5 We are trying to predict the number of uses of automatic bank teller machines as a function of time. The data are given in Table 29. Here, x  number of years after 1980 and y  number of monthly uses of ATMs (in millions) during the given year. The estimated regression equation is yˆ 

102.3  34.8x. We are given that SST  74,100, SSE 

1,298, and StdErr(bˆ 1)  1.76.

a Test H0: b1  0 against Ha: b1  0 for a  0.05.

Interpret the result.

b Find the correlation between x and y.

c Is the 1987 entry an outlier?

d If present trends continue, what is the approximate probability that during 1990, more than 470 million ATM transactions per month will occur? (Hint: Use the fact that the errors are normally distributed.)