17. (25 points) A company offers a 10-lesson program of study to improve students SAT scores. A survey is made of a random sample of 25 students. A scatter plot of improvement in total SAT score versus number of lessons taken is as follows. Improve 100 90 80 70 60 50 40 30 20 10 ° T 2 4 Lessons 10 The computer output of the regression analysis follows, along with a plot and a histogram of the residuals. Regression Analysis: Improvement Versus Lessons Dependent variable: Improvement Predictor Constant Lessons S=9.744 Coef -7.718 SE Coef T P 4.272 -1.81 0.084 9.2854 0.6789 13.68 0.000 R-Sq -89.18 Analysis of Variance MS Source DF 17761 187.06 0.000 Regression 1 Residual Error 23 Total 24. 17761 2184 19945 95 Residual -10- 10- Residuals Versus Lessons (response is Improve) 1 2 3 4 Lessons 10 Frequency Histogram of the Residuals (response is improve) (a) (5 points) What is the equation of the regression line that predicts score improvement as a function of number of lessons? Residual (b) (5 points) Interpret, in context, the slope of the regression line (i.e., coef 9.2854) (c) (5 points) What is the meaning of the R-Sq in the context of this study? 8- (d) (3 points) Calculate the value of the correlation coefficient (e) (7 points) Perform a test of significance for the slope of the regression line. Should you accept or reject Ho and why?