1. Incorrect. The
answer is false not true.
a) ΣThe equation of the line is y=a+bx. The normal equations are
Σy=an+bΣx
Σxy=aΣx+bΣx2.
X |
y |
x2 |
xy |
y2(for part (b)) |
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 |
Σx2=524 |
Σxy=364 |
Σy2=256 |
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+dΣy2.
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.