# 2

The statistical information obtained from a sample of 12 farms on the relationship between the investment and yield in hundreds of thousands of dollars is shown in the following table:

Investment (x) | 11 | 14 | 16 | 15 | 16 | 18 | 20 | 21 | 14 | 20 | 19 | 11 |

Yield (y) | 2 | 3 | 5 | 6 | 5 | 3 | 7 | 10 | 6 | 10 | 5 | 6 |

Calculate:

1 The regression line of the yield with regard to the investment.

2 The estimated investment needed to obtain a yield of $1,250,000.

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

11 | 2 | 121 | 4 | 22 |

14 | 3 | 196 | 9 | 42 |

16 | 5 | 256 | 25 | 80 |

15 | 6 | 225 | 36 | 90 |

16 | 5 | 256 | 25 | 80 |

18 | 3 | 324 | 9 | 54 |

20 | 7 | 400 | 49 | 140 |

21 | 10 | 441 | 100 | 210 |

14 | 6 | 196 | 36 | 84 |

20 | 10 | 400 | 100 | 200 |

19 | 5 | 361 | 25 | 95 |

11 | 6 | 121 | 36 | 66 |

195 | 68 | 3,297 | 454 | 1,163 |

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