Exercise 1415 Algorithmic Given are five observations for tw

{Exercise 14.15 (Algorithmic)}
Given are five observations for two variables, x and y.

The estimated regression equation for these data is  = 1 + 2.6x.

Compute the coefficient of determination r2 (to 3 decimals).


Does this least squares line provide a good fit?
SelectYes, the least squares line provides a very good fitNo, the least squares line does not produce much of a fitItem 5

Compute the sample correlation coefficient (to 4 decimals).

xi	1	2	3	4	5
yi	4	7	7	11	15

Solution

xi

yi

y pre

SSE

SST

SSR

1

4

3.6

0.16

23.04

27.04

2

7

6.2

0.64

3.24

6.76

3

7

8.8

3.24

3.24

0

4

11

11.4

0.16

4.84

6.76

5

15

14

1

38.44

27.04

Total

5.2

72.8

67.6

MEAN Y

8.8

SSE

5.2

SST

72.8

SSR

67.6

Compute the coefficient of determination r2 (to 3 decimals).

=67.6/72.8 =   0.929

Does this least squares line provide a good fit?
SelectYes, the least squares line provides a very good fit

No, the least squares line does not produce much of a fit

Item 5

Compute the sample correlation coefficient (to 4 decimals).

r=sqrt(67.6/72.8) = 0.9636

( regression coefficient is positive.There fore correlation is positive)

The required r= 0.9636

	xi	yi	y pre	SSE	SST	SSR
	1	4	3.6	0.16	23.04	27.04
	2	7	6.2	0.64	3.24	6.76
	3	7	8.8	3.24	3.24	0
	4	11	11.4	0.16	4.84	6.76
	5	15	14	1	38.44	27.04
Total				5.2	72.8	67.6
	MEAN Y	8.8