Question: The Data County court system is seeking a rational way to predict its workload so that it can effectively allocate resources. They think that they can use the number of arrests over the past month to predict the total number of trials three months later. To investigate this possibility, they gather data on the last 48 months and run the following regression, where X is the total number of felony arrests for a month and Y is the total number of trials three months later.

Y=4.3 + .47X

r²=.52, S_YX = 35.6, sb=.07, n=48, Xbar=500, sx=100

a) Explain the meaning of the slope, the intercept, and the coefficient of determination.

b) Test the slope to see if it is significant.

c) How many trials can the court system expect if there are 623 felony arrests? Put a 95% confidence limit around this estimate.