3. You are interested in examining the relationship between SAT scores of incoming freshmen at UCONN and their GPA after one semester. To examine this relationship, you conduct a random survey of 250 students and estimate the following model using OLS: GPA, B. +B, SAT, +, where GPA is the grade point average (0 to 4.5) of student , SAT, is the student's SAT score (0 to 1,600) and is a random disturbance term. Regression results are reported below with standard errors in parentheses. 3c. Explained S.S. = 4,750 Unexplained S.S. = 2,500 GPA, =1.4 +0.0016SAT, (1.6) (0.00032) 3a. Interpret the coefficient on SAT in mathematical terms. (Hint: significance is the next question.) 3b. Test the hypothesis that at the 5% significance level. Show all your work. Calculate a 99% confidence interval for B. 3d. Suppose a person scored 1,000 on the SAT. What is their predicted GPA? 3e. Calculate the of the regression. What does the R mean? Show all your work. 0