(i) You can also build a regression model with one independent variable, say eithed or Z. Use the four important specification criteria given in Chap. 6 to work out the best regression model. Please explain your answer in detail. 4. The Stata data file (elemapi.dta) contains data on 21 school-related variables in 400 U.S. schools. Please refer to the text file (elemapidescription.txt) for a description of these vari- ables. (a) Regress api00 on meals, acs k3, avg ed, and full with the aid of Stata. [Hint: the regression equation is Y # off ,*1 +3 2-*2 +# 3-*s #9 4.*+ .] (b) Find the coefficient of determination,A", with the aid of the computer software. What does the number in R' 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