In business, do nice guys finish first or last? Refer to the Nature (March 20, 2008) study of whether “nice guys finish last” in the business world, Exercise 2.125 (p. 124). Recall that college students repeatedly played a version of the game “prisoner’s dilemma,” where competitors choose cooperation, defection, or costly punishment. (Cooperation meant paying 1 unit for the opponent to receive 2 units, defection meant gaining 1 unit at a cost of 1 unit for the opponent, and punishment meant paying 1 unit for the opponent to lose 4 units.) At the conclusion of the games, the researchers recorded the average payoff and the number of times cooperation, defection, and punishment were used for each player. The scatterplots (next page) plot average payoff (y) against level of cooperation use, defection use, and punishment use, respectively.

a. Consider cooperation use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend?

b. Consider defection use (x) as a predictor of average payoff (y). Based on the scatterplot, is there evidence of a linear trend?

c. Consider punishment use (x) as a predictor of average payoff (y). Based on the scatterplot (reproduced from Exercise 2.125), is there evidence of a linear trend?

d. Refer to part

c. Is the slope of the line relating punishment use (x) to average payoff (y) positive or negative? Scatterplots for Exercise 11.18 11.19 State Math SAT scores. Refer to the Math SAT scores of 2019 and 2020, Exercise 2.27 (p. 79). The first five observations and last two observations in the file are reproduced in the next table. In Exercise 2.128, we examined the relationship between the 2020 and 2019 Math SAT scores with the help of a scatterplot. STATE Math 2019 Math 2020 Alabama 560 551 Alaska 541 543 Arizona 565 568 Arkansas 559 567 California 531 522 f Wisconsin 648 628 Wyoming 615 606 Source: The College Board, 2020. Regression Statistics Multiple R 0.9933 R Square 0.9867 Adjusted R square 0.9864 Standard Error 5.4704 Observations 51 ANOVA df SS MS F Significance F Treatments 1 108506.2769 108506.2769 3625.8777 1.31456E-47 Error 49 1466.3505 29.9255 Total 50 109972.6275 Coefficients Standard Error t-Stat P-value Lower 95% Upper 95% Intercept 44.0173 8.3641 5.2626 3.12462E-06 27.2090 60.8257 MATH2019 0.9082 0.0151 60.2153 1.31456E-47 0.8779 0.9386

a. Write the equation of a straight-line model relating the 2020 Math SAT score (y) to the 2019 Math SAT score (x). A simple linear regression printout for the data is shown. Find the least squares prediction equation.

b. Give a practical interpretation of the y-intercept of the least squares line. If a practical interpretation is not possible, explain why.

c. Give a practical interpretation of the slope of the least squares line. Over what range of x is the interpretation meaningful?