16. Laptops and Learning An informal experiment was conducted at McNair Academic High School in Jersey City, New Jersey. Twenty freshman algebra students were given a survey at the beginning of the semester, measuring his or her skill level. They were then allowed to use laptop computers both at school and at home. At the end of the semester, their scores on the same survey were recorded (x) along with their score on the final examination (y).9 The data and the MINITAB printout are shown here.

a. Construct a scatterplot for the data. Does the assumption of linearity appear to be reasonable?

b. What is the equation of the regression line used for predicting final exam score as a function of the endof-
semester survey score?

c. Do the data present sufficient evidence to indicate that final exam score is linearly related to the end-ofsemester survey score? Use a 5.01.

d. Find a 99% confidence interval for the slope of the regression line.

e. Use the MINITAB printout to find the value of the coefficient of determination, r2. Show that r2 5SSR/Total SS.

f. What percentage reduction in the total variation is achieved by using the linear regression model?

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123456 Student End-of-Semester Survey Final Exam 100 98 96 97 88 88 4 100 100 100 100 96 78 7 80 68 8 68 47 9 92 90 10 96 94 11 88 84 12 92 93 13 68 57 14 84 84 15 84 81 16 88 83 17 72 84 18 88 93 19 72 57 20 88 83