Executive summary

In the 32-car mtcars data, manual-transmission cars have higher observed fuel economy than automatic cars: 24.39 versus 17.15 MPG, a raw difference of 7.24 MPG. A Welch two-sample t-test estimates a 95% confidence interval of 3.21 to 11.28 MPG for manual minus automatic, with p = 0.00137.

That raw comparison does not account for differences in vehicle design. After adjusting for weight and horsepower, the estimated manual-transmission difference is smaller and statistically uncertain. Adding quarter-mile time yields a manual coefficient of 2.93 MPG (95% CI 0.06 to 5.79; p = 0.0458). This final estimate is borderline and sensitive to model specification. The data favor higher MPG among manual cars descriptively, but do not establish a large, model-independent causal benefit from transmission type.

Exploratory analysis

The dataset contains 32 automobiles: 19 automatic and 13 manual. Mean MPG and variability by transmission are:

Fuel economy by transmission type
Transmission n Mean_MPG SD_MPG
Automatic 19 17.15 3.83
Manual 13 24.39 6.17
MPG by transmission and the relationship between MPG and vehicle weight.

MPG by transmission and the relationship between MPG and vehicle weight.

The boxplot shows a higher MPG distribution for manuals, but the scatterplot also shows that heavier cars tend to have lower MPG. Transmission type is associated with other vehicle characteristics, so a raw comparison can confound transmission with the types of cars equipped with each transmission.

Models and selection strategy

I compared three nested linear models. M0 is the unadjusted transmission comparison. M1 adds weight (wt) and horsepower (hp), two plausible predictors of fuel use. M2 adds quarter-mile time (qsec) as a rough performance-related covariate. With only 32 observations, I kept the model compact and did not search over every variable in mtcars. I compared adjusted R-squared and AIC, while also checking whether the transmission estimate changed materially.

Candidate model fit
Model Predictors Adjusted_R2 AIC
M0: transmission only Transmission 0.338 196.48
M1: + weight and horsepower Transmission, weight, horsepower 0.823 156.13
M2: + 1/4-mile time Transmission, weight, horsepower, 1/4-mile time 0.837 154.33
Estimated transmission coefficient across models
Model Manual minus automatic (MPG) 95% confidence interval p-value
M0: transmission only 7.24 3.64 to 10.85 0.000285
M1: + weight and horsepower 2.08 -0.74 to 4.90 0.141268
M2: + 1/4-mile time 2.93 0.06 to 5.79 0.045791

M2 has the lowest AIC among these candidates (AIC 154.33), so it is used as the primary adjusted model. Against the same weight/horsepower/quarter-mile controls, adding transmission improves fit only modestly (nested-model comparison p = 0.0458). AIC differences are not decisive evidence by themselves, and the small sample makes selection uncertain.

Answers to the questions

1. Is an automatic or manual transmission better for MPG? In these data, manual cars have higher observed MPG on average. The unadjusted difference is clear statistically. However, once weight and horsepower are held constant, the estimated difference falls to 2.08 MPG (95% CI -0.74 to 4.90). With quarter-mile time included, the estimate is 2.93 MPG. The adjusted conclusion is therefore less certain than the raw averages suggest.

2. How large is the MPG difference? The descriptive manual-minus-automatic difference is 7.24 MPG (Welch 95% CI 3.21 to 11.28). In the selected adjusted model, the conditional difference is 2.93 MPG (95% CI 0.06 to 5.79). The first figure is an observed group difference; the second compares cars with the same modeled weight, horsepower and quarter-mile time. Neither should be interpreted as a causal effect because this is an observational sample, not a randomized experiment.

Limitations

mtcars is a small historical dataset, not a representative sample of modern vehicles. Several predictors are correlated, and the adjusted transmission coefficient is sensitive to which covariates are included. Confidence intervals reflect model assumptions and sampling variability, not all possible sources of bias. The findings are descriptive and should not be generalized to all cars.

Appendix: model diagnostics

The following standard diagnostic plots are provided for M2. Inspect the residual-versus-fitted plot for curvature or changing variance, the Q-Q plot for substantial tail departures, the scale-location plot for non-constant spread, and the residuals-versus-leverage plot for influential cars. With 32 observations, any high-leverage point can have a noticeable effect, so diagnostics should temper confidence in the adjusted estimate.

Standard linear-model diagnostics for M2: mpg ~ transmission + wt + hp + qsec.

Standard linear-model diagnostics for M2: mpg ~ transmission + wt + hp + qsec.

Three largest Cook’s distances in the selected model
Car Cook_Distance
Chrysler Imperial 0.270
Toyota Corolla 0.154
Fiat 128 0.117

Reproducibility

All analyses use R’s built-in mtcars dataset and standard linear-model functions. To reproduce the report, open this .Rmd file in RStudio and select Knit. The document uses knitr and ggplot2 is not required; the exploratory and diagnostic graphics use base R.