# 4

The following table shows the age (in years) of 10 children and a quantitative measure of their aggressive behavior (measured on a scale of 0 to 10)

Age | 6 | 6 | 6.7 | 7 | 7.4 | 7.9 | 8 | 8.2 | 8.5 | 8.9 |

Aggressive behavior | 9 | 6 | 7 | 8 | 7 | 4 | 2 | 3 | 3 | 1 |

1 Determine the regression line of aggressive behavior according to age.

2 From that line, determine the value of aggressive behavior that would correspond to a child of 7.2 years.

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

6 | 9 | 36 | 81 | 54 |

6.4 | 6 | 40.96 | 36 | 38.4 |

6.7 | 7 | 44.89 | 49 | 46.9 |

7 | 8 | 49 | 64 | 56 |

7.4 | 7 | 54.76 | 49 | 51.8 |

7.9 | 4 | 62.41 | 16 | 31.6 |

8 | 2 | 64 | 4 | 16 |

8.2 | 3 | 67.24 | 9 | 24.6 |

8.5 | 2 | 72.25 | 4 | 17 |

8.9 | 1 | 79.21 | 1 | 8.9 |

75 | 49 | 570.72 | 313 | 345.2 |