Incentive pay and job performance. Tying compensation to performance is typically an efficient method of motivating employees. In the National Football League (NFL), incentive bonuses now account for roughly 25% of player compensation.10 Does tying a player’s salary to performance bonuses result in better individual or team success on the field? usatoday.com contains payroll data for most current NFL players. cbssports.com contains a player rating system that uses game statistics.11 Focusing on linebackers, let’s look at the relationship between a player’s overall 2008 rating and the percent of his 2008 salary from incentive payments. DATADATA DATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATADATADATA DATADATADATA DATADATADATADATADATA DATA FILE LINEBACKERS

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

(b) Neither variable is Normally distributed. Does that necessarily pose a problem for performing linear regression? Explain.

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

(d) Run the simple linear regression and give 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 that you used to make this assessment.