17. Linear regression equation has been estimated Gradei = 16.24 + 2.41Study; + 0.28Sleepi - 0.081Qi + 0.32EQi (14.21) (0.22) (0.04) (0.09) (0.44) In this equation, Grade is the student's mark (out of 100 points), Study is the hours of studying per week, Sleep is the hours of sleeping per week, IQ is the intelligence quotient, and EQ is the measure of emotional intelligence. Below every coefficient a number (in brackets) shows the estimated standard error (SE(B)) for that coefficient. The equation was estimated for a sample of 40 students. The critical t value at 5% significance for a 2-sided Ho is to.025,39 = 2.023. Interpret the slope coefficient (0.28) for Sleep. (2) b. Test the hypothesis that grade does not depend on how much a student sleeps, at 5% significance level. Show your work. (2) Test the hypothesis that each hour (per week) of studying increases the predicted grade by 2 points, 5% significance level. Show your work. (3) d. If a student studies 10 hours/week, sleeps 8 hours/day, has IQ of 120, and EQ of 100, what grade do you predict? Show your work. (1) 18. Your friend says, "I have got 2 workers and I have some information about them. I've got the numbers for their wages (Wg), their education levels (Ed), their work experience (Ex), their heights (Ht), and their high school grades (Gr). I will OLS estimate a linear regression model Wgi = o + BEd + Ex Ht + Gr; using all this information (for i = 1 or 2), and then I will have a very good explanation why their wages differ." Explain to your friend what's wrong with his approach. (3) 16. Carefully explain how the coefficient of determination R is calculated and what it is used for (what question(s) it helps to answer). Then carefully explain how the adjusted R (R) is calculated and what it is used for (what question(s) it helps to answer). (4)