Due Date: March 31, 2025 (by noon)
Submission Format: PDF report + GRETL file (.gretl)

Objective

This assignment applies multiple regression techniques to analyze how distance to the nearest college affects years of completed education, while controlling for student characteristics, family background, and local labor market conditions.

You will:
✔ Compare simple vs. multiple regression results
✔ Test for omitted variable bias
✔ Conduct t-tests and F-tests for statistical significance
✔ Make predictions using regression results

All exercises must be performed in GRETL.

Dataset Description

The College Distance dataset comes from the High School and Beyond Survey (1980) and includes variables on educational attainment, demographics, family background, and local economic conditions.

Key Variables

Variable Description
ed Years of education completed (dependent variable)
dist Distance to nearest 4-year college (in 10s of miles)
bytest Base year composite test score (standardized)
female 1 = Female, 0 = Male
black 1 = Black, 0 = Not Black
hispanic 1 = Hispanic, 0 = Not Hispanic
incomchi 1 = Family income > 25k, 0 = ≤ 25k
ownhome 1 = Family owns home, 0 = Does not own home
dadooll 1 = Father is college graduate, 0 = Not college graduate
cue80 County unemployment rate (1980)
stwmfg80 State hourly manufacturing wage (1980)

Questions

Part 1: Basic Regression Analysis

  1. Run a simple regression of ed on dist:
    • Report the slope coefficient and interpret its meaning.
    • Perform a t-test for the significance of dist (state H₀, t-statistic, p-value, and conclusion at α=0.05).
  2. What is the R² of this regression? What does it tell us about the relationship?

Part 2: Multiple Regression Analysis

  1. Run a multiple regression of ed on:
    dist, bytest, female, black, hispanic, incomchi, ownhome, dadooll, cue80, stwmfg80.

  2. Compare the coefficient on dist from the multiple regression to the simple regression:

    • Has the magnitude changed?
    • What does this suggest about omitted variable bias in the simple regression?

  3. For each coefficient in your multiple regression (except the intercept):

    1. Perform a t-test of significance (α = 0.05):
      • State the null hypothesis (H₀: βⱼ = 0).
      • Report the t-statistic and p-value.
      • Conclusion: Is the variable statistically significant?
    2. Interpret the magnitude and meaning of the coefficient:
      • If the variable is significant, explain its effect on years of education.
      • If insignificant, discuss why it might not matter in this model.
        Example:
    • Variable: dadooll (Father is a college graduate)
      • H₀: “Having a college-educated father does not affect a student’s years of education.”
      • Result: t = 3.2, p = 0.001 → Reject H₀ (significant at 5%).
      • Interpretation: Students with college-educated fathers complete, on average, 0.8 more years of education (holding other factors constant).

Part 3: Hypothesis Testing

  1. F-test for joint significance of additional controls:
    • Restricted model: ed = β₀ + β₁dist + β₂bytest + u
    • Unrestricted model: Full model from Part 2
    • State H₀ (all added coefficients = 0)
    • Calculate F-statistic using R² values
    • Conclusion: Are the extra variables jointly significant?
  2. Test parental education variables (dadooll and momcoll):
    • Run a model excluding both dadooll and momcoll.
    • Perform an F-test vs. the full model.
    • Interpret: Do parental education variables matter?

Part 4: Prediction Exercise

  1. Predict education years for:
    • Student A: Black male, bytest=58, incomchi=1, ownhome=1, dadooll=0, cue80=7.5, stwmfg80=9.75, dist=2 (20 miles).
    • Student B: Same as A, but dist=4 (40 miles).
    • Calculate the difference in predicted education.

Submission Instructions

✔ GRETL file (.gretl) containing all regression models.
✔ PDF report with:
- Regression tables
- Hypothesis test results (t-tests & F-tests)
- Interpretations of coefficients and predictions
✔ Due: March 31, 2025 (noon).

Late submissions will not be accepted.

Good luck!