Assignments 5&6
1. Studying and Grades. A marketing professor at Givens College is interested in the relationship between hours spent studying and total points earned in a course. Data collected on 156 students who took the course last semester are provided in the file MktHrsPts.
a. Develop a scatter chart for these data. What does the scatter chart indicate about the relationship between total points earned and hours spent studying?
b. Develop an estimated regression equation showing how total points earned is related to hours spent studying. What is the estimated regression model?
c. Test whether each of the regression parameters β0 and β1 is equal to zero at a 0.01 level of significance. What are the correct interpretations of the estimated regression parameters? Are these interpretations reasonable?
d. How much of the variation in the sample values of total point earned does the model you estimated in part (b) explain?
e. Mark Sweeney spent 95 hours studying. Use the regression model you estimated in part (b) to predict the total points Mark earned.
f. Mark Sweeney wants to receive a letter grade of A for this course, and he needs to earn at least 90 points to do so. Based on the regression equation developed in part (b), how many estimated hours should Mark study to receive a letter grade of A for this course?
2. NFL Winning Percentage. The National Football League (NFL) records a variety of performance data for individuals and teams. To investigate the importance of passing on the percentage of games won by a team, the following data show the conference (Conf), average number of passing yards per attempt (Yds/Att), the number of interceptions thrown per attempt (Int/Att), and the percentage of games won (Win%) for a random sample of 16 NFL teams for the 2011 season (NFL web site).
Develop the estimated regression equation that could be used to predict the percentage of games won, given the average number of passing yards per attempt. What proportion of variation in the sample values of proportion of games won does this model explain?
Develop the estimated regression equation that could be used to predict the percentage of games won, given the number of interceptions thrown per attempt. What proportion of variation in the sample values of proportion of games won does this model explain?
Develop the estimated regression equation that could be used to predict the percentage of games won, given the average number of passing yards per attempt and the number of interceptions thrown per attempt. What proportion of variation in the sample values of proportion of games won does this model explain?
The average number of passing yards per attempt for the Kansas City Chiefs during the 2011 season was 6.2, and the team’s number of interceptions thrown per attempt was 0.036. Use the estimated regression equation developed in part (c) to predict the percentage of games won by the Kansas City Chiefs during the 2011 season. Compare your prediction to the actual percentage of games won by the Kansas City Chiefs. (Note: For the 2011 season, the Kansas City Chiefs’ record was 7 wins and 9 losses.)
Did the estimated regression equation that uses only the average number of passing yards per attempt as the independent variable to predict the percentage of games won provide a good fit?
