Transmission Type and Fuel Economy: An
Analysis of the mtcars Data
Author: Sonja Sahebzad
September 15, 2026
Executive summary
In the mtcars sample, manual-transmission cars had an
average fuel economy that was 7.24 MPG higher than that
of automatic cars before adjustment. Because the two groups also
differed in weight and performance, several regression models were
compared. Backward AIC selection retained transmission, weight, and
quarter-mile time. After adjustment, manual transmission was associated
with 2.94 additional MPG for cars with the same weight
and quarter-mile time (95% CI 0.05 to 5.83 MPG;
p = 0.047). Manual transmission therefore
appears better for MPG in this sample, although the estimate is
uncertain and the observational data cannot establish a causal
effect.
Data and exploratory analysis
The mtcars data set contains 32 automobiles from the
1973–1974 model year: 19 automatic and 13 manual cars. Fuel economy,
measured in miles per gallon (mpg), is the outcome, and
transmission type (am) is coded as automatic or manual.
Manual cars average 24.39 MPG, compared with 17.15 MPG for automatic
cars, giving an unadjusted difference of 7.24 MPG. The scatterplot shows
that MPG generally decreases as weight increases and that manual cars
tend to be lighter. Weight may therefore confound the observed
relationship, so regression adjustment is needed before attributing the
entire difference to transmission type.
Fuel economy by transmission
| Automatic |
19 |
17.15 |
3.83 |
| Manual |
13 |
24.39 |
6.17 |
Modeling strategy
Several candidate regression models were fitted to separate the
association between transmission and MPG from differences in other
vehicle characteristics. The first model estimated the unadjusted
transmission difference. The second added weight (wt),
which appeared to be an important confounder in the exploratory
analysis. A prespecified candidate model also included horsepower
(hp) and quarter-mile time (qsec) as
performance measures. Finally, a full model containing all available
vehicle characteristics was reduced using backward AIC selection. Lower
AIC values indicate a better balance between model fit and complexity.
Backward selection retained transmission, weight, and quarter-mile time
(mpg ~ transmission + wt + qsec). The selected model had
the lowest AIC among the reported models and remained straightforward to
interpret. Because model selection and inference used the same small
data set, the confidence intervals and p-values should be interpreted
cautiously.
Candidate model comparison
| Unadjusted |
transmission |
196.5 |
0.338 |
| Weight adjusted |
transmission + wt |
168.0 |
0.736 |
| Prespecified candidate |
transmission + wt + hp + qsec |
154.3 |
0.837 |
| AIC-selected |
transmission + wt + qsec |
154.1 |
0.834 |
Answers and coefficient interpretation
The raw manual-versus-automatic estimate was 7.24
MPG (95% CI 3.64 to 10.85). The selected
regression equation is:
Estimated MPG = 9.62 - 3.92(Weight) + 1.23(Quarter-mile time)
+ 2.94(Manual).
1. Is an automatic or manual transmission better for
MPG? Manual transmission is associated with better MPG in this
sample. Holding weight and quarter-mile time constant, changing the
indicator from automatic to manual corresponds to an expected
2.94-MPG increase.
2. What is the MPG difference? The unadjusted
difference is 7.24 MPG. After adjustment, the estimated
difference is 2.94 MPG (95% CI 0.05 to 5.83
MPG, p = 0.047). The interval barely
excludes zero, so the evidence is modest. Each additional 1,000 lb is
associated with 3.92 fewer MPG, while each additional second in
quarter-mile time is associated with 1.23 more MPG, with the other model
terms held constant.
Discussion
Vehicle weight explains a substantial part of the raw transmission
difference. The diagnostic plots in the appendix show mild curvature and
increasing spread, while the Q-Q plot is reasonably close to normal. No
observation has Cook’s distance above 1, although several cars merit
attention. The sample contains only 32 older cars, and other design
differences may remain. The result describes an association and does not
establish that changing transmission type causes better fuel
economy.
Conclusion
For the cars in the mtcars data set, manual transmission is
associated with better fuel economy than automatic transmission. Manual
cars average 7.24 more MPG before adjustment. After holding weight and
quarter-mile time constant, manual transmission is associated with an
estimated 2.94-MPG advantage (95% CI 0.05 to 5.83 MPG). Therefore,
manual transmission appears better for MPG in this sample, although the
adjusted evidence is modest and the observational data do not establish
a causal effect.
Reproducibility
All estimates, tables and figures are generated from R’s built-in
mtcars data when this R Markdown file is knitted. The
complete code is contained in its executable chunks; the main model code
is shown below. No random simulation is used, and
sessionInfo.txt is written during knitting.
data(mtcars, package = "datasets")
cars <- transform(mtcars,
transmission = factor(am, c(0, 1), c("Automatic", "Manual")))
m_unadjusted <- lm(mpg ~ transmission, data = cars)
m_weight <- lm(mpg ~ transmission + wt, data = cars)
m_candidate <- lm(mpg ~ transmission + wt + hp + qsec, data = cars)
m_full <- lm(mpg ~ transmission + cyl + disp + hp + drat + wt +
qsec + vs + gear + carb, data = cars)
m_selected <- MASS::stepAIC(m_full, direction = "backward", trace = FALSE)
coef(summary(m_selected)); confint(m_selected)
References
Henderson, H. V., & Velleman, P. F. (1981). Building multiple
regression models interactively. Biometrics, 37, 391-411.
R Core Team (2026). R: A Language and Environment for Statistical
Computing. R Foundation for Statistical Computing, Vienna,
Austria.
Venables, W. N., & Ripley, B. D. (2002). Modern Applied
Statistics with S (4th ed.). Springer.
