Advanced Statistics

Homework 4: Multiple Regression
1) House prices
The dataset house represents data on 239 recently sold houses including the selling price (in thousands of dollars), the surface of the

house (in square feet), the distance to the city center (in miles), the age of the house in years, and the median annual household income

in the neighborhood (in thousands of dollars). Develop a regression model that can help potential home sellers figure out how much they

might get for their house based on the other variables in the dataset.
a) Write a linear regression model to explain house prices as a function of the other variables.
b) What are the hypothetical signs for your coefficients
c) Estimate your regression equation using gretl.
d) Are all the coefficients significant? Drops the insignificant coefficients and write your final estimated equation.
e) What is the coefficient of determination? Interpret its value.
f) What is the contribution of each explanatory variable in explaining the variability in housing prices?

2) University GPA
The admissions officer of a university is trying to develop a formal system of deciding which students to admit to the university. She

believes that determinants of success include the standard variables: high school grades and SAT scores. However, she also believes that

students who have participated in extracurricular activities are more likely to succeed than those who have not. To investigate the issue,

she randomly sampled 100 fourth-year students and recorded the following variables.
• GPA for the first 3 years at the university (range: 0 to 12)
• GPA from high school (range: 0 to 12)
• SAT score (range: 200 to 800)
• Number of hours on average spent per week in organized extracurricular activities in the last year of high school
a) Write a regression equation that helps the admissions officer decide which students to admit
b) Use gretl to estimate your equation.
c) Are the coefficients significant?
d) What is the coefficient of determination? Interpret its value.
e) What is the contribution of each explanatory variable in explaining the variability in housing prices?