Question - Performance bonuses. In the National Football League (NFL), performance bonuses now account for roughly 25% of player compensation.5 Does tying a player's salary to performance bonuses result in better individual or team success on the field? The Web site usatoday.com has payroll data for most current NFL players. Cbssports.com has a player rating system that uses game statistics.6 Focusing on linebackers, let's look at the relationship between a player's overall 2008 rating and the percent of his 2008 salary devoted to incentive payments.
(a) Use numerical and graphical methods to describe the two variables and summarize your results.
(b) Both variable distributions are non-Normal. Does this necessarily pose a problem for performing linear regression? Explain.
(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.
(d) Run the simple linear regression and give the equation of the least-squares regression line.
(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.