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+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.