Exercise 4 The F-test for multiple linear regression is to test whether there exists any independent variables that are significant. The F-test statistics F can be calculated using sum of squares regression(SSR) and sum of squares error(SSE). The formula for both SSR and SSE is given below. SSE = SSR Sex Syy Sex (4.1) 4.1 Calculate F using SSR and SSE. [4 pts] 4.2 Construct a null and alternative hypothesis for the F-test in (4.1). Explain the intuition behind this equation. (Hint: Think about the difference between fitting a linear regression on the data v.s. simply using the mean(average) of the data) [4 pts] 4.3 Let us say B, is the slope of the linear regression. Represent , in terms of Sxy and Sy as you've learned from class. [4 pts] 4.4 One can also perform a t-test to test whether there exists a linear relationship between dependent and independent variables in linear regression. By using H, : Bi = 0 and test statistics t prove that (F")} = {' holds true. (4 pts] SEC)