# 7

A group of 50 individuals has been surveyed on the number of hours devoted each day to sleeping and watching TV. The responses are summarized in the following table:

No. of sleeping hours (x) | 6 | 7 | 8 | 9 | 10 |

No. of hours of television (y) | 4 | 3 | 3 | 2 | 1 |

Absolute frequencies (f_{i}) |
3 | 16 | 20 | 10 | 1 |

1 Calculate the correlation coefficient.

2 Determine the equation of the regression line of y on x.

3 If a person sleeps eight hours, how many hours of TV are they expected to watch?

x_{i} |
y_{i} |
f_{i} |
x_{i} · f_{i} |
x_{i}^{2 } · f_{i} |
y_{i} · f_{i} |
y_{i2 } · f_{i} |
x_{i} · y_{i }· f_{i} |
---|---|---|---|---|---|---|---|

6 | 4 | 3 | 18 | 108 | 12 | 48 | 72 |

7 | 3 | 16 | 112 | 784 | 48 | 144 | 336 |

8 | 3 | 20 | 160 | 1,280 | 60 | 180 | 480 |

9 | 2 | 10 | 90 | 810 | 20 | 40 | 180 |

10 | 1 | 1 | 10 | 100 | 1 | 1 | 10 |

50 | 390 | 3,082 | 141 | 413 | 1,078 |

There is a strong negative correlation.

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