Question: Suppose that you are interested in examining the determinants of the use of plea bargaining by state prosecutors. During a one-month period, you record for each state in the US, the number plea bargains per 1,000 cases (y) and the average number of cases per prosecutor (x). Your hypothesis is that the average number of cases per prosecutor may explain some of the variation in the use of plea bargaining across states. After collecting your data, you obtain the following statistics:

?y = 12,507
?x = 12,224

?y² = 4,578,619
?x² = 5,639,821
?xy = 4,234,185

[N = 50]. We wish to examine a possible linear regression model.

a. What is the value of b? Interpret.

b. What is the value of (a). What is the regression equation?

c. Using the above regression equation, predict the value of Y (number of plea bargains per 1,000) if the average number of cases per prosecutor is 150.

d. Calculate the correlation coefficient.

e. What is the coefficient of determination from these sample statistics? What does this coefficient indicate?

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