**1. Correct. The
answer is false.**

a) The equation of the line is y=a+bx. The normal equations are

Σy=an+bΣx

Σxy=aΣx+bΣx^{2}.

X |
y |
x |
xy |
y |

1 |
1 |
1 |
1 |
1 |

3 |
2 |
9 |
6 |
4 |

4 |
4 |
16 |
16 |
16 |

6 |
4 |
36 |
24 |
16 |

8 |
5 |
64 |
40 |
25 |

9 |
7 |
81 |
63 |
49 |

11 |
8 |
121 |
88 |
64 |

14 |
9 |
196 |
126 |
81 |

Σx=56 |
Σy=40 |
Σx |
Σxy=364 |
Σy |

Since n=8, the normal equations become

8a=56b=40

56a+524b=364

Solving simultaneously, we obtain a=0.545 and b=0.636 and y=0.545 + 0.636x.

b) The equation of the line is x=c+dy and the normal equations are

Σx=cn+dΣy

Σxy=cΣy+dΣy^{2}.

Using the data from the above table, the normal equations become

8c+40d=56

40c+256d=364.

Solving simultaneously, we obtain c=-0.5 and d=1.5 and x=-0.5 + 1.5y.