Week 4 – Problem Set

Week 4 – Problem Set 1. The following table contains the ACT scores and the GPA (grade point average) for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. For this question, use only a hand- held calculator. i. Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation ^ GPA = ^ β 0 + ^ β 1 ACT Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain. How much higher is the GPA predicted to be if the ACT score is increased by five points? ii. Compute the fitted values and residuals for each observation, and verify that the residuals (approximately) sum to zero. iii. What is the predicted value of GPA when ACT = 20 ? iv. How much of the variation in GPA for these eight students is explained by ACT? Explain. 2. For this question, use the data hprice1.dta. i. Estimate the level-level regression model: price = β 0 + β 1 sqrft + u . Interpret ^ β 1 and the R 2 . ii. Estimate the log-level regression model: ln ( price ) = β 0 + β 1 sqrft + u . Interpret ^ β 1 and the R 2 . iii. Estimate the level-log regression model: price = β 0 + β 1 ln ( sqrft ) + u . Interpret ^ β 1 and the R 2 .