# 3

The number of hours devoted to studying a subject and the marks obtained by eight students in the corresponding examination is:

Hours (x) | 20 | 16 | 34 | 23 | 27 | 32 | 18 | 22 |

Mark (y) | 6.5 | 6 | 8.5 | 7 | 9 | 9.5 | 7.5 | 8 |

Calculate:

1 Line of regression of y on x.

2 The estimated mark a person would obtain who studied 28 hours.

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

16 | 6 | 256 | 36 | 96 |

18 | 7.5 | 324 | 56.25 | 135 |

20 | 6.5 | 400 | 42.25 | 130 |

22 | 8 | 484 | 64 | 176 |

23 | 7 | 529 | 49 | 161 |

27 | 9 | 729 | 81 | 243 |

32 | 9.5 | 1,024 | 90.25 | 304 |

34 | 8.5 | 1,156 | 72.25 | 289 |

192 | 62 | 4,902 | 491 | 1,534 |