10.43 Performance bonuses. In the National Football League (NFL), performance bonuses now account for roughly 25% of player compensation.18 Does tying a player’s salary into performance bonuses result in better individual or team success on the field? Focusing on linebackers, let’s look at the relationship between a player’s end-of-year production rating and the percent of his salary devoted to incentive payments in that same year.

  1. (a) Use numerical and graphical methods to describe the two variables and summarize your results.

  2. (b) Both variable distributions are non-Normal. Does this necessarily pose a problem for performing linear regression? Explain.

  3. (c) Construct a scatterplot of the data and describe the relationship. Are there any outliers or unusual values? Does a linear relationship between the percent of salary and the player rating seem reasonable? Is it a very strong relationship? Explain.

  4. (d) Run the simple linear regression and state the least-squares regression line.

  5. (e) Obtain the residuals and assess whether the assumptions for the linear regression analysis are reasonable. Include all plots and numerical summaries used in doing this assessment.