A math instructor who teaches calculus at a university in Western Pennsylvania believes that there is a relationship between the number of optional homework problems that the students complete during the semester and their final score for the course. To examine this relationship the instructor gathers data (given in the following table) on the homework problems completed and the final score for the course for a randomly selected sample of 16 students:

1. Develop a linear regression equation for the final course score as a function of the average number optional homework problems completed.

2. Forecast a final course score if the average number of homework problems completed is 59.

3. Evaluate the €œgoodness of fit€ of the regression equation by computing the values of R², r, and s_yx and interpret the results.

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Final Score for the Course Student Number of Completed Homework Problems 20 60 45 72 56 78 4 61 70 71 64 67 71 70 85 74 90 77 88 10 79 88 39 66 11 12 52 81 13 28 55 47 14 71 15 35 63 16 80 92