Car Design in the 1970s:
Designed Mileage & Transmission Type

Regression Models

Johns Hopkins University

Author

D.McCabe

Executive Summary (for credit)

The analysis highlights the challenges of working with small, collinear datasets. Although strong associations are evident, causal inference is limited and background engineering knowledge is essential for interpretation.

This project investigates whether cars with manual transmissions achieve higher fuel efficiency than those with automatic transmissions, using the mtcars dataset of 32 vehicles from the 1970s.

A series of statistical analyses, informed by engineering considerations, reveal that while manual cars appear to deliver around seven miles per gallon more than automatics on average, this apparent advantage is largely explained by differences in vehicle weight. Once weight is accounted for, the estimated effect of transmission type falls to near zero.
Other factors were examined to assess whether they confound or mediate this relationship. Horsepower, gear ratios, and performance metrics such as engine displacement and horsepower were found to be highly collinear with weight, limiting their interpretive value. Similarly, variables such as carburettor count and final drive ratio did not yield additional explanatory power, though they may be more relevant in larger datasets.
Predictive models confirm that vehicle weight is by far the most powerful single predictor of fuel consumption. Adding a performance proxy improves fit slightly but transmission type itself contributes little explanatory value once weight is considered. Exploratory analysis of muscle cars (high-power, heavy vehicles) suggested possible outliers where weight alone does not predict fuel economy well, though the sample is too small to draw firm conclusions.

Conclusion: In the mtcars dataset, the commonly reported superiority of manual over automatic transmission for fuel efficiency is not supported once weight is taken into account. Transmission type by itself is not a reliable determinant of mileage.

Methodology

Since the dataset (mtcars) is small the investigation is primarily grounded in background research and contextual reading with the statistical analysis serving to corroborate these findings. The regression modelling in particular is included to illustrate the techniques covered in the course rather than to claim high precision from the limited sample.

The dataset clearly shows manual car models generally have lower emissions than automatics. In order to better understand this relationship the following steps were taken (presented here in approximate chronological order):

Preparatory research: - Exploratory analysis of the source dataset mtcars was performed appendix 0. The summary shows that the dataset is not very large, totalling 32 cars, and that weight and displacement appear strongly correlated and good predictors of fuel economy. - The variance of available car types across the dataset was studied using principal component analysis appendix 1. - A study exploring available car types in 1970s North America was conducted appendix 2 using online research and prior knowledge, and a rule-based car classification scheme was defined to distinguish design types and aid the analysis. - Petrol engines and drive systems were reviewed appendix 3 to better inform analysis objectives, provide insight for building a predictive mpg model and serve as a basis for drawing meaningful conclusions in the main analysis. The research on torque converters was particularly illuminating.

Statistical analysis: - To determine which transmission type is more economical, the relationship between mpg and transmission type was investigated, adjusting for weight and number of gears. - Additionally, confounding effects were studied, including carburetors and final drive ratio. This helped inform the development of two predictive models quantifying the difference in mileage between manual and automatic transmission cars from the 1970s but ultimately the dataset proved to small to observe and test these effects supplemental. - Throughout the study, a causal model was hypothesised and developed with reference to the design features and performance of 1970s vehicles appendix 4.

Statistical Analyses (for credit)

Weight

automatic gearboxes are used in bigger, heavier less economic cars

Cars designed with automatic transmission have poorer mileage because automatic transmission is used on heavier cars while manual tends to be used on lighter more economical cars.

Mileage generally decreases more sharply with weight for manuals than for automatics however, the limited overlap between the two groups along with the influence of very economical and very heavy luxury cars does seems to exaggerate this effect.

muscle and mid-size sports cars have both low mpg and manual transmission

Here we are at (or far beyond) the limits of the data. Nevertheless, we can still glimps something which I do believe exists namely, within the midsized/muscle category we see cars with manual transmission having poorer mileage.

Automatics practical midsized cars (with a few exceptions) indicated by a high quarter mile time: \[\operatorname{qsec}_{auto}\sim N(18.32,3.82^2)\]
Manuals are more heavily punctuated with muscle and high performance sports cars with a 92% quarter mile time on average: \[\operatorname{qsec}_{stick}\sim N(16.83,3.20^2)\] (This design choice saved weight and made gear changes quicker and acceleration higher.)

This suggests that manuals are concentrated among higher performance cars, which explains why their fuel efficiency appears lower in this subset even when controlling for weight.

Gears

gears theoretically improve MPG however, the effect is largely confounded by vehicle weight and transmission type in this dataset

We pre-supposed that more gears provided better mileage however, in the mtcars dataset, the number of gears does not appear as a statistically significant predictor of fuel economy once weight and power-to-weight ratio are accounted for. However, the inclusion of gears reduces model variance, suggesting that gearing contributes meaningfully but collinearity limits its detectability in this sample. In this dataset, automatic cars have 3-4 gears and manuals 4–5, so any inference about higher numbers of gears requires extrapolation beyond the observed range. From an engineering perspective, additional gears (particularly overdrive) would be expected to improve fuel economy substantially, even if this effect is not fully captured in the available data.

Analysis of Variance Table

Response: mpg
          Df Sum Sq Mean Sq F value    Pr(>F)    
wt         1 847.73  847.73 99.8379 9.799e-11 ***
gear       1   1.14    1.14  0.1339    0.7172    
wt:gear    1  39.44   39.44  4.6445    0.0399 *  
Residuals 28 237.75    8.49                      
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

     wt    gear wt:gear 
37.2302 16.5908 24.7211

the interaction term makes the fit unstable but its inclusion accounts for the difference in gradient of the two transmission groups.

Predictive Modelling (for credit) ¹

A Simple Model

A Higher Bias, Lower Variance Model

MPG, weight, horsepower, and engine displacement all appear to be mutually collinear. Weight is the strongest predictor of MPG, reducing the residual sum of squares to the lowest value ($245.44$). This is already a strong model and, given the limited volume of data, it is the most transferable, although the prediction intervals are wide.

Note: These models are not nested, so formal ANOVA comparisons are not valid. The table simply illustrates the residual variance associated with each predictor individually.

Analysis of Variance Table

Model 1: mpg ~ hp + am
Model 2: mpg ~ wt + am
Model 3: mpg ~ disp + am
  Res.Df    RSS Df Sum of Sq F Pr(>F)
1     29 245.44                      
2     29 278.32  0   -32.880         
3     29 300.28  0   -21.962

summary(lm(mpg~wt+am,dt))


Call:
lm(formula = mpg ~ wt + am, data = dt)

Residuals:
    Min      1Q  Median      3Q     Max 
-4.5295 -2.3619 -0.1317  1.4025  6.8782 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) 37.32155    3.05464  12.218 5.84e-13 ***
wt          -5.35281    0.78824  -6.791 1.87e-07 ***
ammanual    -0.02362    1.54565  -0.015    0.988    
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 3.098 on 29 degrees of freedom
Multiple R-squared:  0.7528,    Adjusted R-squared:  0.7358 
F-statistic: 44.17 on 2 and 29 DF,  p-value: 1.579e-09

After adjusting for weight, the difference in predicted MPG between manual and automatic cars is negligible; prediction variance is very slightly higher for light automatics and lower for heavy automatics.

\[ \boxed{ \hat{\text{mpg}} = 37.322 - 5.353 \cdot \text{wt} - 0.024 \cdot \text{am} + \varepsilon} \] Where:

$\hat{\text{mpg}}$ is the predicted mileage (Miles/(US) gallon)
$\text{wt}$ is the weight of the car (1000 lbs)
$\text{am}$ is the (dummy coded) variable for transmission (1 = manual, 0 = automatic)
$\varepsilon$ is the residual error term

Better Models

A Lower Bias, Higher Variance Model

To attempt to explain more of the residual variance observed in the Simple Model, we construct a more complex model with additional predictors. This model aims to reduce bias at the expense of increased variance, recognising that with more terms, the prediction intervals may become less stable, especially given the limited dataset.

The rationale for the terms is as follows:

Weight was the strongest predictor of MPG, so we will use this as the principal predictor in the new model. Other terms are omitted because they are collinear with weight, and including them could destabilise the model. Weight primarily captures the main effect of a car’s “bulk” on fuel efficiency.
Power-to-weight ratio appears important as it reflects the energy and fuel consumption required to quickly accelerate the car, as well as its “sportiness”. This ratio is represented indirectly by the quarter-mile time (a measure of drag performance). Using this metric allows us to account for horsepower without including it directly which would cause collinearity issues.
Transmission Type Included to quantify the difference between manual and automatic after adjusting for weight and performance. This variable reflects both design philosophy (luxury and comfort vs. economy and sportiness) and mechanical differences (e.g., torque converter losses, gearbox weight, fewer gears in early automatics). It also acts as a proxy for correlated drivetrain covariates such as number of gears and rear axle ratio, which are not included directly to avoid collinearity.

An analysis of variance for the Big Model shows that weight remains the strongest predictor of MPG (F = 122.02, p < 0.001), while quarter-mile time (qsec) also contributes significantly (F = 11.93, p ≈ 0.0018), capturing additional variance related to power-to-weight. The number of carburetors (carb) does not provide a significant effect (F = 0.13, p ≈ 0.72). The residual sum of squares is 194.53, considerably lower than that of the Simple Model, indicating that the additional terms reduce unexplained variance. Variance inflation factors are all below 2.5, suggesting that multicollinearity is not a concern.

Analysis of Variance Table

Response: mpg
          Df Sum Sq Mean Sq  F value    Pr(>F)    
wt         1 847.73  847.73 140.2143 2.038e-12 ***
qsec       1  82.86   82.86  13.7048 0.0009286 ***
am         1  26.18   26.18   4.3298 0.0467155 *  
Residuals 28 169.29    6.05                       
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

      wt     qsec       am 
2.482952 1.364339 2.541437


Call:
lm(formula = mpg ~ wt + qsec + am, data = dt)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.4811 -1.5555 -0.7257  1.4110  4.6610 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   9.6178     6.9596   1.382 0.177915    
wt           -3.9165     0.7112  -5.507 6.95e-06 ***
qsec          1.2259     0.2887   4.247 0.000216 ***
ammanual      2.9358     1.4109   2.081 0.046716 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.459 on 28 degrees of freedom
Multiple R-squared:  0.8497,    Adjusted R-squared:  0.8336 
F-statistic: 52.75 on 3 and 28 DF,  p-value: 1.21e-11

\[ \boxed{\hat{\text{mpg}} = 9.618 - 3.917 \cdot \text{wt} + 1.226 \cdot \text{qsec} + 2.936 \cdot \text{am} + \varepsilon} \] Where:

$\hat{\text{mpg}}$ is the predicted mileage (Miles/(US) gallon)
$\text{wt}$ is the weight of the car (1000 lbs)
$\text{qsec}$ is the quarter-mile time² (seconds)
$\text{am}$ is the (dummy coded) variable for transmission (1 = manual, 0 = automatic)
$\varepsilon$ is the residual error term

Given the very limited size of the dataset, such inferences are inappropriate. An interesting avenue for future study would be to explore more sophisticated models using a larger dataset and to examine how transmission technologies evolved throughout the 1970s as fuel economy became a greater design consideration.

Conclusions (for credit)

“Is an automatic or manual transmission better for MPG””“

The torque converter in old automatic transmissions caused significant energy losses, making manual transmissions of the period more efficient.

This advantage is confounded by vehicle weight and performance orientation: heavier, bulkier cars were more likely to have automatic transmissions, whereas lighter, more economical cars were usually manual. Muscle cars and heavy sports cars are a notable exception.
The fluid coupling in the torque converter is a major source of inefficiency in automatics of the period. Our predictive mileage model provided only slight statistical evidence for this.

“Quantify the MPG difference between automatic and manual transmissions”

TBH The challenge of this exercise was to shoehorn regression techniques into an analysis that didn’t really require them and couldn’t fully justify them. Here’s the long and short of it…

[1] "We might infer the following from the `mtcars` training dataset:"

[1] "Average automatic mpg: 17"

[1] "Average manual mpg: 24"

[1] "Automatic transmissions have 70% of the mileage of manuals"

This difference is largely explained by vehicle weight; after adjusting for weight the transmission effect becomes negligible. This is supported by the statistical model that was built: \[\hat{\text{mpg}} = 37.322 - 5.353 \cdot \text{wt} - 0.024 \cdot \text{am} + \varepsilon\]
The dataset is small, so all inferences are drawn cautiously.

Supplemental Analyses (not for credit)

These studies were conducted to better understand fuel economy but ultimately led to dead ends and hypotheses that were not clearly supported by the limited dataset.

Carburetors

carburetors themselves are not a statistically significant predictor of fuel efficiency

The relationship between transmission type and mileage was examined while adjusting for the number of carburettors. We observe that the primary effect of transmission on mileage remains largely unchanged after this adjustment. Additionally, there is a negative correlation between mileage and the number of carburettors, indicating that cars with more carburettors tend to be less fuel-efficient. This aligns with the observation that more wasteful, bulkier or sportier vehicles typically use more carburettors. However, there are a few high-influence sports cars that deviate from this general trend.

my preconceived theory regarding carburettors wasting fuel is not evidenced

Analysis of Variance Table

Response: mpg
          Df Sum Sq Mean Sq  F value    Pr(>F)    
wt         1 847.73  847.73 133.8014 3.526e-12 ***
cyl        1  87.15   87.15  13.7554  0.000912 ***
carb       1  13.77   13.77   2.1738  0.151536    
Residuals 28 177.40    6.34                       

---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

      wt      cyl     carb 
2.581453 2.920519 1.385647

I noticed that the number of carburetors appears to affect mileage in the additive model mpg ~ wt + disp + carb. However, the variance inflation factors for weight and displacement were high indicating collinearity between the two. The number of carburetors does not appear to be overly associated with the bulk (PC1) score but it does contribute positively to the sportiness score. This aligns with our expectation that vehicles with more carburetors tend to be overpowered and less fuel-efficient (see qsec vs carb. When we model mpg with cylinders instead, we see that previously the number of carburettors was simply acting as a proxy for performance-oriented cars.

Final drive ratio

automatics are designed with lower final drive ratios as they tend to be bigger than automatics

Fuel efficiency tends to increase with the final drive ratio. This trend is likely because larger vehicles generally require more powerful engines and lower output-to-input gearing ratios:

Lower ratios help provide the additional torque needed for acceleration in heavier vehicles.
Lower gearing ratios also compensate for the lower engine RPMs, which are constrained by the larger centrifugal forces present in bigger engines.

These assumptions are supported by principal component analysis: vehicles with lower gearing ratios tend to score higher on bulkiness, suggesting a link between vehicle size, gearing, and engine characteristics.

Appendices (not for credit)

A0) `mtcars` overview (summary of correlations)

A1) Statistical variation in car design

To explore statistical variation in available car design in 1970’s USA we can look at how variance is distributed in the mtcars dataset using PCA. It reveals there are three orthogonal directions containing most of the variance; 60%, 24% and 6%.

Importance of components:
                          PC1    PC2     PC3     PC4     PC5     PC6    PC7
Standard deviation     2.5707 1.6280 0.79196 0.51923 0.47271 0.46000 0.3678
Proportion of Variance 0.6008 0.2409 0.05702 0.02451 0.02031 0.01924 0.0123
Cumulative Proportion  0.6008 0.8417 0.89873 0.92324 0.94356 0.96279 0.9751
                           PC8    PC9    PC10   PC11
Standard deviation     0.35057 0.2776 0.22811 0.1485
Proportion of Variance 0.01117 0.0070 0.00473 0.0020
Cumulative Proportion  0.98626 0.9933 0.99800 1.0000

Car bulkiness

The first principal component - the direction of greatest variance in the data is driven mainly by weight and engine size, with mileage (closely linked to engine size) and to a lesser extent the final drive ratio also contributing. This dimension approximates “bulk” i.e. large, heavy cars with powerful engines and poor mileage score high while smaller, lighter, more efficient cars score low.

#! echo: false
pc1_loadings <- pca_result$rotation[, 1]
filtered_pc1 <- pc1_loadings[abs(pc1_loadings) > 0.25]
filtered_pc1[order(-abs(filtered_pc1))]

    cyl.V1    disp.V1     mpg.V1      wt.V1      hp.V1      vs.V1    drat.V1 
 0.3739160  0.3681852 -0.3625305  0.3461033  0.3300569 -0.3065113 -0.2941514

bulk_scores <-pca_result$x[,1]

Car sportiness

The second principal component - the direction of greatest variance orthogonal to bulkiness lies in the direction of drag ability, transmission design (gears and type), the no. of carburettors and to a lesser extent the final drive ratio.

This second measure align the sportiness controlled for bulk. Cars with V-6 and V-8 instead of inline engines and slightly bigger power to weight ratios score higher in terms of sportiness than cars of similar bulk which do not.

#! echo: false
pc2_loadings <- pca_result$rotation[, 2]
filtered_pc2 <- pc2_loadings[abs(pc1_loadings) > 0.25]
filtered_pc2[order(-abs(filtered_pc2))]

    drat.V1       hp.V1       vs.V1       wt.V1     disp.V1      cyl.V1 
 0.27469408  0.24878402 -0.23164699 -0.14303825 -0.04932413  0.04374371 
     mpg.V1 
 0.01612440

sport_scores <-pca_result$x[,2]

A2) U.S. car type classification in 1970s

The dataset (mtcars) spans a wide variety of car types. I applied a basic ruleset to classify cars into distinct types. Classification boundaries are shown below, along with rough efficiency strata estimates³, the bulk direction in the hp ~ wt plane at the data mean (arrow indicating the principal component direction), and the actual sportiness measure for each car (point size).

Here’s the ruleset (in the spirit of the course, we could have identified these points as outliers, high-leverage or influential but I believe this approach is clearer and more transferable)…

getType <- function(hp, wt) {
  type <- rep("economy/compact", length(hp))
  type[wt > 3.0] <- "midsized/muscle"
  type[wt > 4.5] <- "luxury/superheavy"
  type[hp / wt > 60] <- "sports/muscle (hp)"
  return(as.factor(type))
}

sports/muscle (hp) (any car producing $60+$ hp per half-ton): Sports cars of the 1970s as today, tended to be light for manoeuvrability and speed while maintaining a high power-to-weight ratio. Even lower-powered roadsters such as the Lotus Europa were stripped down and very basic inside to maximise performance through a high power-to-weight ratio.
luxury/superheavy: any other car exceeding $4.5$ half-tons. This class is exemplified by the Cadillac - heavy steel-bodied cars with big-block V8s that prioritised comfort over performance, resulting in low power-to-weight ratios. They were purposfully built big and heavy with weight and long wheelbase allowing the car to glide over potholes.
midsized/muscle: any other car exceeding $3$ half-tons. Cars in this range are midsized saloon or two door cars fitted with big-block engines, creating the classic American muscle car. These vehicles were tuned for straight-line acceleration, emphasising horsepower and torque over handling or efficiency while still being practical enough to serve as everyday cars.
economy/compact: few small, economical cars were produced domestically so this category mostly consisted of European and Japanese imports. These cars were lightweight, fuel-efficient and designed for practicality with smaller engines and simple interiors.

A3) Engine and drive system effect on mileage

A car’s efficiency curve is convex due to two competing effects;

fuel consumption increases generally increases with power (speed)
power (speed) is useful output which increases efficiency

The mechanical efficiency of various drive system components detailed below:

Engine Efficiency: Fuel consumption increases with engine RPM

A four-stroke (Otto) cycle:

aspiration
compression
ignition/combustion (not a stroke)
expansion
exhaust

Ideally, engine RPM would match wheel RPM (avoiding gearbox losses) while still providing torque for acceleration in a lightweight, compact design. Engines use less fuel at lower RPM but face efficiency limits at idle. Lubrication relies on an oil sump where sloshing creates resistance and energy losses.

Note: engine power mtcars$hp is measured directly at the crank prior to any transmission losses (so called brake horsepower). Some discrepancies were noted regarding engine data were noted ⁴.

Carburettor Efficiency: carburettor reduce mileage

In the days before fuel injection, engines drew air through a carburettor where it was mixed with fuel. The air-fuel ratio was determined by airflow (via the Bernoulli principle) and by prior tuning. For cold starts, a choke allowed the driver to temporarily enrich the mixture.

An enriched mixture made starting easier but reduced fuel economy. Sometimes unburned fuel would ignite in the hot exhaust, causing the familiar backfire of older cars. A lean mixture on the other hand, could make the engine stall or cause sluggish throttle response. Striking the right balance was always a challenge, especially in engines with multiple carburettors which tended to favour performance and enrichment over efficiency.

Transmission Efficiency:

Gearboxes introduce mechanical losses. In top gear, the ratio is typically close to 1:1, so the crankshaft and driveshaft turn in unison, matching engine and wheel RPM. Lower gears provide torque for acceleration, while higher gears enable efficient cruising.

Fuel consumption decreases with number of gears

Progressing sequentially through the gears allows the car to reach cruising speed quickly while keeping the engine near its optimal RPM. Too low a gear wastes fuel by over-revving; too high a gear lacks torque, slows acceleration and may even stall the engine. More gears provide finer steps improving efficiency and fuel economy.

automatics of the 1970s were less efficient than manuals

In the 1970s, manual gear changes were more efficient than automatics, which were heavy, mechanically complex, and relied on inefficient clutch designs. Modern electronic control has largely eliminated this disadvantage.

Torque Converter Losses and Transmission Efficiency

See: (CARinfo3d, 2025), (Wikipedia contributors, 2025).

Automatic transmissions in 1970s cars typically used torque converters, a fluid coupling that allows the engine to rotate independently of the gearbox.

Hydraulically controlled clutches within the gearbox engaged different gears based on vehicle speed, while the torque converter accommodated the sudden mismatch in RPM between the engine and the gearbox, bringing them smoothly back into synchronisation.

The torque converter’s allowance for slip, combined with its hydrodynamic design, dissipates energy as heat and reduces fuel efficiency.

In contrast, manual transmissions provide a direct mechanical connection via a clutch, minimising energy loss.

Differential Efficiency: lower final drive ratio increases efficiency

rear differential mockup illustrating mechanism

The rear axle ratio is the gearing between the transmission output and the average rear wheels with a higher ratio meaning more engine turns per wheel rotation. In top gear the gearbox ratio is typically close to 1:1 so the rear axle (aka final drive) ratio defines the overall gearing at cruising speed.

\[\boxed{\operatorname{drat}=\frac{\text{no. ring gear (output) teeth}}{\text{no. pinion (input) teeth}}}\]

In the mockup the gearing ratio between there worm gear and the gear on the outside of the differential housing determines the final gearing ratio ⁵.

A4) Proposed Caual Relationship Between Variables {a4}

flowchart LR
  CarSpec[<i>Confounder</i>:<br>Market Specification]
  DesignWeight[<i>Confounder</i>:<br>Design Weight]
  HP[<i>Confounder</i>:<br>Power Requirements - HP]
  Engine[<i>Confounder</i>:<br>Engine - Alignment and Displacement]
  Carburettors[<i>Confounder</i>:<br>Carburettors]
  FinalDriveRatio[<i>Confounder</i>:<br>Final Drive Ratio]
  subgraph CausalPathway [<b><i>The Causal Pathway</i></b>]
    direction LR
    Transmission[<b>Exposure</b>:<br>Transmission<br>Manual/Automatic]
    Gears[<i>Mediator</i>:<br>Number of Gears]
    MPG[<b>Output</b>:<br>MPG]
  end
  
  %% Big heavy cars improve ride features, weight reduced for sport
  CarSpec -->|<i>Luxury</i>: more features, better ride<br><i>Sport</i>: high power to weight ratio| DesignWeight
  %% Size determines Power requirements
  DesignWeight -->|power requirements| HP
  %% Power is desirable for sports
  CarSpec -->|<i>Sport</i>: high power to weight ratio| HP
  %% Large engines me hp demands and increase MPG
  HP -->|power requirements| Engine --> MPG
  %% Carboretors meet hp demands and increase MPG
  HP -->|power requirements| Carburettors --> MPG
  Engine --> Carburettors --> MPG
  %% Automatics for luxury, manuals for economy and  sport
  CarSpec -->|<i>Luxury</i>: automatic<br><i>Sport</i>: manual| Transmission
  %% automatics less gears worse mileage
  Transmission --> Gears -->|efficient engine operation| MPG
  %% Bigger engine - lower rpm - more gearing
  Engine -->|optimal RPM| FinalDriveRatio --> MPG
  %% Bigger car - more gearing for top gear acceleration
  DesignWeight -->|torque requirements?| FinalDriveRatio

References

CARinfo3d. (2025). Torque converter - how does it work? (3D animation). https://www.youtube.com/watch?v=3iwkgLxxGyM.

DATAtab. (2025). ANCOVA (analysis of covariance): A mix of ANOVA and···. https://www.youtube.com/watch?v=PngndHgZOgY.

Kmiec, P. (2016). The unofficial LEGO technic builder’s guide, 2nd edition. No Starch Press. https://www.nostarch.com/technicbuilder2

McCabe, D. (2025a). ANOVA workflows. R Pubs. https://rpubs.com/mccabe08/1303319

McCabe, D. (2025b). Regression i: Practical linear multivariable regression. R Pubs. https://rpubs.com/mccabe08/1335788

Peng, R. D. (2015). Regression models. Johns Hopkins University; Coursera. https://www.coursera.org/learn/regression-models/home/module/4

Wikipedia contributors. (2025). Torque converter — wikipedia, the free encyclopedia. https://en.wikipedia.org/wiki/Torque_converter.

Footnotes

Although the dataset is relatively small and this approach may be questionable I am obliged to explore several models given that this is an assignment for a regression modelling course.↩︎
Interestingly, MPG increases with quarter mile time, suggesting that this covariate captures fuel economy rather than sportiness as originally intended - unsurprising since cars are rarely driven at maximum acceleration in everyday use.↩︎
Predicted efficiency strata were calculated using a simple multivariable regression model (mpg ~ hp * wt * disp). I acknowledge that both these predicted strata and the car type decision boundaries are highly dataset-specific and somewhat subjective. The coplanar nature of the predictors makes the model fit extremely unstable, and the large number of parameters leaves few residual degrees of freedom. I include this model here mainly as a note: introducing interaction terms means the response surface is no longer a flat plane, and taking a lower-dimensional cross-section (as I have done) produces non-linear contours that illustrate how efficiency varies across combinations of power, weight, and displacement.↩︎
Both Mazda RX-4 cars in the dataset are incorrectly recorded as having V-shaped engines - they famously are in fact Wankel rotary engines. The Mercedes 240D uses a diesel engine.↩︎
The lego differential mockup serves to show function not the precice mechanism found in cars. Five small gears are housed inside the rotating casing with one external gear. The two small opposing coaxial lateral gears act as ring gears dribing the rear left and right axle while the other three act as the would-be pinion gear. The gearing ratio inside the housing is 1:1 since the internal gears are all identical. The gearing ratio of the whole assembly is decided by ratio between the external gear and the gear which drives it.↩︎