Regressor Residual Residual Sum of Squares (SSR) Response Variable R -squared Sample Regression Function (SRF) Semi-elasticity Simple Linear Regression Model Slope Parameter Standard Error of ˆ 1 Standard Error of the Regression (SER) Sum of Squared Residuals (SSR) Total Sum of Squares (SST) Zero Conditional Mean Assumption
62 Part 1 Regression Analysis with Cross-Sectional Data (i) Estimate the relationship between GPA and ACT using OLS; that is, obtain the intercept and slope estimates in the equation 1 GPA ˆ 0 ˆ 1 ACT . Comment on the direction of the relationship. Does the intercept have a useful inter- pretation 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. 2.4 The data set BWGHT.RAW contains data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces ( bwght ), and an explanatory variable, average number of cigarettes the mother smoked per day during pregnancy ( cigs ). The following simple regression was estimated using data on n 1,388 births: 1 bwght 119.77 0.514 cigs (i) What is the predicted birth weight when cigs 0? What about when (i) Interpret the intercept in this equation, and comment on its sign and magnitude.(ii) What is the predicted consumption when family income is $30,000?