# We are trying to predict the number of uses of automatic bank teller machines as a function of time….

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.

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We are trying to predict the number of uses of automatic bank teller machines as a function of time….
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 x y 0 100 1 130 2 170 3 200 4 260 5 300 6 305 7 330 8 380

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  = 102.3 + 34.8x. We are given that SST = 74,100, SSE = 1,298, and StdErr() = 1.76.

a Test H0: β1 = 0 against Hα: β1 ≠ 0 for α = 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.)