Question 10.19

10.19 Incentive pay and job performance.

In the National Football League (NFL), incentive bonuses now account for roughly 25% of player compensation.¹¹ Does tying a player’s salary to 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-the-year production rating and the percent of his salary devoted to incentive payments in that same year.

perplay

Use numerical and graphical methods to describe the two variables and summarize your results.
Neither variable is Normally distributed. Does that necessarily pose a problem for performing linear regression? Explain.
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 from incentive payments and player rating seem reasonable? Is it a very strong relationship? Explain.
Run the simple linear regression and give the least-squares regression line.
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.

10.19

(a) Percentage is strongly right-skewed; a lot of players have a small percent of their salary devoted to incentive payments. Rating is also right-skewed. (b) Only the residuals need to be Normal; because they are somewhat right-skewed, it could pose a threat to the results. (c) The relationship is quite scattered. The direction is positive, but any linear relationship is weak. A large number of observations fall close to 0 percent. (d) . (e) The residual plot looks good, no apparent violations. The Normal quantile plot shows the violation of Normality and the right skew we saw earlier.