Moderation Test: Fuel Type (Gasoline vs. Diesel) on Engine Size

[hikmetmodule4]

Code

```

import pandas as pd

import numpy as np

import statsmodels.formula.api as smf

# 1) Load

df = pd.read_csv("vehicles.csv", low_memory=False)

# 2) Keep needed columns and coerce numeric

df = df[["displ", "highway08", "fuelType"]].copy()

df["displ"] = pd.to_numeric(df["displ"], errors="coerce")

df["highway08"] = pd.to_numeric(df["highway08"], errors="coerce")

# 3) Normalize fuel labels and restrict to Gasoline vs Diesel

def norm_fuel(s):

    s = str(s).lower()

    if "diesel" in s: return "Diesel"

    if "gasoline" in s or "premium" in s or "regular" in s: return "Gasoline"

    return np.nan

df["fuel2"] = df["fuelType"].apply(norm_fuel)

df = df.dropna(subset=["displ", "highway08", "fuel2"])

df = df[df["fuel2"].isin(["Gasoline", "Diesel"])].copy()

# 4) Center X (optional but helpful)

df["displ_c"] = df["displ"] - df["displ"].mean()

# 5) OLS with interaction (the formula must be a STRING)

# Baseline is 'Diesel' or 'Gasoline' depending on category order;

# to force baseline, you can re-order the category levels as needed.

df["fuel2"] = pd.Categorical(df["fuel2"], categories=["Gasoline", "Diesel"])

model = smf.ols(formula="highway08 ~ displ_c * C(fuel2)", data=df).fit()

print(model.summary())

# 6) Simple slopes (MPG change per +1L displacement) for each fuel type

b = model.params

# With 'Gasoline' as baseline:

slope_gasoline = b["displ_c"]

slope_diesel   = b["displ_c"] + b.get("displ_c:C(fuel2)[T.Diesel]", 0.0)

print("\nSimple slopes (MPG change per +1L displacement):")

print(f"Gasoline: {slope_gasoline:.3f} MPG per liter")

print(f"Diesel:   {slope_diesel:.3f} MPG per liter") ```

[hikmetmodule4]

Results

```

OLS Regression Results ============================================================================== Dep. Variable: highway08 R-squared: 0.516 Model: OLS Adj. R-squared: 0.516 Method: Least Squares F-statistic: 1.704e+04 Date: Wed, 31 Dec 2025 Prob (F-statistic): 0.00 Time: 01:02:56 Log-Likelihood: -1.3758e+05 No. Observations: 47982 AIC: 2.752e+05 Df Residuals: 47978 BIC: 2.752e+05 Df Model: 3 Covariance Type: nonrobust ============================================================================================== coef std err t P>|t| [0.025 0.975] ---------------------------------------------------------------------------------------------- Intercept 24.4590 0.020 1241.266 0.000 24.420 24.498 C(fuel2)[T.Diesel] 5.4961 0.125 43.815 0.000 5.250 5.742 displ_c -3.2444 0.015 -217.958 0.000 -3.274 -3.215 displ_c:C(fuel2)[T.Diesel] -0.1426 0.066 -2.175 0.030 -0.271 -0.014 ============================================================================== Omnibus: 7416.957 Durbin-Watson: 0.998 Prob(Omnibus): 0.000 Jarque-Bera (JB): 23746.133 Skew: 0.796 Prob(JB): 0.00 Kurtosis: 6.057 Cond. No. 8.84 ============================================================================== Notes: [1] Standard Errors assume that the covariance matrix of the errors is correctly specified. Simple slopes (MPG change per +1L displacement): Gasoline: -3.244 MPG per liter Diesel: -3.387 MPG per liter

```

[hikmetmodule4]

[hikmetmodule4]

[hikmetmodule4]

what is this?

Engine displacement is negatively related to highway MPG (larger engines → lower MPG). The fuel type moderates this relationship: the MPG drop per additional liter of displacement differs between Gasoline and Diesel. In my run, the Gasoline slope was ≈ –3.25 MPG per liter, and the Diesel slope was ≈ –3.39 MPG per liter (interaction term significant), confirming moderation by fuel type. At the mean engine size, Diesel vehicles show a higher MPG level than Gasoline, but both lose MPG as displacement increases.

Based on the FuelEconomy.gov dataset, Diesel vehicles show higher highway MPG than Gasoline at comparable engine sizes, meaning Diesel is more fuel‑efficient in this sample.

[hikmetmodule4]

Moderation Test: Fuel Type (Gasoline vs. Diesel) on Engine Size → Highway MPG

Data: FuelEconomy.gov vehicles table (1984–current). Columns used: displ (engine liters), highway08 (highway MPG), fuelType (fuel category). The dataset and field definitions are publicly documented on Download Fuel Economy Data, and detailed field descriptions (including displ, highway08, and fuelType) are available via the vehicle fields list. Sources: FuelEconomy.gov Download page; Vehicle fields documentation.