Question

Given are five observations for two variables, x and y. The estimated regression equation for these data is y = 1 + 2.4x
(A) Compute SSE, SST, and SSR
(B) Compute the coefficient of determination, R^2.
(C) Compute the sample correlation coefficient.

x	y
1	3
2	8
3	5
4	12
5	13

Answer 1

Given,

x	y
1	3
2	8
3	5
4	12
5	13

(A)

The estimated regression equation for these data is = 1 + 2.4x

SST = SSR+SSE

n : number of pairs of observation = 5

	x	y
	1	3
	2	8
	3	5
	4	12
	5	13
Total	15	41

	x	y	= 1+2.4x
	1	3	1+2.4 x 1	3.4
	2	8	1+2.4 x 2	5.8
	3	5	1+2.4 x 3	8.2
	4	12	1+2.4 x 4	10.6
	5	13	1+2.4 x 5	13
Total	15	41		41

	x	y		y-				y-
	1	3	3.4	-0.4	0.16	-4.8	23.04	-5.2	27.04
	2	8	5.8	2.2	4.84	-2.4	5.76	-0.2	0.04
	3	5	8.2	-3.2	10.24	0	0	-3.2	10.24
	4	12	10.6	1.4	1.96	2.4	5.76	3.8	14.44
	5	13	13	0	0	4.8	23.04	4.8	23.04
Total	15	41	41		17.2	0	57.6	0	74.8

Also SSR + SSE = 57.6+17.2 = 74.8 which is nothing but SST

(B)

Coefficient of Determination : R²

i.e 77.01%

(C)

Sample Correlation

	x	y	xy	x2	y2
	1	3	3	1	9
	2	8	16	4	64
	3	5	15	9	25
	4	12	48	16	144
	5	13	65	25	169
Total	15	41	147	55	411

Sample Correlation = 0.8775