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 (1) the number plea bargains per 1,000 cases (y), (2) the average number of cases per prosecutor (x1), and (3) the average number of empty beds in the state's correctional institution (x2). Your hypothesis is that the average number of cases per prosecutor and the average number of empty correctional beds may explain some of the variation in the use of plea bargaining across states. More precisely, you hypothesize that as the average number cases per prosecutor increases, plea bargaining may also increase. On the other hand, you hypothesize that as the average number of empty beds in the state's correctional institution increases, the use of plea bargaining may decrease. After collecting your data, you obtain the following statistics:
a. What would the values of b1 and b2 be from the above sample statistics? Interpret these coefficients.
b. From your calculated partial slope coefficients and sample means, solve for the value of the intercept (a). What is the complete multiple regression equation?
c. Using the above multiple regression equation, predict the value of Y (number of plea bargains per 1,000) if the average number of cases per prosecutor is 150 and the average number of empty beds is two.
d. Calculate the Beta weights for each of the partial slope coefficients above. What do they tell you about the relative importance of each independent variable?
e. Calculate the multiple coefficient of determination from these sample statistics. What does this coefficient indicate?
The solution answers a multipart question about hypothesis testing for the use of the plea bargain. Attached as Word document.