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Auto Dataset Analysis

This notebook analyzes the Auto dataset to investigate how vehicle characteristics relate to fuel efficiency (mpg).
We apply simple linear regression (Q8) and multiple linear regression (Q9), including diagnostic plots and transformations.

import pandas as pd
import statsmodels.api as sm
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np

# Load Auto.csv (make sure it's in the same folder)
auto = pd.read_csv("/assets/Auto/Auto.csv")

# Convert columns to numeric if necessary
auto['horsepower'] = pd.to_numeric(auto['horsepower'], errors='coerce')
auto = auto.dropna()  # drop rows with missing values

auto.head()

	mpg	cylinders	displacement	horsepower	weight	acceleration	year	origin	name
0	18.0	8	307.0	130.0	3504	12.0	70	1	chevrolet chevelle malibu
1	15.0	8	350.0	165.0	3693	11.5	70	1	buick skylark 320
2	18.0	8	318.0	150.0	3436	11.0	70	1	plymouth satellite
3	16.0	8	304.0	150.0	3433	12.0	70	1	amc rebel sst
4	17.0	8	302.0	140.0	3449	10.5	70	1	ford torino

Question 8 — Simple Linear Regression

We model mpg as the response and horsepower as the predictor.

# Simple linear regression
X = sm.add_constant(auto["horsepower"])
y = auto["mpg"]

model_simple = sm.OLS(y, X).fit()
model_simple.summary()

OLS Regression Results

Dep. Variable:	mpg	R-squared:	0.606
Model:	OLS	Adj. R-squared:	0.605
Method:	Least Squares	F-statistic:	599.7
Date:	Fri, 21 Nov 2025	Prob (F-statistic):	7.03e-81
Time:	10:22:31	Log-Likelihood:	-1178.7
No. Observations:	392	AIC:	2361.
Df Residuals:	390	BIC:	2369.
Df Model:	1
Covariance Type:	nonrobust

	coef	std err	t	P>|t|	[0.025	0.975]
const	39.9359	0.717	55.660	0.000	38.525	41.347
horsepower	-0.1578	0.006	-24.489	0.000	-0.171	-0.145

Omnibus:	16.432	Durbin-Watson:	0.920
Prob(Omnibus):	0.000	Jarque-Bera (JB):	17.305
Skew:	0.492	Prob(JB):	0.000175
Kurtosis:	3.299	Cond. No.	322.

Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.

Interpretation

• Relationship: Strong negative relationship — higher horsepower → lower mpg.
• Strength: R² ~0.60 → 60% of mpg variation explained by horsepower.
• Prediction: For horsepower = 98, see below.

new_value = pd.DataFrame({"const":[1], "horsepower":[98]})
pred_simple = model_simple.get_prediction(new_value).summary_frame(alpha=0.05)
pred_simple

	mean	mean_se	mean_ci_lower	mean_ci_upper	obs_ci_lower	obs_ci_upper
0	24.467077	0.251262	23.973079	24.961075	14.809396	34.124758

Scatter Plot with Regression Line

fig, ax = plt.subplots(figsize=(10,6))
ax.scatter(auto["horsepower"], auto["mpg"], s=20, alpha=0.7)
ax.plot(auto["horsepower"], model_simple.predict(X), color='red')
ax.set_xlabel("Horsepower")
ax.set_ylabel("MPG")
ax.set_title("MPG vs Horsepower with Regression Line")
plt.show()

Diagnostic Plots for Simple Regression

fig = plt.figure(figsize=(12,10))
sm.graphics.plot_regress_exog(model_simple, "horsepower", fig=fig)
plt.show()

Question 9 — Multiple Linear Regression

We now include all other variables (except name) to predict mpg.
We also explore correlations, interactions, and transformations.

# Convert horsepower to numeric (some values may be '?')
auto['horsepower'] = pd.to_numeric(auto['horsepower'], errors='coerce')

# Drop rows with missing values
auto = auto.dropna()

# Create numeric-only dataframe (drop 'name' column)
auto_numeric = auto.drop(columns=['name'])

# Select key variables for scatterplot matrix
subset = ["mpg", "horsepower", "weight", "year"]

# Create the scatterplot matrix
sns.pairplot(auto_numeric[subset], height=2.5)
plt.suptitle("Scatterplot Matrix: Key Predictors vs MPG", y=1.02)
plt.show()

Multiple Linear Regression

# Multiple regression
X_multi = auto_numeric.drop(columns=['mpg'])
X_multi = sm.add_constant(X_multi)
y_multi = auto_numeric['mpg']

model_multi = sm.OLS(y_multi, X_multi).fit()
model_multi.summary()

Interpretation of Multiple Regression

• Relationship: The overall F-test and p-values indicate that predictors collectively explain mpg.
• Significant predictors: Weight, horsepower, year, etc. (check p-values < 0.05).
• Coefficient of year: Positive → newer cars tend to have higher mpg, all else equal.

# Diagnostic plots for multiple regression
fig = plt.figure(figsize=(12,10))
sm.graphics.plot_regress_exog(model_multi, "weight", fig=fig)
plt.show()

Interactions & Transformations

We can try interactions (e.g., horsepower*weight) or transformations (log, sqrt, squared) to improve the model.
Check p-values for significance and whether plots look better.

# Example: interaction between horsepower and weight
X_inter = auto_numeric.copy()
X_inter['hp_weight'] = X_inter['horsepower'] * X_inter['weight']
X_inter = sm.add_constant(X_inter.drop(columns=['mpg']))
y_inter = auto_numeric['mpg']

model_inter = sm.OLS(y_inter, X_inter).fit()
model_inter.summary()

Example Transformation

• Try log or squared transformations to see if model fit improves:
• log(horsepower), sqrt(weight), weight^2, etc.

X_trans = auto_numeric.copy()
X_trans['log_horsepower'] = np.log(X_trans['horsepower'])
X_trans['weight_squared'] = X_trans['weight'] ** 2

X_trans = sm.add_constant(X_trans.drop(columns=['mpg']))
y_trans = auto_numeric['mpg']

model_trans = sm.OLS(y_trans, X_trans).fit()
model_trans.summary()

Conclusion

• Simple regression: mpg decreases as horsepower increases.
• Multiple regression: multiple variables (weight, year, horsepower) significantly affect mpg.
• Interactions & transformations: can improve model fit, but must be interpreted carefully.
• Diagnostics: always check residuals, leverage, and spread to ensure reliable predictions.

Reflective Summary

Working through this analysis helped me understand how vehicle characteristics like horsepower, weight, and year influence fuel efficiency. I learned how to interpret regression coefficients, evaluate model fit using diagnostic plots, and explore improvements through interactions and transformations. This project also strengthened my skills in presenting data analysis clearly in a professional blog format.