The Stata data file (elemapi.dta) contains data on 21 school-related variables in 400 U.S. schools. Please refer to the text file (elemapi description.txt) for a description of these variables. (a) Regress api00 on meals, acs k3, avg ed, and full with the aid of Stata. [Hint: the regression equation is Y = 0 + 1X1 + 2X2 + 3X3 + 4X4 + .] (b) Find the coefficient of determination, R2 , with the aid of the computer software. What does the number in R2 imply? (c) Find the value of the F test. What does the F test say about the overall significance of this model? (d) Test the null hypothesis at the 0.05 significance level that the regression coefficient of the population regression, 1, is 0.0 versus the alternative hypothesis that this regression coefficient is not 0.0. (e) Test the null hypothesis at the 0.05 significance level that the regression coefficient of the population regression, 2, is 0.0 versus the alternative hypothesis that this regression coefficient is not 0.0. (f) Test the null hypothesis at the 0.05 significance level that the regression coefficient of the population regression, 3, is 0.0 versus the alternative hypothesis that this regression coefficient is not 0.0. (g) Test the null hypothesis at the 0.05 significance level that the regression coefficient of the population regression, 4, is 0.0 versus the alternative hypothesis that this regression coefficient is not 0.0. (h) Use Variance Inflation Factor (VIF) to detect potential multi-collinearity. 4 (i) Regress api00 on meals, acs k3, and full with the aid of Stata. [Hint: the regression equation is Y = 0 + 1X1 + 2X2 + 3X3 + .] Use all your knowledge about multiple regression, compare this regression model with the model used in part (a). Which regression model perform better? Why?