# 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.

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 H_{0}: β_{1} = 0 against Hα: β_{1} ≠ 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.)