Question

Do nice guys really finish last in business? Refer to the Nature (March 20, 2008) study of whether “nice guys finish last” in business, Exercise 11.18 (p. 653). Recall that college students repeatedly played a version of the game “prisoner’s dilemma,” where competitors choose cooperation, defection, or costly punishment. At the conclusion of the games, the researchers recorded the average payoff and the number of times punishment was used for each player. Based on a scatter plot of the data, the simple linear regression relating average payoff (y) to punishment use (x) resulted in SSE = 1.04.

a. Assuming a sample size of n = 28, compute the estimated standard deviation of the error distribution, s.

b. Give a practical interpretation of s.

Short answer

1. The estimated standard deviation of the error distribution is 0.2.
2. It is preferable if it is small.

Step-by-step solution

Introduction

The standard error shows how far the population mean is expected to deviate from the sample mean. It indicates how much the sample mean will change if the research is repeated with new samples from the same population.

Finding s

$$\begin{gathered} \mathit{s}\mathbf{=}\sqrt{\frac{\mathbf{S}\mathbf{S}\mathbf{E}}{\mathbf{n}\mathbf{-}\mathbf{2}}} \\ \mathbf{=}\sqrt{\frac{\mathbf{1}\mathbf{.}\mathbf{04}}{\mathbf{28}\mathbf{-}\mathbf{2}}} \\ \mathbf{=}\sqrt{\frac{\mathbf{1}\mathbf{.}\mathbf{04}}{\mathbf{26}}} \\ \mathbf{=}\sqrt{\mathbf{0}\mathbf{.}\mathbf{04}} \\ \mathbf{=}\mathbf{0}\mathbf{.}\mathbf{2} \end{gathered}$$

Therefore, the standard deviation of the error distribution s is 0.2.

Providing a practical interpretation of s 

“s” is a measure of the predicted value's variability around the regression line. It is preferable if it is small.