictions must not follow, such as a person's age, sex or origin; for ordinary properties of the data it needs no action. For 2 pairs an input a model reads and a column the Fairness chapter compares go together with an association of at least 0.5 on a scale from 0 to 1. The closest: City-mpg with Fuel-system (0.748); Engine-size with Engine-type (0.644). A model that reads such an input can tell the column's groups apart, so leaving the column out of the inputs would not keep it out of the predictions. The Fairness chapter compares the model across its groups. An association, not a cause.

How to read this

Data-quality, model-quality, and deployment-risk issues detected during the analysis appear below, ordered by severity. Critical concerns are listed first; Warning and Info entries follow.

Discovered Relations

Quality and error measured on the 40 held-out rows
Target	Formula	Quality	Complexity	Error
Class	Class = 0.3 × (Engine-size − 0.26 × Length) + 0.7419 × csch(atan2(City-mpg, 50^2))	82.79 %	16.2 %	13.66 %

How to read this

One model per target, each a formula with its quality, complexity and error. Higher quality at lower complexity describes the data most clearly. The findings below read the models together; the per-target chapters in the Model section carry each formula, its predictions and its diagnostics.

Questions & Answers

1 question was asked with this analysis:

Not answered by this analysis. The analysis would need a clear question or term to provide an answer.

N answered: 0
N questions: 1

Model

The model's output moves mostly with city-mpg among three inputs, and quality holds a share of variation explained of 0.842. A concern was flagged about accuracy on high-magnitude predictions; see the Concerns chapter.

Most notable in the Model section:

City-mpg carries most of the model (80% of its reliance on inputs)

How to read this

The Model section presents one model per target: its formula, its predictions on held-out rows, the inputs it relies on, the baselines it is measured against, and diagnostics of how it behaves. With more than one target, the Composite Model, Multi-Output and Leaderboard chapters read the models as a set.

Class

The Model section builds one model for Class: a formula that expresses it through the other columns. Diafunc searches the space of mathematical expressions for the formula that balances accuracy against simplicity, so the result is not a black box but an expression that can be read, evaluated and questioned. The chapters that follow show the formula, score it on rows it never saw during training, and take it apart term by term.

Class Model

The model's output relies most on City-mpg, with the strongest input share at 80%, and falls as City-mpg rises; it also rises with Engine-size and falls with Length.

Class = 0.3 × (Engine-size − 0.26 × Length) + 0.7419 × csch(atan2(City-mpg, 50^2))

Quality 82.79 % · Error 13.66 % on 40 held-out rows · Complexity 16.2 %

Constants of the formula
Value	Role	Input	Unit
0.3	Scale
-0.26	Slope	Length	Output units per unit of Length
0.7419	Coefficient
50	Argument

Share of the output's variation they carry: 101.97 %
Rows the search trained on, measured: 138
Rows the search trained on: 138
Held out R²: 0.8419 (95 % CI 0.7501 – 0.9012)
Constants in the formula: 4
Terms that reach 95% of the output's variation: 2
Training rows: 153
Held-out rows: 40
Inputs the formula reads: 3
Terms in the formula: 3
Inputs the formula does not read: Aspiration, Body-style, Bore, Compression-ratio, Curb-weight, Drive-wheels, Engine-location, Engine-type, Fuel-system, Fuel-type, Height, Highway-mpg, Make, Num-of-cylinders, Num-of-doors, Peak-rpm, Price, Stroke, Symboling, Wheel-base, Width

How to read this

The three gauges score the model on the held-out rows: rows that were set aside before the search and that the model never saw. They are the figures to quote for how the model does on new data.

Metric	Meaning
Quality	How well the model predicts on the held-out rows, marked down for the size of its formula: 100% is an exact prediction, 0% is no better than always predicting the average. It is not R², and sits at or just below it
Error	How far the predictions lie from the held-out values, as a share of the miss of always predicting the average: 0% is an exact prediction, 100% is no better than the average
Complexity	The size of the formula as a share of the complexity the search was allowed: a low figure is a short formula

The figures under During the search are the same measures on the training rows. They are what the search ranked its candidates by, so they describe the search and tend to flatter the model it chose. The Generalization chapter sets the training rows beside the held-out rows, and the Baselines chapter sets the model beside its baselines. The time and credit gauges account for the computation that produced the model, not for the model itself.

Prediction

The model predicts Class for any row that supplies the other columns. This chapter applies it to the held-out rows, the rows set aside before training, so that the predictions can be compared with values the model never saw. The rows themselves and the function that predicts them are kept as reference under Foundation, with the processed data.

Prediction Chart

Error: 13.66 % (95 % CI 8.43 % – 22.07 %)
MAE: 9.598 (95 % CI 7.261 – 12.44)
N: 40
Held-out rows offered: 41
Training rows: 153
Held-out rows scored: 4000 %
N without target: 1
Quality: 82.79 % (95 % CI 72.18 % – 89.37 %)
R²: 0.8419 (95 % CI 0.7501 – 0.9012)
Target: Class

How to read this

Actual Class on the horizontal axis against the model's predicted value on the vertical axis, for the held-out rows the model never saw during training. Points on the diagonal are perfect predictions; systematic vertical offsets reveal bias, vertical spread reveals noise, and points far from the diagonal are rows the model handles poorly. With 10,000 held-out rows or more, the rows are counted instead of drawn one point each: each cell is a range of the actual and a range of the predicted value, its colour the number of rows that fall in both, and the cells whose two ranges match hold the rows the model predicts well.

Residual Distribution

Bias: -0.1663 (95 % CI -3.748 – 3.814)
N: 40
Held-out rows offered: 41
N without target: 1
P50: -2.152 (95 % CI -6.885 – 0.9368)
P90: 14.56 (95 % CI 5.303 – 28.62)
P95: 28.62 (95 % CI 7.865 – 40.63)
P99: 35.94 (95 % CI 21.26 – 40.63)
Std: 13.14 (95 % CI 9.122 – 16.73)

How to read this

How the held-out residuals (actual Class minus predicted) are distributed. Bias is their mean: a value away from zero means the model is systematically high or low rather than merely imprecise. The standard deviation and the percentiles describe the spread, and the tail percentiles say how large the worst misses get. Every figure carries a bootstrap 95% confidence interval; with a small held-out set those intervals are wide, and that width is itself the finding.

Which inputs matter most

Input	Share of importance	Permutation importance	Sensitivity	Residual correlation	Occurrences	Model's output as the input rises	Change, first to third quartile
City-mpg	80.05 %	4.767	3.542	0.1992	1	Falls (3036 of 3036 steps)	-35.8 (19 to 30)
Engine-size	19.27 %	1.148	0.3	0.06586	1	Rises (4692 of 4692 steps)	+14.4 (98 to 146)
Length	0.68 %	0.040	0.078	0.1341	1	Falls (138 of 138 rows)	-1.232 (167.3 to 183.1)

Rows the search trained on, measured: 138
Inputs the formula does not read: Aspiration, Body-style, Bore, Compression-ratio, Curb-weight, Drive-wheels, Engine-location, Engine-type, Fuel-system, Fuel-type, Height, Highway-mpg, Make, Num-of-cylinders, Num-of-doors, Peak-rpm, Price, Stroke, Symboling, Wheel-base, Width

How to read this

The chart ranks the inputs of the Class model by permutation importance: how much the model's error rises when that input's values are shuffled across rows so that it carries no information. A longer bar means the model relies on the input more. The order says which columns the model reads most, and those are the columns where measurement quality and data collection matter most. A short bar marks an input the model barely uses, which is a fact about this model and not a verdict on the column. Importance describes the model's reliance and nothing more: an input can rank high because it stands in for something the data does not contain. Where the search measured it, an input also carries the direction in which the model's output moves as the input rises, counted on the rows the search trained on, and the change of the output when the input alone goes from its first to its third quartile; both describe the formula inside the observed range and say nothing about causes.

Baselines

Best yardstick's score: 0.774 (95 % CI 0.6746 – 0.8477)
Best baseline R²: 0.774
Effect size d: 0.2404 (95 % CI -0.06743 – 0.5061)
Effect size d magnitude: small
Margin over the best yardstick: 0.06793 (95 % CI -0.0106 – 0.1594)
Margin's interval stays above zero: No
Model MAE: 9.598 (95 % CI 7.261 – 12.44)
Model: 0.8419 (95 % CI 0.7501 – 0.9012)
Model R²: 0.8419 (95 % CI 0.7501 – 0.9012)
Held-out rows: 40
Held-out rows without an answer: 0
Target: Class
Rows where the model is closer: 52.5 % (95 % CI 37.5 % – 67.06 %)
Rows compared: 40
Rows level: 0
Regression yardstick trained with gaps filled (too few complete rows): No
Training rows of the regression yardstick: 153

How to read this

The table scores the model for Class against simple yardsticks on the same held-out rows. A yardstick is a predictor simple enough to need no explanation: a constant (the average, the middle value, the most common class or level, the average count), a plain regression on the numeric inputs (a straight line, a logistic regression, a Poisson regression), and for a series over time a forecast from its own past (the last value, the value one season back, the recent trend extended). Which of them appear depends on what kind of column Class is. They are yardsticks only: the analysis has one model, and it is the last row. A regression yardstick answers every row the model answers: where one of its numeric inputs is empty, it reads the average of that input over the training rows. Nothing is filled in for the model. A yardstick whose row is empty could not be scored, and the summary then says what the margin is measured against.

Read the columns from top to bottom. Each kind of target is scored by the measure it is judged on: R² and MAE for a continuous value, with MASE added for a series (below 1 means a typical miss is smaller than the series' usual step from one row to the next); accuracy and balanced accuracy for a yes/no value, with the Brier score where a probability is predicted; accuracy and macro F1 for a class; weighted kappa and the distance in levels for an ordered level; Poisson deviance and RMSE for a count. When the model clears every yardstick by a wide margin, its structure earns its place. When it is level with the regression yardstick, a plain regression describes the data as well. When it is level with the constant, the inputs carry no usable signal for Class.

The margin over the best yardstick comes with an interval. When that interval includes zero, the lead is not settled on this many held-out rows. The share of rows on which the model is closer than the best yardstick is counted only on the rows where the two differ; for a yes/no value or a class these are the rows where the two disagree.

Generalization

Generalization gap: -0.04822
N test: 40
Target: Class
Test error: 9.598 (95 % CI 7.261 – 12.44)
Test R²: 0.8419 (95 % CI 0.7501 – 0.9012)
Train error: 0.1441
Train R²: 0.7937
Verdict: Generalizing

How to read this

The chart sets the score of the Class model on the rows it trained on beside its score on the held-out rows it never saw, and the gap between the two bars is the finding. The score is the one that suits the target: R² for a quantity, balanced accuracy for a yes/no target, weighted kappa for ordered levels. The held-out figure carries a bootstrap 95% confidence interval, which says how far it could move with a different held-out draw; the training bar has none, because it is measured on the rows that shaped the model.

The verdict reads from the two figures. Generalizing: the held-out score is strong, or training and held-out agree closely; the structure the formula encodes carries to new rows. Overfit: training is far ahead of held-out and the held-out score is not strong on its own; the formula has absorbed noise from the training rows, and the training figure overstates what to expect on new data. Underfit or noisy: held-out is far ahead of training; this is not strength, it usually means an outlier or a flat region in the training rows that the held-out rows happen to avoid. Insufficient: fewer than 30 held-out rows and no strong held-out score, too little evidence for a negative verdict. A model that predicts the same value for every held-out row gets no verdict: there is nothing that could carry over. In every case the width of the held-out interval says how much weight the gap can bear.

How each term responds to its inputs

Additive: Yes
Rows the search trained on, measured: 138
Terms in the formula: 3
Notation: 0.3 × (Engine-size − 0.26 × Length) + 0.7419 × csch(atan2(City-mpg, 50^2))
Target: Class

How to read this

The formula for Class is split into its additive terms, and each term is traced as one of its inputs moves across the training range while the other inputs stay at their medians. Each curve is therefore a profile of the term at the typical row, not an average over the data: it shows what the term contributes at every value of that input when everything else is ordinary.

A term that depends on several inputs gets one curve per input; a constant term gets none. Terms the formula subtracts are drawn with their sign, so a curve below zero pulls the prediction down. At any fixed row, the terms add up to the model's prediction. Where the search measured it, a term also carries its share of the variation of the model's output on the rows the search trained on; that is a share of what the formula returns, not of Class itself. The notebook lets the reader trim each range to the central 95% of the input. When the formula has no additive structure, the chapter traces the whole formula as a single term along each of its inputs, and the Sensitivity chapter is the better read for how the inputs combine.

How the formula behaves outside the data

The model diverges beyond the observed range of engine_size, length: predictions there are not supported by the formula's shape. How the model behaves beyond the observed range of city_mpg could not be determined from the formula, so extrapolation there is not assessed. Extrapolate with caution.

Bounded at infinity: No
Rows the search trained on, measured: 138
Inputs the formula reads: 3
N singularities: 0
Risky inputs: engine_size, length
Target: Class

Limits at neg infinity
Input	Kind
Engine-size	Negative infinity
Length	Positive infinity
City-mpg	Unknown

Limits at pos infinity
Input	Kind
Engine-size	Positive infinity
Length	Negative infinity
City-mpg	Unknown

How to read this

The formula for Class is read as a mathematical object, without data, to state how it behaves beyond the range it was trained on. A black box cannot answer that question; a formula can. For each input the chapter reports the limit as the input grows without bound in either direction (whether the formula diverges, settles to a finite value or oscillates, with the sign tracked exactly, so that a term like minus two times the cube of the input is reported as diverging downward on the right and upward on the left), whether the formula stays finite in every direction, and any singularity with its solved location: a division whose denominator reaches zero, a logarithm or square root whose argument leaves its domain, or a periodic pole.

The inputs along which the formula diverges or meets a singularity are listed as the risky ones; along them the formula's shape gives no support for extrapolation. A formula that stays finite everywhere with no singularity carries no structural hazard when extrapolated; the data still ends where it ends, and a prediction outside the training range remains unsupported by evidence. The plain-language summary at the end states the same facts in one paragraph.

Contributions per term

Additive: Yes
N rows: 5

The notebook draws this chapter's figure from each held-out row; the row-by-row detail is there.

How to read this

For up to five representative held-out rows, the chapter draws one bar chart showing how each additive term of the formula builds that row's prediction of Class. The five rows are the worst prediction (largest absolute residual), the best (smallest), the median miss, the row with the smallest prediction and the row with the largest. When two roles fall on the same row, which is common with few held-out rows, the earlier role keeps it and fewer than five charts appear.

In each chart the bars stack the terms' contributions at the row's input values, terms the formula subtracts sit below zero, and the bars sum to the prediction. The dashed line marks the actual value; the distance between it and the top of the stack is the residual. The bars are evaluated at the same precision as the predictions, so they agree with the Prediction Chart. When the formula has no additive structure, each chart holds one bar for the whole formula, and the Sensitivity chapter is the better read for how individual inputs move it.

What each term is worth

Full-formula R² is 0.842. Each bar below shows how much R² drops when that term is replaced by its mean contribution. Large drop: load-bearing term; near zero: decoration the formula could lose; negative: overfit signal (ablation improves R²).

Additive: Yes
Baseline R²: 0.8419
Held-out rows offered: 41
Held-out rows: 40
N without target: 1

The notebook draws this chapter's figure from each held-out row; the row-by-row detail is there.

How to read this

For each additive term of the formula for Class, the chart shows how much the held-out R² drops when that term is replaced by its mean contribution, so that it no longer varies from row to row. The bars are sorted from the largest drop down, and the dashed line marks the R² of the full model.

A large drop means the term carries real predictive work; the complexity it adds is paid for. A small drop means the term adds little beyond its average value: it may refine a stronger term, or its curve in the chapter "How each term responds to its inputs" may be nearly flat. A negative drop means the held-out R² rises without the term, which is a sign that the term tracks noise in the training rows. Each figure describes what a term contributes inside the model as discovered; the chart diagnoses the model, it is not a guide to removing terms. When the formula has no additive structure, the chart shows one bar for the whole formula.

What-If

The prediction at the typical row: every input at its median or most common value
Item	Value
City-mpg	24
Engine-size	120
Length	173.2
Term 1 adds	36
Term 2 adds	-13.51
Term 3 adds	77.29
Prediction	99.78

Additive: Yes
Held-out rows for the interval: 40
Terms in the formula: 3
Residual P5: -14.41
Residual P95: 28.62
Residual std: 13.14

How to read this

The chapter shows the model's prediction for Class at one input combination, with the contribution of each term stacked beneath it. The inputs start at their training medians, so the first view is the prediction for a typical row, and each input can move within the range the training rows cover; the notebook lets the reader change the inputs and watch the prediction and the stack update.

In the stack, a long bar marks the term that dominates at this input combination, often the one whose removal costs most in the chapter "What each term is worth". A short bar marks a term that makes a small adjustment here; the chapter "How each term responds to its inputs" shows whether it stays small everywhere or grows toward the edges of the range. A negative bar marks a term that pulls the prediction down at this point, either because the formula subtracts it or because it evaluates below zero.

The inputs stay inside the training range for a reason: the formula computes a value anywhere, but outside that range no training row supports it. When the formula has no additive structure, the stack holds a single bar for the whole formula and the inputs move the prediction directly.

Sensitivity

The prediction responds to 3 inputs. The formula is additive: each curve below shows the change in the prediction per unit of one input (∂ŷ/∂xᵢ) independently. Flat curves mean a constant linear response, bent curves a non-linear response that depends on the position in the range, and zero crossings a response that reverses sign between regions.

Additive: Yes
Terms in the formula: 3

How to read this

For each input, the chart traces the rate at which the predicted Class changes as that input moves across its training range, with the other inputs held at their medians. The rate is the local slope of the prediction with respect to the input, measured by a small finite difference at each point. A table summarizes each input with the mean, minimum and maximum of the absolute slope, which ranks the inputs by how strongly the prediction responds to them.

A flat curve means the model is close to linear in that input: the prediction responds at the same rate everywhere in the observed range, which is easy to state and says nothing about values beyond that range. A curve that grows or shrinks marks diminishing or accelerating returns, and whether that is plausible is a question for the domain. A curve that crosses zero means the prediction rises with the input in one part of the range and falls in another, which is either a real optimum or a sign that the formula bends around a few rows. A curve with a large magnitude marks an input to which the prediction is highly responsive; the chapter "What each term is worth" says whether the term behind it also carries predictive work.

In the table, the mean absolute slope ranks the inputs by typical responsiveness. A minimum close to the maximum means the responsiveness is nearly constant; a wide gap means it varies strongly across the range. The chapter reads the whole formula, so it applies whether or not the formula splits into terms.

How two inputs act together

Engine_size and length enter linearly. No term reads two inputs, so the grid below renders empty; each input's contribution can be read independently in the chapter "How each term responds to its inputs".

Additive: Yes
Inputs in different terms act separately: Yes
Rows the search trained on, measured: 138
Inputs the formula is linear in: Engine-size, Length
Terms in the formula: 3
Input pairs not tested: 0

How to read this

When a single term of the formula combines two or more inputs, the prediction's response to one of them depends on the value of the other. This chapter draws one surface for each such pair: the predicted Class across the plane of the two inputs, with every other input held at its training median. Pairs that never share a term have no interaction by construction, and the curves in the chapter "How each term responds to its inputs" already say everything about them. Where the search tested a pair, the summary says on how many pairs of rows the two inputs acted together in the model's output; that is a statement about the formula, not a finding that the data hold no other interaction.

Parallel stripes mean the two inputs act almost independently, so the surface is close to a sum of two one-input curves. Curved contours mean a real interaction, where the slope along one input changes with the other; the location of the peak or trough matters. A saddle, rising along one axis and falling along the other, marks a trade-off between the two. A sharp edge or cliff means the formula encodes a change of regime, and the curve for the same input in the chapter "How each term responds to its inputs" shows whether the bend appears there too.

The grid is deliberately coarse, and the color scale runs from low to high predictions. When the formula has no additive structure, the single whole-formula term holds every input, so every pair appears; the number of surfaces is capped for models with many inputs.

Worst Predictions

Actual	Predicted	Residual	City-mpg	Engine-size	Length
160.0	119.4	+40.6	19	121	186.6
162.0	133.4	+28.6	17	130	188.8
162.0	133.4	+28.6	17	130	188.8
161.0	134.6	+26.4	19	171	183.5
97.0	119.1	-22.1	19	120	186.7
115.0	130.1	-15.1	18	136	176.6
110.0	124.4	-14.4	19	136	180.2
110.0	123.4	-13.4	19	136	192.7
143.0	129.8	+13.2	19	151	168.9
62.0	75.1	-13.1	31	92	158.7

Additive: Yes
N extrapolated: 0
Held-out rows: 40
Held-out rows for the interval: 40
Residual P5: -14.41
Residual P95: 28.62
Residual std: 13.14

How to read this

The held-out rows on which the model misses Class by the most, sorted by absolute residual with the largest first and capped at ten. Each card shows the row's actual value, the prediction, the residual, the contribution of every additive term at that row and the row's input values. R² and MAE say how good the model is on average; these cards say where it fails and let each failure be read input by input and term by term.

A large residual with one dominant term means that term produced the wrong value at this row; the row's value for that input, read against its curve in the chapter "How each term responds to its inputs", shows whether it fell in a region the formula models poorly. A large residual with balanced contributions means every term was a little off and the sum still missed, which points to a shape the formula cannot represent in that region. Residuals that change sign from card to card mean the misses are not a consistent bias but scattered errors on particular rows. When the formula has no additive structure, each card shows a single whole-formula contribution.

Prediction Interval Coverage

Across 40 held-out rows, the 95% prediction interval actually covers 90% of the rows. The normal band is wider than needed for this residual distribution (worst gap 7.50 percentage points), often because a few large residuals inflate σ above what the bulk requires. Real uncertainty for typical rows is tighter than the interval suggests.

Nominal level	Half-width	Empirical coverage
50 %	8.863	57.5 %
80 %	16.84	87.5 %
90 %	21.61	87.5 %
95 %	25.76	90 %

Largest miss (percentage points): 7.5
Held-out rows offered: 41
Held-out rows: 40
N without target: 1
Residual P2.5: -15.25
Residual P97.5: 28.92
Verdict: Underconfident

How to read this

Each held-out prediction of Class carries a prediction interval, and this chapter checks whether that interval covers the actual value as often as it claims. The interval reported with each prediction is built from the held-out residuals themselves: its bounds are the 2.5th and 97.5th percentiles of the residuals added to the prediction, so it is asymmetric when the residuals are skewed and assumes no particular error distribution.

The coverage table checks a second, simpler band: the symmetric interval that a normal error distribution with the residuals' standard deviation would give. At four nominal levels (50%, 80%, 90% and 95%) it lists the half-width of that normal band and the share of held-out rows whose actual value falls inside it. Empirical coverage close to nominal means the residuals are close enough to normal that the two bands agree and the interval can be taken at face value. Empirical coverage below nominal means the normal band is too narrow, the residuals have heavier tails than a normal distribution, and the percentile-based interval is the one to trust. Empirical coverage above nominal means the normal band is wider than the data needs, usually because a few large residuals inflate the standard deviation. Every figure comes from the same held-out residuals the intervals are built from.

Regression Diagnostics

40 held-out residuals, with a spread up to 40.6 in absolute terms. Mean residual is -0.166, close to zero. The model is approximately unbiased on these held-out rows (a small held-out set makes this less reliable; the Prediction Chart chapter states R² and the mean absolute error with their 95% confidence intervals). The charts below check whether the errors look like noise: a pattern in residuals-vs-fitted or a curving Q-Q means a structural miss. The held-out rows are a random draw, so their order carries no time and the autocorrelation of the residuals is not assessed.

Abs residual vs predicted r: 0.4928
Bias: -0.1663
Bias over residual sd: -0.01266
Held-out rows: 40
Order: shuffled
Residual sd: 13.14
Share within normal band: 0.9

The notebook draws this chapter's figure from each held-out row; the row-by-row detail is there.

How to read this

Four residual diagnostics for Class, all computed from the held-out residuals. Each asks in its own way whether the model's errors look like noise, which is what remains when a model has captured all the structure the data holds.

Residuals against predicted values: Each held-out row is plotted with the model's prediction on the horizontal axis and its residual on the vertical axis, around a zero line. A symmetric cloud around zero means errors of similar size across the predicted range and no systematic bias. A funnel or fan means the size of the errors depends on the predicted value: the model is more uncertain in some regions than in others, and its prediction interval is not equally trustworthy everywhere. A curved pattern, a smile or a frown, means the model misses a structural component; the chapters "How each term responds to its inputs" and "How two inputs act together" show the shapes the formula does capture.

Normal Q-Q plot: The sorted residuals are plotted against the quantiles of a normal distribution, with the diagonal marking a perfectly normal set of residuals. Points that hug the line mean approximately normal residuals, so the normal band in the Prediction Interval Coverage chapter will hold. An S-shape means heavier or lighter tails than normal; heavier tails (below the line at the left, above it at the right) mean the model occasionally produces large errors. A banana or arc means skewed residuals: the model is systematically high or low in part of the range.

Histogram: The residuals binned into equal-width intervals. A bell centered on zero means symmetric errors with no bias. An off-center bell means the model is biased, with a mean error away from zero. A long tail or two peaks mean outliers or two regimes inside the prediction range.

Autocorrelation: For each lag, the correlation of the residual sequence with itself shifted by that many rows, with the band that pure noise would stay inside at plus or minus 1.96 divided by the square root of the row count. Bars inside the band mean uncorrelated residuals with no order-dependent structure left. A bar at lag 1 outside the band means the residuals of neighbouring dates correlate: structure in time that the model has not captured. A wave across the lags means periodic structure remains, and the Time Series chapter in the Data section is where to look for its period.

Autocorrelation carries meaning only when the row order itself does. When the data has a date column, the held-out rows are the most recent ones in date order, and the autocorrelation is assessed. Without a date column the held-out rows are a random draw: the row after a held-out row is an arbitrary other row, so the autocorrelation is not assessed and the summary above says so.

Search Progress

The search ran for 35 generations, ending at quality 0.818 (gain +0.0581 from generation 2). The curve shows a substantial climb. The last improvement came after 100% of the search time: the search was still improving when it stopped, so a longer time limit is likely to find a better model.

First generation: 2
First quality: 76.03 %
Last generation: 36
Last improvement ms: 4,499,678
Last quality: 81.85 %
Max quality: 81.85 %
N points: 35
N total generations: 35
Search time ms: 4,499,678
Stop reason: Maximum runtime reached

How to read this

The line traces the best quality the search for the Class model had reached at each generation, from the first generation to the last. Quality is the technology's combined score on the training rows, the figure the Model Metrics chapter defines. A curve that flattens well before the last generation means the search converged: the budget was more than enough, and the model is the one the search settled on. A curve still rising at the last generation means the budget ended before the search settled, and the model is the best the search reached within it. The chart describes the search, not the data: it says whether the search had time to settle, not whether more rows would help.

Model Constraints

Across 41 held-out predictions, the formula is mathematically well-behaved: every output is finite, stays inside the training-target ±2σ band, and no prediction runs away beyond the bounded-prediction limit. It is safe to consume downstream at face value.

Name	Status	Detail
Output coherent	Pass	no non-finite predictions across 41 rows
Within domain	Pass	no rows outside the training target's ±2σ range across 41 rows
Bounded predictions	Pass	no runaway predictions beyond ±10σ across 41 rows

Held-out rows: 41
N non finite: 0
N outside domain: 0
N runaway: 0
Verdict: Clean

How to read this

Sanity checks on the Class formula, run against the held-out rows. Three checks: every prediction is a finite number (output coherent), predictions stay within the range of the training target widened by two standard deviations on each side (within domain), and no single prediction runs away more than ten standard deviations from the training mean (bounded predictions).

These are pass or fail guards, not quality measures: a formula can clear all three and still predict poorly. A failure is the stronger signal. It means the formula misbehaves numerically somewhere in the data it was shown, and any downstream use of it should wait until that is understood.

Modeling

Measured during the search, on the rows the model was trained on

MAE of a straight line through the inputs (same rows): 9.033
RMSE of a straight line through the inputs (same rows): 11.8
Training MAE (rows the search trained on): 11.4
MAE of always predicting the mean (same rows): 30.86
RMSE of always predicting the mean (same rows): 39.19
Training R² (rows the search trained on): 0.8387
Training RMSE (rows the search trained on): 15.74
Rows the search trained on, measured: 138
Error: 14.41 %
Inputs the straight line used: 16
N train: 164
Quality: 81.38 %

How to read this

The function below trains the model for Class on the processed data. Its output is the model that every other chapter of this section scores and dissects.

Findings

1 finding from the model diagnostics (1 Critical) is listed in the Concerns chapter at the top of the analysis.

Data

Most of the spread in class is explained by only a few columns, despite many associations among the inputs. No columns had high missing values or exceeded six strongly skewed columns out of 25.

Most notable in the Data section:

Length correlates 0.878 with Highway-mpg but carries only 0.7% of the model's reliance: another input likely carries the same information
Compression-ratio and Fuel-system go together (association 0.989)
City-mpg and Highway-mpg move together (correlation 0.971)

How to read this

The Data section describes the table as supplied, before any modeling: the Column Profiles overview of every column and its role, one chapter per column with its distribution and correlations, a closer look at columns with notable characteristics, Duplicate Rows, Leakage Suspicion, a map for paired coordinate columns, and the General chapter with descriptive statistics, correlations, missing values, outlier ranges, clusters and segments across all columns.

Column Profiles

Profiled 25 columns across 205 rows (17 numeric, 8 non-numeric): every column is at least 75% populated. Distributional statistics on numeric columns can be read at face value. 6 columns are strongly skewed: the mean of such a column is pulled toward its long tail, so the median is the better guide to a typical value.

Columns
Name	Role	Type	N	Missing	Mean	Std	Min	P25	Median	P75	Max	Skewness	CV
Class	Target	integer	203	2 (0.98 %)	104.26	39.71	48	70	95	116	288	1.391	0.3809
Aspiration	Input	text	205	0
Body-style	Input	text	205	0
Bore	Input	number	201	4 (1.95 %)	3.330	0.274	2.540	3.150	3.310	3.590	3.940	0.02002	0.08215
City-mpg	Input	integer	205	0	25.22	6.54	13	19	24	30	49	0.6637	0.2594
Compression-ratio	Input	number	205	0	10.143	3.972	7.000	8.600	9.000	9.400	23.000	2.611	0.3916
Curb-weight	Input	integer	205	0	2556	521	1488	2145	2414	2935	4066	0.6814	0.2037
Drive-wheels	Input	text	205	0
Engine-location	Input	text	205	0
Engine-size	Input	integer	205	0	126.9	41.6	61	97	120	141	326	1.948	0.3281

The first 10 rows of 25. The other 15 are in the notebook.

N columns: 25
N high missing: 0
N rows: 205
N strongly skewed: 6
Table branch: main
Table ID: f3fa0613-5191-44b5-ac37-24bdafc0b6a2

How to read this

One row per column of the analyzed table: its role in the analysis (the target being predicted, an input it is predicted from, or the segment column), its type, value count and missing count, and for numeric columns the mean, standard deviation, minimum, quartiles, maximum and interquartile range. A column with 25% or more missing values is flagged; its mean and quartiles describe only the rows that have a value.

Two further figures describe the shape of a numeric column. The skewness says whether the values lean to one side: close to zero the column is symmetric, from 0.5 it is moderately skewed and from 1 strongly skewed, with the longer tail on the high side when the figure is positive and on the low side when it is negative. In a strongly skewed column the mean is pulled toward the tail, and the median is the better guide to a typical value. The coefficient of variation is the standard deviation divided by the mean: it compares how widely columns spread regardless of their units, and is given only for a column whose mean is positive.

These are the columns as supplied, before any modeling: the reference against which every later chapter reads.

Aspiration

Aspiration: 2 distinct values, most often std.

How to read this

A column chapter profiles one column: its distribution in figures and charts, and how it relates to the other columns. It opens with one line on what the column holds. The Description chapter carries its figures, with every other column summarized for each of its values where it has few, and its association with every other column where it is numeric. The Visualization chapter carries its charts. A table with a date column adds an Over Time and a Time Series chapter; a target with classes adds a Class Balance chapter.

Description

Aspiration
Statistic	Value
Type	text
Values present	205
Distinct values	2
Continuous	no
Mode	std

Rows per value
Variable	Value	Rows	Share
Aspiration	std	168	81.95 %
Aspiration	turbo	37	18.05 %

How to read this

The figures below summarize Aspiration in numbers: where its values center (mean, median, mode), how far they spread (range, variance, standard deviation, interquartile range) and how they are distributed across percentiles. They are the reference for every chart in the Visualization chapter and for the correlation measures further down.

The figures for Aspiration are grouped: the column itself first, then where its values center, how far they spread, the shape of their distribution and its percentiles. Each statistic is explained in the Description chapter under General in the Data section.

By Value

Mean per value of Aspiration
Aspiration	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
std	168	3.102	9.593	4.405	12542.2	2476.4	25.84	99.76	31.57	53.63	5166.9	98.03	172.7	3.222	3.302	0.869	65.61	124.8
turbo	37	3.222	12.64	4.27	16254.8	2915.2	22.41	124.4	27.03	54.18	4939.2	102.1	180.2	3.404	3.452	0.6757	67.28	136.5

How to read this

The rows are grouped by the value of Aspiration, and every other column is summarized within each group with the same descriptive statistics. A statistic that shifts from group to group marks a column that moves with Aspiration; one that stays level marks a column that does not. Groups with few rows produce unstable figures, so the row count of each group is the first thing to read. Where the groups differ in a target by more than chance would give, the chapter states by how much; it states that the two go together, not that one brings the other about.

Visualization

The charts in this chapter were chosen from the type of Aspiration and of the columns it is compared with: a numeric column gets a histogram, a box plot and, when its row order carries a pattern, a value sequence, a categorical column gets a frequency chart, and its relation to each target of the analysis, and to the segment column when there is one, gets the chart that suits the pair, with the target on the vertical axis where it is a number. A column is not charted against every other column; which columns move together is shown under Strongest Correlations. The charts complement the figures in the Description chapter; the shape of a distribution and the position of its outliers are easier to see than to read.

Body-style

Body-style: 5 distinct values, most often sedan.

Description

Body-style
Statistic	Value
Type	text
Values present	205
Distinct values	5
Continuous	no
Mode	sedan

Rows per value
Variable	Value	Rows	Share
Body-style	sedan	96	46.83 %
Body-style	hatchback	70	34.15 %
Body-style	wagon	25	12.2 %
Body-style	hardtop	8	3.902 %
Body-style	convertible	6	2.927 %

By Value

Mean per value of Body-style
Body-style	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
convertible	6	2	8.933	5	21890.5	2801.7	20.5	131.7	26	51.43	5158.3	92.7	170.4	3.043	3.492	2.833	65.58	157.2
hardtop	8	2	10.73	5.125	22208.5	2810.6	21.63	142.3	27.25	52.85	5031.3	98.5	176.9	3.323	3.609	1.875	66.61	176.3
hatchback	70	2.286	9.027	4.114	9957.4	2348.2	26.31	101.3	32.17	52.11	5232.6	95.54	166.6	3.28	3.239	1.586	65.25	114.4
sedan	96	3.681	10.94	4.51	14459.8	2610.6	25.32	103.1	30.83	54.34	5081.8	100.6	177.6	3.267	3.339	0.3333	66.26	130.8
wagon	25	4	10.32	4.24	12372	2784.2	24.04	97.75	28.72	56.73	5014.6	102.2	181.3	3.176	3.406	-0.16	66.26	123.8

Bore

Bore: 2.54 to 3.94, median 3.31, 38 distinct values, 2% missing; moves with Curb-weight most (r 0.649).

Description

Bore
Statistic	Value
Type	number
Values present	201
Distinct values	38
Continuous	yes
Decimal places	2
Minimum	2.54
Maximum	3.94
Mean	3.33
Median	3.31
Mode	3.62

The first 10 rows of 17. The other 7 are in the notebook.

By Value

Bore accounts for 53% of the spread in Class: 3.74 averages 145 above 3.05 (95% interval 145 to 145). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	3.74	3	207	207 to 207
Class	3.54	6	152	89.88 to 214.1
Class	3.59	3	145	145 to 145
Class	3.43	8	142.3	107.8 to 176.7
Class	3.58	6	128.5	118.8 to 138.2
Class	3.78	8	127.4	106.4 to 148.3
Class	3.27	7	117	68.81 to 165.2
Class	3.17	3	116	116 to 116
Class	3.62	23	113.1	97.17 to 129
Class	3.46	7	113	86.45 to 139.5

The first 10 rows of 21. The other 11 are in the notebook.

Mean per value of Bore
Bore	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Symboling	Width	Engine-size
	0	2	9.4	2	13,020	2411.3	16.75	109.5	23	49.6	6000	95.3	169		3	65.7	72.5
2.54	1	2	9.3	4	15,040	2707	21	110	28	56.1	5250	99.1	186.6	2.07	3	66.5	121
2.68	1	2	9	6	16,500	2823	19	154	26	52.4	5000	94.5	171.2	3.47		65.5	152
2.91	7	2.286	9.429	3.857	6405.3	1823.3	36.43	67.14	41.29	52.44	5628.6	91.31	149.1	3.307	1.286	63.44	85.71
2.92	1	4	9.2	4	7295	2024	30	76	34	58.3	6000	96.5	157.1	3.41		63.9	92
2.97	12	3	9.401	4	6402.3	1969	32.5	68	38.75	50.73	5500	93.7	159	3.23	1.25	63.95	91.17
2.99	1	2	21.9	4	7099	2017	45	55	50	54.5	4800	94.5	165.3	3.47		63.8	103
3.01	5	3.6	23	4.4	12,316	2528	34	69.2	39.8	55.54	4680	100.3	176.8	3.4	1	66.46	106.6
3.03	12	2.545	8.733	4	6981.1	1983.2	30.92	80	36.42	52.28	5300	93.71	158.3	3.217		63.87	93
3.05	6	3.333	9	4	6961.3	2286.7	30.33	62	36	56.8	4800	95.7	164.2	3.03		63.6	92

The first 10 rows of 39. The other 29 are in the notebook.

Correlation

Correlations
Column	Pair of	Association	Pearson's r	95% CI (Pearson)	Spearman's ρ	Kendall's τ	q-value	Rows
Make	a number and a category	0.7672					< 0.001	201
Engine-size	two numbers	0.7247	0.5941	0.4965 to 0.6768	0.7247	0.5587	< 0.001	201
Curb-weight	two numbers	0.7005	0.649	0.561 to 0.7225	0.7005	0.5348	< 0.001	201
Price	two numbers	0.6493	0.5434	0.4368 to 0.635	0.6493	0.4928	< 0.001	197
Class	two numbers	0.6466	0.5773	0.4764 to 0.6631	0.6466	0.478	< 0.001	199
Length	two numbers	0.6417	0.6075	0.5121 to 0.688	0.6417	0.4974	< 0.001	201
Highway-mpg	two numbers	0.6266	-0.5946	-0.6772 to -0.4971	-0.6266	-0.4673	< 0.001	201
City-mpg	two numbers	0.6195	-0.5946	-0.6773 to -0.4971	-0.6195	-0.4625	< 0.001	201
Width	two numbers	0.611	0.5592	0.4561 to 0.6475	0.611	0.4494	< 0.001	201
Drive-wheels	a number and a category	0.6018					< 0.001	201

The first 10 rows of 24. The other 14 are in the notebook.

How to read this

Each row pairs Bore with one other column, numeric or categorical, and reports how strongly the two go together on an association from 0 to 1, and whether an association this strong could be chance. For another numeric column the row adds the direction: Pearson's coefficient measures a straight-line relationship, and Spearman's rho and Kendall's tau measure a monotonic relationship on ranks, which makes them resistant to outliers and lets them see a curved but consistently rising or falling pattern. For a categorical column the association is the correlation ratio η, which has no direction. A strong association is not an explanation: two columns can go together when a third one moves both.

The table lists every other numeric or categorical column against Bore, with the pair's kind and association, three correlation coefficients and a confidence interval where the other column is numeric, the q-value and the rows the pair was measured on.

Measure	Meaning
Kind	What the other column holds: a number (numeric) or categories (numeric_categorical). A categorical column is one that is not numeric and holds between 2 and 50 distinct values
Association	The strength of the pair from 0 to 1. With a numeric column: the stronger of Pearson's coefficient and Spearman's ρ, without its sign. With a categorical column: the correlation ratio η, the square root of the share of Bore's spread that lies between the categories
Covariance	Numeric partner only. The direction of the relationship (positive or negative) in the units of the two columns. It is not standardized, so its size says little about strength without the columns' own spread
Pearson's Correlation Coefficient	Numeric partner only. The strength and direction of a linear relationship, from -1 (a perfect falling line) through 0 (no linear relationship) to 1 (a perfect rising line)
Spearman's ρ	Numeric partner only. The strength and direction of a monotonic relationship, computed on ranks rather than values, from -1 to 1. It follows a curved pattern as long as it rises or falls consistently, and outliers move it little
Kendall's τ	Numeric partner only. The strength and direction of association from the agreement and disagreement of rank order across pairs of rows, from -1 to 1. It is the steadier of the two rank measures when the rows are few
q-value	How likely a pair this strong is among unrelated columns, adjusted for the number of pairs involving Bore (Benjamini-Hochberg). Among all pairs reported with q below 0.05, about 5% or fewer are expected to be false discoveries
95% CI (Pearson)	Numeric partner only. The lower and upper bounds of the 95% confidence interval on the Pearson coefficient, from the Fisher z-transform. An interval that contains 0 leaves the direction of the relationship open
Rows	The rows in which both columns hold a value. The q-value and the interval of a pair rest on this count

Visualization

The rows of Bore are not charted in their order: consecutive rows are no more alike than rows picked at random (a correlation of -0.03 between each value and the next), so the order carries no pattern to show.

City-mpg

City-mpg: 13 to 49, median 24, 29 distinct values; moves with Highway-mpg most (r 0.971).

Description

City-mpg
Statistic	Value
Type	integer
Values present	205
Distinct values	29
Continuous	yes
Decimal places	0
Minimum	13
Maximum	49
Mean	25.22
Median	24
Mode	31

The first 10 rows of 17. The other 7 are in the notebook.

By Value

City-mpg accounts for 73% of the spread in Class: 15 averages 115 above 37 (95% interval 106 to 125). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	15	3	178	169.4 to 186.6
Class	17	13	167.7	135.1 to 200.2
Class	16	6	161.5	142.6 to 180.4
Class	20	3	146	91.86 to 200.1
Class	19	27	134.1	123.8 to 144.4
Class	18	3	130.3	95.88 to 164.8
Class	22	4	123	123 to 123
Class	21	8	113	108.9 to 117.1
Class	23	10	108.5	100.7 to 116.3
Class	24	22	102.4	96.77 to 108

The first 10 rows of 19. The other 9 are in the notebook.

Mean per value of City-mpg
City-mpg	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
13	1	2	11.5	12	36,000	3950	262	17	47.8	5000	102	191.7	2.76	3.54		70.6	326
14	2	3	8	8	43,180	3807.5	184	16	56.05	4500	116.5	203.7	3.35	3.8		71.85	306
15	3	4	8.067	6	34893.3	3879	178	19.33	53.97	4966.7	112	198.7	3.91	3.627		70.03	241.7
16	6	2.667	8.167	5.833	31,392	3264.7	161.5	20.83	53.05	5300	102.3	185.5	3.276	3.458	0.8333	68.43	182.8
17	13	2.769	8.908	4.846	20738.4	2895.5	167.7	23.31	52.66	5596.2	96.87	176.7	3.132	3.582	1.538	67.01	148.4
18	3	4	7.933	5	19028.3	2988.7	130.3	23	55.27	5533.3	105.5	184	3.16	3.46	0.3333	67.87	147.7
19	27	3.037	8.415	4.593	16248.9	2938.7	134.1	24.74	53.77	5192.6	102	182.1	3.285	3.468	1.222	67.58	144.7
20	3	3.333	9.167	6	18937.7	3054	146	24.33	53.93	4883.3	103.6	186.8	3.297	3.283	1	67.03	168.7
21	8	2.75	9.151	4.5	15,830	2673.6	113	27.75	53.83	4937.5	97	179.7	2.878	3.34	2	65.48	134
22	4	3.5	21.5	5	28,394	3632.5	123	25	56.6	4350	110.6	193	3.64	3.58	-0.75	70.65	183

The first 10 rows of 29. The other 19 are in the notebook.

Correlation

Correlations
Column	Pair of	Association	Pearson's r	95% CI (Pearson)	Spearman's ρ	Kendall's τ	q-value	Rows
Highway-mpg	two numbers	0.9713	0.9713	0.9624 to 0.9782	0.9677	0.8925	< 0.001	205
Class	two numbers	0.9125	-0.8036	-0.8475 to -0.7488	-0.9125	-0.7672	< 0.001	203
Price	two numbers	0.8313	-0.6866	-0.7534 to -0.6057	-0.8313	-0.6613	< 0.001	201
Curb-weight	two numbers	0.8129	-0.7574	-0.8103 to -0.6922	-0.8129	-0.6533	< 0.001	205
Fuel-system	a number and a category	0.7479					< 0.001	205
Engine-size	two numbers	0.7301	-0.6537	-0.7257 to -0.5675	-0.7301	-0.5925	< 0.001	205
Width	two numbers	0.6877	-0.6427	-0.7166 to -0.5545	-0.6877	-0.5216	< 0.001	205
Length	two numbers	0.6709	-0.6709	-0.7399 to -0.5879	-0.67	-0.5073	< 0.001	205
Make	a number and a category	0.6634					< 0.001	205
Bore	two numbers	0.6195	-0.5946	-0.6773 to -0.4971	-0.6195	-0.4625	< 0.001	201

The first 10 rows of 24. The other 14 are in the notebook.

Visualization

The rows of City-mpg are not charted in their order: consecutive rows are no more alike than rows picked at random (a correlation of -0.06 between each value and the next), so the order carries no pattern to show.

Class

Class: 48 to 288, median 95, skewed to high values, 1% missing; moves with Engine-size most (r 0.811).

Description

Class
Statistic	Value
Type	integer
Values present	203
Distinct values	59
Continuous	yes
Decimal places	0
Minimum	48
Maximum	288
Mean	104.3
Median	95
Mode	68

The first 10 rows of 17. The other 7 are in the notebook.

Correlation

Correlations
Column	Pair of	Association	Pearson's r	95% CI (Pearson)	Spearman's ρ	Kendall's τ	q-value	Rows
City-mpg	two numbers	0.9125	-0.8036	-0.8475 to -0.7488	-0.9125	-0.7672	< 0.001	203
Highway-mpg	two numbers	0.8844	-0.7709	-0.8214 to -0.7084	-0.8844	-0.7283	< 0.001	203
Price	two numbers	0.8505	0.8105	0.7568 to 0.8534	0.8505	0.6665	< 0.001	199
Engine-size	two numbers	0.8195	0.8108	0.7577 to 0.8532	0.8195	0.6576	< 0.001	203
Curb-weight	two numbers	0.807	0.751	0.6841 to 0.8054	0.807	0.6186	< 0.001	203
Make	a number and a category	0.7289					< 0.001	203
Fuel-system	a number and a category	0.702					< 0.001	203
Width	two numbers	0.6921	0.6425	0.5538 to 0.7168	0.6921	0.514	< 0.001	203
Num-of-cylinders	two numbers	0.6916	0.6916	0.6122 to 0.7572	0.578	0.4752	< 0.001	203
Length	two numbers	0.6631	0.555	0.4518 to 0.6435	0.6631	0.4771	< 0.001	203

The first 10 rows of 24. The other 14 are in the notebook.

Visualization

The rows of Class are not charted in their order: consecutive rows are no more alike than rows picked at random (a correlation of 0.03 between each value and the next), so the order carries no pattern to show.

Compression-ratio

Compression-ratio: 7 to 23, median 9, skewed to high values, 32 distinct values; moves opposite to Peak-rpm most (r -0.436).

Description

Compression-ratio
Statistic	Value
Type	number
Values present	205
Distinct values	32
Continuous	yes
Decimal places	2
Minimum	7
Maximum	23
Mean	10.14
Median	9
Mode	9.0

The first 10 rows of 17. The other 7 are in the notebook.

By Value

Compression-ratio accounts for 39% of the spread in Class: 8 averages 104 above 22.5 (95% interval 76.8 to 131). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	8	8	165.5	140.6 to 190.4
Class	10	3	163.3	-104.9 to 431.5
Class	8.3	3	150	128.5 to 171.5
Class	7	7	146.7	141.2 to 152.2
Class	7.5	5	134.4	103.1 to 165.7
Class	9.5	13	127.7	97.1 to 158.3
Class	21.5	4	123	123 to 123
Class	9.3	11	122.5	109.6 to 135.4
Class	8.8	3	112	64.67 to 159.3
Class	7.6	4	102	102 to 102

The first 10 rows of 21. The other 11 are in the notebook.

Mean per value of Compression-ratio
Compression-ratio	Rows	Num-of-doors	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
7.0	7	2.286	4.143	14310.8	2927.4	18.43	146.7	23.71	51.29	5157.1	98.14	175.8	3.707	3.527	2.143	66.81	149.3
7.5	5	3.6	4	13177.4	2675.6	20.6	134.4	26.8	53.26	5340	99.5	179.1	3.336	3.35	0	66.12	118
7.6	4	2	4	8040.3	2148	24	102	30	50.75	5500	93.53	157.3	3.39	3.03		63.8	98
7.7	2	4	4	11476.5	2580	23.5	111	26	54.6	4800	96.95	172.8	2.64	3.62		65.4	108
7.8	1	2	6	19,699	3139	17	200	23	49.7	5200	91.3	170.7	3.27	3.43	3	67.9	181
8.0	8	3.25	5.875	30943.5	3266.8	16.38	165.5	21.13	55.16	5087.5	107.1	189.6	3.319	3.649	0.5	68.74	206.9
8.1	2	4	6	33,900	4066	15	176	19	52.8	4750	113	199.6	4.17	3.63		69.6	258
8.3	3	3.333	7	31038.3	3503.7	16.33	150	18.67	54.4	5000	106	191.9	3.2	3.35	1	71.2	199.7
8.4	5	4	4	14,649	3137	19	96.2	24	57.1	5000	110.4	191.6	2.79	3.46		68.4	120
8.5	14	3.429	4.286	10,968	2469.4	23.21	95.14	29.29	54.41	5228.6	98.93	175.2	3.419	3.275	0.9286	65.84	123.1

The first 10 rows of 32. The other 22 are in the notebook.

Correlation

Correlations
Column	Pair of	Association	Pearson's r	95% CI (Pearson)	Spearman's ρ	Kendall's τ	q-value	Rows
Fuel-system	a number and a category	0.9894					< 0.001	205
Fuel-type	a number and a category	0.9844					< 0.001	205
City-mpg	two numbers	0.4789	0.3247	0.1964 to 0.4421	0.4789	0.3769	< 0.001	205
Make	a number and a category	0.4602					0.003691	205
Highway-mpg	two numbers	0.4451	0.2652	0.133 to 0.3881	0.4451	0.337	< 0.001	205
Peak-rpm	two numbers	0.4362	-0.4362	-0.5414 to -0.3176	-0.02566	-0.002317	< 0.001	203
Class	two numbers	0.3554	-0.2059	-0.3341 to -0.07015	-0.3554	-0.2742	0.007707	203
Aspiration	a number and a category	0.2955					< 0.001	205
Height	two numbers	0.2612	0.2612	0.1288 to 0.3845	0.000231	-0.01883	< 0.001	205
Engine-type	a number and a category	0.2542					0.05027	205

The first 10 rows of 24. The other 14 are in the notebook.

Visualization

The rows of Compression-ratio are not charted in their order: consecutive rows are no more alike than rows picked at random (a correlation of -0.00 between each value and the next), so the order carries no pattern to show.

Curb-weight

Curb-weight: 1,488 to 4,066, median 2,414, skewed to high values; moves with Length most (r 0.878).

Description

Curb-weight
Statistic	Value
Type	integer
Values present	205
Distinct values	171
Continuous	yes
Decimal places	0
Minimum	1488
Maximum	4066
Mean	2555.6
Median	2414
Mode	2385

The first 10 rows of 17. The other 7 are in the notebook.

Correlation

Correlations
Column	Pair of	Association	Pearson's r	95% CI (Pearson)	Spearman's ρ	Kendall's τ	q-value	Rows
Price	two numbers	0.9138	0.8344	0.7869 to 0.8721	0.9138	0.7443	< 0.001	201
Length	two numbers	0.8904	0.8777	0.842 to 0.9058	0.8904	0.7231	< 0.001	205
Engine-size	two numbers	0.8777	0.8506	0.8077 to 0.8845	0.8777	0.7249	< 0.001	205
Width	two numbers	0.867	0.867	0.8284 to 0.8974	0.8638	0.6872	< 0.001	205
Highway-mpg	two numbers	0.8344	-0.7975	-0.8424 to -0.7415	-0.8344	-0.6734	< 0.001	205
Make	a number and a category	0.8265					< 0.001	205
City-mpg	two numbers	0.8129	-0.7574	-0.8103 to -0.6922	-0.8129	-0.6533	< 0.001	205
Class	two numbers	0.807	0.751	0.6841 to 0.8054	0.807	0.6186	< 0.001	203
Wheel-base	two numbers	0.7764	0.7764	0.7155 to 0.8256	0.7653	0.6073	< 0.001	205
Bore	two numbers	0.7005	0.649	0.561 to 0.7225	0.7005	0.5348	< 0.001	201

The first 10 rows of 24. The other 14 are in the notebook.

Visualization

The rows of Curb-weight are not charted in their order: consecutive rows are no more alike than rows picked at random (a correlation of 0.09 between each value and the next), so the order carries no pattern to show.

Drive-wheels

Drive-wheels: 3 distinct values, most often fwd.

Description

Drive-wheels
Statistic	Value
Type	text
Values present	205
Distinct values	3
Continuous	no
Mode	fwd

Rows per value
Variable	Value	Rows	Share
Drive-wheels	fwd	120	58.54 %
Drive-wheels	rwd	76	37.07 %
Drive-wheels	4wd	9	4.39 %

By Value

Drive-wheels accounts for 33% of the spread in Class: rwd averages 47.7 above fwd (95% interval 37.2 to 58.3). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	rwd	76	133.7	124.2 to 143.2
Class	4wd	9	95.33	70.82 to 119.8
Class	fwd	118	85.97	81.4 to 90.55

Mean per value of Drive-wheels
Drive-wheels	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
4wd	9	3.556	8.344	4.222	10,241	2609.1	23.11	95.33	27.22	55.4	4911.1	96.82	171.4	2.896	3.391	0.4444	65.21	110.1
fwd	120	3.153	9.934	4.083	9244.8	2264.4	28.32	85.97	34.23	53.52	5176.3	96.43	168.8	3.288	3.197	0.9417	65.06	108.8
rwd	76	3.026	10.69	4.868	19757.6	3008.9	20.58	133.7	25.68	53.85	5071.7	102.7	182.7	3.246	3.543	0.7105	67.33	157.5

Engine-location

Engine-location: 2 distinct values, most often front.

Description

Engine-location
Statistic	Value
Type	text
Values present	205
Distinct values	2
Continuous	no
Mode	front

Rows per value
Variable	Value	Rows	Share
Engine-location	front	202	98.54 %
Engine-location	rear	3	1.463 %

By Value

Engine-location accounts for 9.6% of the spread in Class: rear averages 104 above front (95% interval 99.0 to 110). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	rear	3	207	207 to 207
Class	front	200	102.7	97.42 to 108

Mean per value of Engine-location
Engine-location	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
front	202	3.14	10.15	4.356	12884.1	2552.4	25.34	102.7	30.84	53.76	5113.8	98.89	174.1	3.261	3.324	0.802	65.92	125.9
rear	3	2	9.5	6	34,528	2770.7	17	207	25	51.6	5900	89.5	168.9	2.9	3.74	3	65	194

Engine-size

Engine-size: 61 to 326, median 120, 44 distinct values; moves with Price most (r 0.872).

Description

Engine-size
Statistic	Value
Type	integer
Values present	205
Distinct values	44
Continuous	yes
Decimal places	0
Minimum	61
Maximum	326
Mean	126.9
Median	120
Mode	92

The first 10 rows of 17. The other 7 are in the notebook.

By Value

Engine-size accounts for 85% of the spread in Class: 194 averages 141 above 97 (95% interval 137 to 144). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	194	3	207	207 to 207
Class	209	3	182	182 to 182
Class	181	6	162.7	143 to 182.3
Class	171	3	159.3	152.2 to 166.5
Class	156	5	145	145 to 145
Class	130	4	136.5	89.65 to 183.4
Class	121	6	126.7	99.57 to 153.8
Class	183	4	123	123 to 123
Class	164	3	121	121 to 121
Class	141	7	120.6	104.5 to 136.7

The first 10 rows of 24. The other 14 are in the notebook.

Mean per value of Engine-size
Engine-size	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Width	Symboling
61	1	2	9.5	3	5151	1488	47	48	53	53.2	5100	88.4	141.1	3.03	2.91	60.3	2
70	3	2	9.4	2	12,145	2381.7	17	101	23	49.6	6000	95.3	169			65.7	3
79	1	2	10.1	4	5399	1837	38	60	42	52.6	5500	93.7	150	3.07	2.91	64
80	1	2	9.4	2	15,645	2500	16	135	23	49.6	6000	95.3	169			65.7	3
90	12	3.167	9.468	4	6384.2	1928.1	34.33	68.67	40.17	51.13	5466.7	93.97	157.9	3.19	2.99	63.73
91	5	2.8	9	4	6435	1918	30.8	68	36.6	54.1	5000	93.1	162.2	3.15	3.04	64.2
92	15	2.8	9.187	4	6773.1	2069.9	32.07	67.6	37.4	54.19	5340	93.93	157.8	3.222	2.979	63.9	1
97	14	3	13.26	4	7815.6	2088.4	32.43	66.43	38.64	54.43	5021.4	95.51	167.7	3.255	3.144	64.36	1.286
98	14	2.923	8.686	4	8170.9	2161.9	27.93	85	33.79	52.04	5307.1	94.59	164.5	3.154	3.136	64.07
103	1	2	21.9	4	7099	2017	45	55	50	54.5	4800	94.5	165.3	3.47	2.99	63.8

The first 10 rows of 44. The other 34 are in the notebook.

Correlation

Correlations
Column	Pair of	Association	Pearson's r	95% CI (Pearson)	Spearman's ρ	Kendall's τ	q-value	Rows
Curb-weight	two numbers	0.8777	0.8506	0.8077 to 0.8845	0.8777	0.7249	< 0.001	205
Price	two numbers	0.8723	0.8723	0.8347 to 0.9019	0.8284	0.6613	< 0.001	201
Num-of-cylinders	two numbers	0.846	0.846	0.802 to 0.8809	0.6917	0.5846	< 0.001	205
Class	two numbers	0.8195	0.8108	0.7577 to 0.8532	0.8195	0.6576	< 0.001	203
Make	a number and a category	0.8146					< 0.001	205
Length	two numbers	0.7826	0.6834	0.6028 to 0.7501	0.7826	0.6021	< 0.001	205
Width	two numbers	0.7706	0.7354	0.6655 to 0.7926	0.7706	0.5935	< 0.001	205
City-mpg	two numbers	0.7301	-0.6537	-0.7257 to -0.5675	-0.7301	-0.5925	< 0.001	205
Bore	two numbers	0.7247	0.5941	0.4965 to 0.6768	0.7247	0.5587	< 0.001	201
Highway-mpg	two numbers	0.7213	-0.6775	-0.7453 to -0.5957	-0.7213	-0.5818	< 0.001	205

The first 10 rows of 24. The other 14 are in the notebook.

Visualization

The rows of Engine-size are not charted in their order: consecutive rows are no more alike than rows picked at random (a correlation of 0.04 between each value and the next), so the order carries no pattern to show.

Engine-type

Engine-type: 7 distinct values, most often ohc.

Description

Engine-type
Statistic	Value
Type	text
Values present	205
Distinct values	7
Continuous	no
Mode	ohc

Rows per value
Variable	Value	Rows	Share
Engine-type	ohc	148	72.2 %
Engine-type	ohcf	15	7.317 %
Engine-type	ohcv	13	6.341 %
Engine-type	dohc	12	5.854 %
Engine-type	l	12	5.854 %
Engine-type	rotor	4	1.951 %
Engine-type	dohcv	1	0.4878 %

By Value

Engine-type accounts for 31% of the spread in Class: ohcv averages 75.8 above ohc (95% interval 55.6 to 96.1). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	ohcv	13	169.5	149.7 to 189.4
Class	dohc	12	146	129.3 to 162.7
Class	ohcf	15	110.4	81.9 to 138.9
Class	rotor	4	109.5	82.45 to 136.6
Class	l	12	95.5	82.75 to 108.2
Class	ohc	146	93.7	88.84 to 98.55

Mean per value of Engine-type
Engine-type	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
dohc	12	2.833	9	5	18116.4	2976.8	20	146	24.83	52.73	5375	100.4	182.5	3.283	3.403	1.417	66.4	157.3
dohcv	1	2	10	8		3366	17	288	28	50.5	5750	98.4	175.7	3.11	3.94		72.3	203
l	12	3.833	13.63	3.917	14627.6	3076.6	24.5	95.5	28.83	56.85	4704.2	108.4	187	3.149	3.527	0.1667	67.72	129.6
ohc	148	3.137	10.21	4.169	11567.4	2422.3	26.8	93.7	32.57	53.78	5133.9	98	172	3.326	3.261	0.7703	65.53	117.5
ohcf	15	3.2	8.953	4.4	13738.6	2407.1	24.47	110.4	29.6	53.32	5000	94.84	168.9	2.673	3.644	1	64.96	124.5
ohcv	13	2.923	8.823	7.077	25098.4	3355.8	16.77	169.5	21.23	53.12	5015.4	102.6	185.6	3.202	3.454	0.7692	68.78	216.7
rotor	4	2	9.4	2	13,020	2411.3	16.75	109.5	23	49.6	6000	95.3	169			3	65.7	72.5

Fuel-system

Fuel-system: 8 distinct values, most often mpfi.

Description

Fuel-system
Statistic	Value
Type	text
Values present	205
Distinct values	8
Continuous	no
Mode	mpfi

Rows per value
Variable	Value	Rows	Share
Fuel-system	mpfi	94	45.85 %
Fuel-system	2bbl	66	32.2 %
Fuel-system	idi	20	9.756 %
Fuel-system	1bbl	11	5.366 %
Fuel-system	spdi	9	4.39 %
Fuel-system	4bbl	3	1.463 %
Fuel-system	mfi	1	0.4878 %
Fuel-system	spfi	1	0.4878 %

By Value

Fuel-system accounts for 48% of the spread in Class: mpfi averages 58.9 above 2bbl (95% interval 50.4 to 67.3). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	mpfi	92	131.9	123.9 to 140
Class	spdi	9	125.8	111.2 to 140.4
Class	4bbl	3	101	101 to 101
Class	idi	20	84.45	72.3 to 96.6
Class	1bbl	11	76.55	69.91 to 83.18
Class	2bbl	66	73.09	70.71 to 75.47

Mean per value of Fuel-system
Fuel-system	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
1bbl	11	2.727	9.245	4	7555.5	2045.5	31.45	76.55	36.55	53.36	5772.7	93.94	158.7	3.441	2.998	0.6364	64.16	97.36
2bbl	66	3.152	9.088	3.985	7433.2	2120.5	30.15	73.09	36.02	53.44	5059.1	95.3	165.3	3.149	3.191	0.7727	64.28	100.2
4bbl	3	2	9.4	2	12,145	2381.7	17	101	23	49.6	6000	95.3	169			3	65.7	70
idi	20	3.684	22.01	4.3	15838.2	2898.8	30.3	84.45	34.75	55.84	4435	104.4	182	3.486	3.375	0.1	67.43	135.7
mfi	1	2	7	4	12,964	2811	19	145	24	50.2	5000	95.9	173.2	3.9	3.6	3	66.3	156
mpfi	94	3.161	8.803	4.84	17605.1	2849.2	20.65	131.9	26.19	54.01	5204.9	101	180.9	3.218	3.454	0.8511	66.98	148.7
spdi	9	2.444	7.3	4	10990.4	2549.7	21.44	125.8	27.33	50.56	5277.8	95.47	169.5	3.622	3.324	1.889	65.44	127.8
spfi	1	2	9.2	4	11,048	2734	24	90	29	51.4	5000	96	172.6	3.23	3.43	2	65.2	119

Fuel-type

Fuel-type: 2 distinct values, most often gas.

Description

Fuel-type
Statistic	Value
Type	text
Values present	205
Distinct values	2
Continuous	no
Mode	gas

Rows per value
Variable	Value	Rows	Share
Fuel-type	gas	185	90.24 %
Fuel-type	diesel	20	9.756 %

By Value

Mean per value of Fuel-type
Fuel-type	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
diesel	20	3.684	22.01	4.3	15838.2	2898.8	30.3	84.45	34.75	55.84	4435	104.4	182	3.486	3.375	0.1	67.43	135.7
gas	185	3.065	8.86	4.389	12916.4	2518.5	24.67	106.4	30.32	53.5	5200.8	98.15	173.2	3.23	3.325	0.9135	65.74	126

Height

Height: 47.8 to 59.8, median 54.1, 49 distinct values; moves with Wheel-base most (r 0.589).

Description

Height
Statistic	Value
Type	number
Values present	205
Distinct values	49
Continuous	yes
Decimal places	1
Minimum	47.8
Maximum	59.8
Mean	53.72
Median	54.1
Mode	50.8

The first 10 rows of 17. The other 7 are in the notebook.

By Value

Height accounts for 31% of the spread in Class: 49.7 averages 111 above 59.1 (95% interval 54.0 to 169). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	49.7	3	173.3	116 to 230.7
Class	51.6	7	147	94.03 to 200
Class	50.2	6	144.7	143.8 to 145.5
Class	56.1	7	130.3	106.8 to 153.8
Class	56.2	3	130	61.16 to 198.8
Class	57.5	3	130	61.16 to 198.8
Class	55.1	5	114	67.14 to 160.9
Class	52	12	111.8	88.97 to 134.7
Class	49.6	4	109.5	82.45 to 136.6
Class	54.3	8	106.8	95.83 to 117.7

The first 10 rows of 24. The other 14 are in the notebook.

Mean per value of Height
Height	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Peak-rpm	Wheel-base	Length	Stroke	Bore	Width	Engine-size	Symboling
47.8	1	2	11.5	12	36,000	3950	13	262	17	5000	102	191.7	2.76	3.54	70.6	326
48.8	2	2	9	4	14997.5	2548	21	111	27	5000	88.6	168.8	2.68	3.47	64.1	130	3
49.4	2	2	8	4	9229	2349	24	102	31	5250	96.3	173	3.46	3.26	65.4	116	3
49.6	4	2	9.4	2	13,020	2411.3	16.75	109.5	23	6000	95.3	169			65.7	72.5	3
49.7	3	2	8.6	6	18432.3	3116.3	18.33	173.3	24.33	5200	93.93	173.3	3.27	3.43	67.9	181	2.333
50.2	6	2	7.417	4	14955.5	2847.8	19	144.7	24.5	5083.3	95.67	172.5	3.742	3.648	66.63	155.2	3
50.5	2	2	9.35	6	9895	2913	20	288	29.5	5750	97.25	176.3	3.505	3.7	69.45	167.5	1.5
50.6	5	4	9.04	4	7063.4	2020.6	29.6	74.8	36.4	5500	93.7	157.3	3.262	2.982	63.8	91.6
50.8	14	2.286	8.936	4.286	8718.7	2095.3	31	81.36	36.64	5432.1	92.84	158.6	3.281	3.009	64.42	103.3	1.5
51.0	1	2	9.1	4	10,345	2293	25	100	31	5500	96.5	169.1	3.58	3.15	66	110

The first 10 rows of 49. The other 39 are in the notebook.

Correlation

Correlations
Column	Pair of	Association	Pearson's r	95% CI (Pearson)	Spearman's ρ	Kendall's τ	q-value	Rows
Make	a number and a category	0.7042					< 0.001	205
Wheel-base	two numbers	0.6329	0.5894	0.4922 to 0.6722	0.6329	0.4617	< 0.001	205
Body-style	a number and a category	0.6291					< 0.001	205
Num-of-doors	two numbers	0.5477	0.5477	0.4434 to 0.6373	0.5471	0.4541	< 0.001	203
Symboling	two numbers	0.541	-0.541	-0.6313 to -0.4364	-0.5231	-0.4132	< 0.001	205
Length	two numbers	0.5251	0.491	0.3795 to 0.5885	0.5251	0.3746	< 0.001	205
Fuel-system	a number and a category	0.4645					< 0.001	205
Engine-type	a number and a category	0.4203					< 0.001	205
Width	two numbers	0.3503	0.2792	0.1478 to 0.4009	0.3503	0.259	< 0.001	205
Curb-weight	two numbers	0.3459	0.2956	0.1652 to 0.4158	0.3459	0.245	< 0.001	205

The first 10 rows of 24. The other 14 are in the notebook.

Visualization

The rows of Height are not charted in their order: consecutive rows are no more alike than rows picked at random (a correlation of 0.02 between each value and the next), so the order carries no pattern to show.

Highway-mpg

Highway-mpg: 16 to 54, median 30, 30 distinct values; moves with City-mpg most (r 0.971).

Description

Highway-mpg
Statistic	Value
Type	integer
Values present	205
Distinct values	30
Continuous	yes
Decimal places	0
Minimum	16
Maximum	54
Mean	30.75
Median	30
Mode	25

The first 10 rows of 17. The other 7 are in the notebook.

By Value

Highway-mpg accounts for 59% of the spread in Class: 22 averages 94.4 above 42 (95% interval 76.4 to 112). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	22	8	158.4	140.8 to 176
Class	26	3	158	149.4 to 166.6
Class	25	19	135.9	117.3 to 154.5
Class	24	17	133.4	119 to 147.7
Class	28	13	126.2	96.7 to 155.8
Class	23	7	126.1	92.97 to 159.3
Class	27	5	118.2	99.88 to 136.5
Class	30	16	108.1	102.7 to 113.6
Class	29	10	96.7	87.75 to 105.7
Class	33	9	87.11	81.56 to 92.66

The first 10 rows of 18. The other 8 are in the notebook.

Mean per value of Highway-mpg
Highway-mpg	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
16	2	3	8	8	43,180	3807.5	14	184	56.05	4500	116.5	203.7	3.35	3.8		71.85	306
17	1	2	11.5	12	36,000	3950	13	262	47.8	5000	102	191.7	2.76	3.54		70.6	326
18	2	3	8.3	8	34,620	3712.5	16	155	53.65	4750	106.1	191.5	3.1	3.46	1	71.1	234
19	2	4	8.1	6	33,900	4066	15	176	52.8	4750	113	199.6	4.17	3.63		69.6	258
20	2	4	8.15	5.5	30377.5	3295.5	16	161	56.1	5450	107.9	194.9	3.395	3.375		71.15	170
22	8	3.5	8	5.25	22113.3	3135	16.75	158.4	55.08	5300	101.9	185.2	3.303	3.458	-0.125	67.06	163.4
23	7	2.571	8.843	3.429	14,994	2635.1	17.86	126.1	51.21	5642.9	96.93	172.7	2.927	3.543	2	66.43	107.4
24	17	3.059	8.088	4.529	14876.7	2998.2	19.06	133.4	53.8	5111.8	103.4	183	3.319	3.465	1.176	67.36	144.9
25	19	3.263	12.91	5.105	22344.2	3099.1	20.26	135.9	54.66	5013.2	103.2	184.8	3.286	3.542	0.6842	68.2	164.4
26	3	2.667	9	4.667	17756.7	2826	19	158	54.87	5333.3	97.57	181.5	3.203	3.253	2	66.17	131.3

The first 10 rows of 30. The other 20 are in the notebook.

Correlation

Correlations
Column	Pair of	Association	Pearson's r	95% CI (Pearson)	Spearman's ρ	Kendall's τ	q-value	Rows
City-mpg	two numbers	0.9713	0.9713	0.9624 to 0.9782	0.9677	0.8925	< 0.001	205
Class	two numbers	0.8844	-0.7709	-0.8214 to -0.7084	-0.8844	-0.7283	< 0.001	203
Curb-weight	two numbers	0.8344	-0.7975	-0.8424 to -0.7415	-0.8344	-0.6734	< 0.001	205
Price	two numbers	0.8273	-0.7047	-0.7682 to -0.6275	-0.8273	-0.6518	< 0.001	201
Engine-size	two numbers	0.7213	-0.6775	-0.7453 to -0.5957	-0.7213	-0.5818	< 0.001	205
Fuel-system	a number and a category	0.7048					< 0.001	205
Length	two numbers	0.7047	-0.7047	-0.7676 to -0.6283	-0.6979	-0.5319	< 0.001	205
Width	two numbers	0.701	-0.6772	-0.7451 to -0.5954	-0.701	-0.5256	< 0.001	205
Make	a number and a category	0.6645					< 0.001	205
Bore	two numbers	0.6266	-0.5946	-0.6772 to -0.4971	-0.6266	-0.4673	< 0.001	201

The first 10 rows of 24. The other 14 are in the notebook.

Visualization

The rows of Highway-mpg are not charted in their order: consecutive rows are no more alike than rows picked at random (a correlation of -0.06 between each value and the next), so the order carries no pattern to show.

Length

Length: 141 to 208, median 173; moves with Curb-weight most (r 0.878).

Description

Length
Statistic	Value
Type	number
Values present	205
Distinct values	75
Continuous	yes
Decimal places	1
Minimum	141.1
Maximum	208.1
Mean	174
Median	173.2
Mode	157.3

The first 10 rows of 17. The other 7 are in the notebook.

Correlation

Correlations
Column	Pair of	Association	Pearson's r	95% CI (Pearson)	Spearman's ρ	Kendall's τ	q-value	Rows
Wheel-base	two numbers	0.9124	0.8746	0.838 to 0.9034	0.9124	0.7459	< 0.001	205
Curb-weight	two numbers	0.8904	0.8777	0.842 to 0.9058	0.8904	0.7231	< 0.001	205
Width	two numbers	0.8882	0.8411	0.7958 to 0.8771	0.8882	0.724	< 0.001	205
Make	a number and a category	0.8241					< 0.001	205
Price	two numbers	0.8103	0.6906	0.6106 to 0.7567	0.8103	0.6364	< 0.001	201
Engine-size	two numbers	0.7826	0.6834	0.6028 to 0.7501	0.7826	0.6021	< 0.001	205
Highway-mpg	two numbers	0.7047	-0.7047	-0.7676 to -0.6283	-0.6979	-0.5319	< 0.001	205
City-mpg	two numbers	0.6709	-0.6709	-0.7399 to -0.5879	-0.67	-0.5073	< 0.001	205
Class	two numbers	0.6631	0.555	0.4518 to 0.6435	0.6631	0.4771	< 0.001	203
Fuel-system	a number and a category	0.6601					< 0.001	205

The first 10 rows of 24. The other 14 are in the notebook.

Visualization

The rows of Length are not charted in their order: consecutive rows are no more alike than rows picked at random (a correlation of 0.09 between each value and the next), so the order carries no pattern to show.

Make

Make: 22 distinct values, most often toyota.

Description

Make
Statistic	Value
Type	text
Values present	205
Distinct values	22
Continuous	no
Mode	toyota

Rows per value
Variable	Value	Rows	Share
Make	toyota	32	15.61 %
Make	nissan	18	8.78 %
Make	mazda	17	8.293 %
Make	honda	13	6.341 %
Make	mitsubishi	13	6.341 %
Make	subaru	12	5.854 %
Make	volkswagen	12	5.854 %
Make	peugot	11	5.366 %
Make	volvo	11	5.366 %
Make	dodge	9	4.39 %

The first 10 rows of 22. The other 12 are in the notebook.

By Value

Make accounts for 47% of the spread in Class: porsche averages 148 above chevrolet (95% interval 84.7 to 211). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	porsche	5	210.4	146.5 to 274.3
Class	jaguar	3	204.7	81.32 to 328
Class	mercedes-benz	8	146.3	123.5 to 169
Class	bmw	8	138.9	108.2 to 169.5
Class	volvo	11	128	112.9 to 143.1
Class	saab	6	126.7	99.57 to 153.8
Class	alfa-romero	3	125.3	63.66 to 187
Class	audi	7	121	101.6 to 140.4
Class	mitsubishi	13	104.1	86.52 to 121.6
Class	nissan	18	102.6	79.71 to 125.4

The first 10 rows of 20. The other 10 are in the notebook.

Mean per value of Make
Make	Rows	Num-of-doors	Compression-ratio	Num-of-cylinders	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
alfa-romero	3	2	9	4.667	15498.3	2639.7	20.33	125.3	26.67	50	5000	90.57	169.6	2.943	3.207	2.333	64.57	137.3
audi	7	3.429	8.4	4.857	17859.2	2800.7	18.86	121	24.14	54.43	5500	102.3	183.8	3.4	3.173	1.286	68.71	130.7
bmw	8	3.25	8.575	5.5	26118.8	2929.4	19.38	138.9	25.38	54.83	5068.8	103.2	184.5	3.168	3.474	0.375	66.48	166.9
chevrolet	3	2.667	9.567	3.667	6007	1757	41	62.67	46.33	52.4	5300	92.47	151.9	3.083	2.99	1	62.5	80.33
dodge	9	3	8.634	4	7875.4	2151.3	28	86.33	34.11	51.64	5388.9	95.01	161	3.366	3.094	1	64.17	102.7
honda	13	2.769	9.215	4	8184.7	2096.8	30.38	80.23	35.46	53.24	5753.8	94.33	160.8	3.462	3.022	0.6154	64.38	99.31
isuzu	4	3	9.225	4	8916.5	2213.5	31	77	36	52.23	5150	94.83	163.8	3.17	3.2	0.75	63.55	102.5
jaguar	3	3.333	9.233	8	34,600	4027.3	14.33	204.7	18.33	51.13	4833.3	109.3	197	3.7	3.6		69.93	280.7
mazda	17	2.875	10.49	3.529	10652.9	2297.8	25.71	85.53	31.94	53.36	5108.8	97.02	170.8	3.299	3.287	1.118	65.59	103
mercedes-benz	8	3.25	14.83	6.5	33,647	3696.3	18.5	146.3	21	55.73	4487.5	110.9	195.3	3.433	3.605	0	71.06	226.5

The first 10 rows of 22. The other 12 are in the notebook.

Num-of-cylinders

Num-of-cylinders: 2 to 12, median 4, skewed to high values, 7 distinct values; moves with Engine-size most (r 0.846).

Description

Num-of-cylinders
Statistic	Value
Type	integer
Values present	205
Distinct values	7
Continuous	yes
Decimal places	0
Minimum	2
Maximum	12
Mean	4.38
Median	4
Mode	4

The first 10 rows of 17. The other 7 are in the notebook.

By Value

Num-of-cylinders accounts for 51% of the spread in Class: 8 averages 103 above 4 (95% interval 34.6 to 171). An association, not a cause.

Groups
Target	Value	Rows	Average or share	95% interval
Class	8	5	193.2	125 to 261.4
Class	6	24	161.9	149.9 to 173.9
Class	5	11	122.5	112.1 to 132.9
Class	2	4	109.5	82.45 to 136.6
Class	4	157	90.55	86.48 to 94.63

Mean per value of Num-of-cylinders
Num-of-cylinders	Rows	Num-of-doors	Compression-ratio	Price	Curb-weight	City-mpg	Class	Highway-mpg	Height	Peak-rpm	Wheel-base	Length	Stroke	Bore	Symboling	Width	Engine-size
2	4	2	9.4	13,020	2411.3	16.75	109.5	23	49.6	6000	95.3	169			3	65.7	72.5
3	1	2	9.5	5151	1488	47	48	53	53.2	5100	88.4	141.1	3.03	2.91	2	60.3	61
4	159	3.159	10.12	10303.2	2394.5	27.12	90.55	32.77	53.8	5113.1	97.76	171.4	3.237	3.306	0.8113	65.31	112.8
5	11	3.455	13.03	22007.6	3132.6	19.55	122.5	23.91	55.29	5081.8	105.3	187.5	3.487	3.321	0.3636	69.48	152.2
6	24	3.083	9.429	23671.8	3134	18.29	161.9	23.83	53.39	5143.8	101.2	182.9	3.314	3.425	0.8333	67.14	185.3
8	5	2.8	8.52	38,900	3681.2	15.4	193.2	19.2	53.98	4850	108.7	193.2	3.202	3.692	0.8	71.64	256.6
12	1	2	11.5	36,000	3950	13	262	17	47.8	5000	102	191.7	2.76	3.54		70.6	326

Correlation

This section continues in the notebook.

Implications

Multiple groups in the data mostly fall inside the training range, but 9.8% of the held-out rows did not. Two columns could stand in as proxies, so fairness checks are advised; concerns are discussed in the Concerns chapter.

Most notable in the Implications section:

9.8% of the held-out rows lie outside the range the model was trained on

How to read this

The Implications section states how to act on the models: the Stakeholder Summary and the Recommended Next Data, where the models hold and where they weaken (Quality by Input Range, Rows unlike the ones the model learned from, Per-Segment Predictions, Fairness), what to weigh before relying on them (Causal Honesty, Deployment Readiness), and the Provenance & Audit trail a reviewer needs to retrace the analysis.

Stakeholder Summary

Recommended Next Data

Collect more rows with high values of the model's output, especially where predictions are largest. Reason: the diagnostics warn that the model is systematically less accurate on high-magnitude predictions and that residual variance grows sharply with predicted value.
Collect more rows representing every group in the columns Aspiration, Body-style, Drive-wheels, Engine-type, Fuel-system, and Fuel-type. Reason: the diagnostics flag prediction parity gaps and group differences in model error for these columns, indicating the model's errors differ between groups or show bias.
Add columns that capture the factors behind variation in the model's output at higher predicted values. Reason: the model is less accurate as the prediction rises, so candidate inputs that explain the gap would make the model stronger in that range.

Quality by Input Range

Quality by Input Range splits the held-out rows by every usable input and compares the model's quality on each segment with its quality on all held-out rows. For a number the quality is R², the share of variation explained; for a yes-or-no target it is accuracy, the share of rows classified correctly, the measure the Classification Performance chapter reports. A numeric input is split into quartiles; a categorical input with at most ten values is split by value. A segment with fewer than three held-out rows is left out, because its gap would be noise.

The chart is sorted from the worst gap to the best. Each bar is the segment's figure minus the figure on all held-out rows.

Negative bars: the model is weaker on these rows than on all held-out rows. A segment 0.25 or more below the overall value (25 points of accuracy) reads much weaker; a segment 0.10 to 0.25 below reads weaker. These are the segments to treat with caution.
Positive bars: the model is stronger on these rows than overall. A strong segment can mask weakness elsewhere, so the negative segments come first.

Class by Input Range

Segment num_of_doors in the highest quarter (4) performs in line with the aggregate (24 held-out rows): segment R² 0.758 against aggregate R² 0.842 (gap -0.0841). No quality drift detected.

Segment	Rows	R²	Gap to all rows	Verdict
Num-of-doors = q4	24	0.7578	-0.0841	In line with all rows
Body-style = sedan	21	0.8086	-0.0333	In line with all rows
Drive-wheels = fwd	26	0.8177	-0.0242	In line with all rows
Num-of-cylinders = q4	39	0.8313	-0.0106	In line with all rows
Fuel-type = gas	36	0.8345	-0.0074	In line with all rows
Engine-location = front	40	0.8419	+0.0000	In line with all rows
Engine-type = ohc	29	0.8611	+0.0192	In line with all rows
Aspiration = std	30	0.8838	+0.0419	In line with all rows
Engine-type = dohc	3	-14.1684	-15.0103	Too few rows to judge
Highway-mpg = q3	9	-0.2062	-1.0481	Too few rows to judge

The first 10 rows of 24. The other 14 are in the notebook.

Aggregate R²: 0.8419
Measure: r2
Target: Class

Rows unlike the ones the model learned from

Target	Inputs measured	Line	Held-out rows	Beyond the line	Share
Class	City-mpg, Engine-size, Length	3.368	41	4	9.76 %

Score bins · 24 of 30 rows shown
Count	From	To
0	0	0.16
2	0.16	0.32
2	0.32	0.481
5	0.481	0.641
0	0.641	0.801
0	0.801	0.961
3	0.961	1.121
4	1.121	1.281
4	1.281	1.442
3	1.442	1.602

The first 10 rows of 24. The other 14 are in the notebook.

How to read this

Out-of-distribution detection finds held-out rows that lie far from the training rows of a model. It looks only at the numeric inputs the model reads. Each of them is standardized against the mean and standard deviation of the training rows, and the standardized values are combined into one distance per row. The line a row is read against depends on the number of inputs: it is the distance that 99 in 100 rows like the training rows stay below. A row beyond the line is flagged as out of distribution, and the held-out figures are unlikely to apply to it. When the held-out rows resemble the training rows, about one row in a hundred is flagged.

The chart shows one bar per held-out row in row order; the flagged rows are the bars at or above the line. With more than one target, the chart shows the model with the largest flagged share, and the figures name it.

The check treats inputs independently, so it will not notice a rare combination of values that are each ordinary on their own, such as a large height with a small weight. It is a first screen. A decision that depends on catching unusual inputs needs a dedicated check.

Fairness

This chapter checks the held-out predictions for uneven treatment of groups. For every categorical column with two to ten distinct values, other than the target, it reports per group the row count, mean actual value, mean prediction and mean residual, with R² and MAE for a number or accuracy, the share of rows classified correctly, for a yes-or-no target, and two measures across the groups.

Prediction parity ratio: the smallest group mean prediction divided by the largest, in absolute value. A ratio of 1.0 is perfect parity. Below 0.80, the four-fifths rule, some group receives systematically different predictions.
Largest mean residual: the largest absolute mean residual of any group. Above 30% of the overall residual standard deviation, at least one group is systematically over- or under-predicted.

The verdict combines the two: balanced when neither measure trips, parity gap or residual bias when one does, parity gap and residual bias when both do, and insufficient data when fewer than two groups have enough held-out rows.

Diafunc does not decide which columns are protected attributes; it reports every plausible one. A flagged column matters where it is a protected attribute in the decision the model supports, and can be set aside where it is not.

Class Fairness

Aggregate residual std: 13.14
Held-out rows offered: 41
N columns: 6
N proxies: 21
N without target: 1
Proxy threshold: 0.5

Columns
Bias max abs residual mean	Column	Groups	Interpretation	N groups	N proxies	Prediction parity ratio	Verdict
11.8	Aspiration	turbo, std	Column Aspiration splits the held-out rows into 2 groups. The prediction-parity ratio is 0.835 (smallest over largest mean prediction), the largest absolute group residual mean is 11.8 (0.898 times the overall residual standard deviation). Residual bias: at least one group is systematically over- or under-predicted. The model's errors are not zero-mean across groups; its predictions for the affected groups deserve caution. fuel_system goes closely with aspiration (association 0.61 on a scale from 0 to 1): a model that reads fuel_system can tell the groups of aspiration apart, so leaving aspiration out of the inputs does not keep it out of the predictions.	2	1	0.8353	Residual bias
3.899	Body-style	wagon, hatchback, sedan	Column Body-style splits the held-out rows into 3 groups. The prediction-parity ratio is 0.785 (smallest over largest mean prediction), the largest absolute group residual mean is 3.90 (0.297 times the overall residual standard deviation). Parity gap: at least one group receives systematically smaller predictions on average. Whether that is a property of the target itself or a model bias against the group needs checking. num_of_doors goes closely with body_style (association 0.759 on a scale from 0 to 1, and 2 more columns at 0.5 or above): a model that reads num_of_doors can tell the groups of body_style apart, so leaving body_style out of the inputs does not keep it out of the predictions.	3	3	0.7852	Prediction parity gap
2.129	Drive-wheels	rwd, fwd	Column Drive-wheels splits the held-out rows into 2 groups. The prediction-parity ratio is 0.731 (smallest over largest mean prediction), the largest absolute group residual mean is 2.13 (0.162 times the overall residual standard deviation). Parity gap: at least one group receives systematically smaller predictions on average. Whether that is a property of the target itself or a model bias against the group needs checking. curb_weight goes closely with drive_wheels (association 0.683 on a scale from 0 to 1, and 4 more columns at 0.5 or above): a model that reads curb_weight can tell the groups of drive_wheels apart, so leaving drive_wheels out of the inputs does not keep it out of the predictions.	2	5	0.7313	Prediction parity gap
19.18	Engine-type	dohc, ohcf, ohc, l	Column Engine-type splits the held-out rows into 4 groups. The prediction-parity ratio is 0.614 (smallest over largest mean prediction), the largest absolute group residual mean is 19.2 (1.46 times the overall residual standard deviation). Parity gap and residual bias: the model both predicts systematically lower for some groups and errs systematically against at least one group. This is the worst-case fairness signal on this column; review before deployment. num_of_cylinders goes closely with engine_type (association 0.778 on a scale from 0 to 1, and 4 more columns at 0.5 or above): a model that reads num_of_cylinders can tell the groups of engine_type apart, so leaving engine_type out of the inputs does not keep it out of the predictions.	4	5	0.6141	Parity and bias
6.087	Fuel-system	mpfi, 1bbl, idi, 2bbl	Column Fuel-system splits the held-out rows into 4 groups. The prediction-parity ratio is 0.635 (smallest over largest mean prediction), the largest absolute group residual mean is 6.09 (0.463 times the overall residual standard deviation). Parity gap and residual bias: the model both predicts systematically lower for some groups and errs systematically against at least one group. This is the worst-case fairness signal on this column; review before deployment. compression_ratio goes closely with fuel_system (association 0.989 on a scale from 0 to 1, and 4 more columns at 0.5 or above): a model that reads compression_ratio can tell the groups of fuel_system apart, so leaving fuel_system out of the inputs does not keep it out of the predictions.	4	5	0.6347	Parity and bias
4.346	Fuel-type	gas, diesel	Column Fuel-type splits the held-out rows into 2 groups. The prediction-parity ratio is 0.966 (smallest over largest mean prediction), the largest absolute group residual mean is 4.35 (0.331 times the overall residual standard deviation). Residual bias: at least one group is systematically over- or under-predicted. The model's errors are not zero-mean across groups; its predictions for the affected groups deserve caution. fuel_system goes closely with fuel_type (association 0.985 on a scale from 0 to 1, and 1 more column at 0.5 or above): a model that reads fuel_system can tell the groups of fuel_type apart, so leaving fuel_type out of the inputs does not keep it out of the predictions.	2	2	0.9661	Residual bias

Causal Honesty

Diafunc found a formula that captures the structure in the training data. That structure is correlative: it states what predicts what in this data. It does not establish that any input causes the target.

A correlative model is the right tool for predicting the target on new rows like these, for exploring which inputs carry information about the target, and for an early-stage diagnostic or screening tool.

A correlative model is not the right tool for claiming that intervening on an input will change the target, for attributing a target's values to specific causes for accountability, or for choosing between policies that act on the inputs.

The Quality by Input Range, Fairness and Concerns chapters show the most common confounding patterns in the data.

The model is correlative: it captures which columns predict the target in the training data, not whether changing one would change the other. Predictions are reliable for inputs that look like the training distribution; they are not evidence that intervening on an input will change the target. The 4 upgrade pathways below show what evidence would support a causal claim.

Upgrade pathways
Name	Summary
Controlled experiment	Randomize the input to be acted on, then analyze again. Randomization breaks confounding, so any change in the target is attributable to the input.
Natural experiment	Find a setting where the input varied for reasons unrelated to the target, an instrumental variable. Variation of that kind supports causal inference.
Causal graph	Write out what plausibly causes what, then check whether the model's terms are consistent with the conditional independences the graph implies.
Control for confounders	If a third variable plausibly moves both the input and the target, stratify by it or condition on it before training again. Gaps in the Quality by Input Range chapter are a clue.

Deployment Readiness

The analysis ran with the configuration below. The checks and the verdict of this chapter are read against it.

Targets: 1 target: class
Rows: 205 rows
Per-Segment Predictions: not produced, because no segment column was chosen
Fairness: compared across 8 categorical columns (aspiration, body_style, drive_wheels, engine_location, engine_type, fuel_system, fuel_type, make); which of them are protected attributes is not decided here
Out-of-Distribution: held-out rows are scored against the training rows; predictions made outside this report are not scored
Provenance & Audit: recorded in the chapter of that name

Name	Status	Detail
Generalization	Pass	held-out quality holds up against training quality
Prediction Interval Coverage	Warn	intervals are wider than their level requires, largest gap 7.50 percentage points
Baseline Lift for Class	Pass	beats the best baseline, R² lift 0.0679
Model Constraints	Pass	every held-out prediction is finite and within the training range
Fairness	Fail	6 columns compared, 6 flagged: Aspiration (a group is systematically over- or under-predicted), Body-style (a group receives systematically smaller predictions), Drive-wheels (a group receives systematically smaller predictions), Engine-type (a group both receives smaller predictions and is systematically mis-predicted), Fuel-system (a group both receives smaller predictions and is systematically mis-predicted), Fuel-type (a group is systematically over- or under-predicted)
Out-of-Distribution	Pass	9.8% of held-out rows are out of distribution

N critical concerns: 1
N fail: 1
N pass: 4
N warn: 1
Overall verdict: Not ready

Provenance & Audit

This record captures the inputs and configuration that produced the report, so the analysis can be reproduced or the result defended in an audit.

Item	Value
Analysis ID	27b5ec60-c685-11f1-b558-07fc56137a66
Run time	2026-10-24 17:46 UTC
Total rows	205
Modeled targets	Class
Segment column	not available
Time limit	1 h 0 min
Time taken	1 min 24 s
Credit budget	500 credits
Ufinq version	0.3.40
Models kept from	run 96cdbc60-ca61-11f1-9fa9-c35ef749fe28, whose search found them; this report was built again around them

Findings

1 finding from the implications diagnostics (1 Info) is listed in the Concerns chapter at the top of the analysis.

The report continues in the notebook.