Q1) Assume that you are interested in studying determinants of use of plea-bargaining by state prosecutors. In a one-month period, you record for each state in US, the number plea-bargains per 1,000 cases (y) and average number of cases per prosecutor (x). Your hypothesis is that average number of cases per prosecutor may describe some of variation in use of plea bargaining across states. After gathering your data, you get the following statistics:
Sy = 12,507
Sx = 12,224
Sy2 = 4,578,619
Sx2 = 5,639,821
Sxy = 4,234,185
[N = 50].
a) Determine the value of b? Interpret.
b) What is the value of (a). What is the regression equation?
c) Using above regression equation, predict 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?