Assume that you're interested in examining the determinants of use of plea-bargaining by state prosecutors. Throughout a one-month period, you record for each state in 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 might describe some of the variation in the employ of plea bargaining across states. After collecting your data, you obtain following statistics:
Sy = 12,507
Sx = 12,224
Sy^{2} = 4,578,619
Sx^{2} = 5,639,821
Sxy = 4,234,185
[N = 50]. We wish to examine a possible linear regression model.
a. Find out the value of b? Interpret.
b. Find out the value of (a). Find out the regression equation?
c. Using the above regression equation, Find the value of Y (number of plea bargains per 1,000) if the average number of cases per prosecutor is 150.
d. Compute the correlation coefficient.
e. What is the coefficient of determination from such sample statistics? What does this coefficient indicate?