Why This Topic?

  • Goal: predict the probability a car has a manual transmission using logistic regression.
  • Dataset: mtcars, augmented with labels to mimic fleet planning.
  • Audience: a car‑sharing startup choosing models balancing performance and economy.

Data Snapshot

model mpg wt hp transmission efficient
Mazda RX4 21.0 2.620 110 Manual Inefficient
Mazda RX4 Wag 21.0 2.875 110 Manual Inefficient
Datsun 710 22.8 2.320 93 Manual Efficient
Hornet 4 Drive 21.4 3.215 110 Automatic Inefficient
Hornet Sportabout 18.7 3.440 175 Automatic Inefficient
Valiant 18.1 3.460 105 Automatic Inefficient

Logistic Model

We model \(p_i = \Pr(\text{Manual}_i = 1)\) with a logit link:

\[ \text{logit}(p_i) = \log\!\left(\frac{p_i}{1-p_i}\right) = \beta_0 + \beta_1\,\text{wt}_i + \beta_2\,\text{hp}_i . \]

Interpretation at the margin:

  • \(e^{\beta_1}\): multiplicative change in the odds of Manual for each +1000 lbs of weight.
  • \(e^{\beta_2}\): multiplicative change in the odds of Manual for each +1 hp.

Fit the Model (code)

glm_fit <- glm(am ~ wt + hp, data = mtcars, family = binomial())
summary(glm_fit)$coefficients
##               Estimate Std. Error   z value    Pr(>|z|)
## (Intercept) 18.8662987 7.44355806  2.534581 0.011258199
## wt          -8.0834752 3.06867511 -2.634191 0.008433813
## hp           0.0362556 0.01773415  2.044394 0.040914646

Weight vs Transmission (ggplot)

Horsepower Density (ggplot)

3D Efficiency Explorer (plotly)

Coefficients → Odds Ratios

Term Estimate Odds Ratio Std. Error Z p-value
(Intercept) 18.866 1.561455e+08 7.444 2.535 0.011
wt -8.083 0.000000e+00 3.069 -2.634 0.008
hp 0.036 1.037000e+00 0.018 2.044 0.041

Takeaways

  • Favor lighter vehicles; weight strongly reduces the odds of a manual gearbox.
  • Manuals skew to higher hp configurations—consider marketing to enthusiasts.
  • Next: add telematics/road‑type and cost data to the model for operational decisions.