# 5

The values of two variables x and y are distributed according to the following table:

y/x | 100 | 50 | 25 |
---|---|---|---|

14 | 1 | 1 | 0 |

18 | 2 | 3 | 0 |

22 | 0 | 1 | 2 |

It calls for:

1 Calculate the covariance.

2 Obtain and interpret the linear correlation coefficient.

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

Turn the double entry table into a single table.

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} |
---|---|---|---|---|---|---|---|

100 | 14 | 1 | 100 | 10,000 | 14 | 196 | 1,400 |

100 | 18 | 2 | 200 | 20,000 | 36 | 648 | 3,600 |

50 | 14 | 1 | 50 | 2,500 | 14 | 196 | 700 |

50 | 18 | 3 | 150 | 7,500 | 54 | 972 | 2,700 |

50 | 22 | 1 | 50 | 2,500 | 22 | 484 | 1,100 |

25 | 22 | 2 | 50 | 1,250 | 44 | 968 | 1,100 |

10 | 600 | 43,750 | 184 | 3,464 | 10,600 |

There is a weak negative correlation.

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