Practice Exam 1: Answer Key
1. approximately 76%
2. No, the adjusted R-squared is lower in Model 2. (Note, however, that there was a mistake in the appendix. Model 2 should have been based on a sample of 108 houses, not just 12.)
3. SQFT, AGE, BASE
4. According to the null hypothesis, all of the population parameters (betas) are 0. According to the alternative hypothesis, at least one of the population parameters (betas) differs from 0.
Reject the null hypothesis at the 1% level of significance because the p-value is less than .01 (in fact, it is less than .0001).
The results suggest that there is a linear relationship between the set of independent variables in the model – square footage, age, number of bathrooms, number of bedrooms, and the presence of a basement – and the dependent variable – price.
5. No. First, none of the correlation coefficients between pairs of independent variables exceeds .7 in absolute value. Second, the highest correlation coefficient between the dependent variable and an independent variable exceeds the highest correlation coefficient between two independent variables. Third, the t statistics and the F statistic are large. Individually three out of 5 coefficients are significantly different from 0 at the 1% level of significance and one is significantly different from 0 at the 10% level. Collectively, we find evidence of a linear relationship between the set of independent variables and the dependent variable.
6. Controlling for the age of the house, the number of bathrooms, the number of bedrooms, and whether there is a basement, each additional square foot is associated with a $42 increase in selling price, on average. Controlling for the size of the house, the age of the house, the number of bathrooms, the number of bedrooms, and whether there is a basement, location in Apple Valley reduces the selling price by about $296 on average. Controlling for the size of the house, the number of bathrooms, the number of bedrooms, and whether there is a basement, each additional year of age reduces the selling price by about 1% on average. Controlling for the age and size of the house, the number of bathrooms, and the number of bedrooms, the presence of a basement increases the price by about 14%.
7. Model 3. The residual plot looks better. There is no systematic pattern here. In contrast, the residual plot for Model 1 looks like the assumption of constant variance or independence may be violated.