Question

The data is given as follow. xi 2 6 9 13 20 yi 7 18 9 26 23 The estimated regression equation for these data is = 7.6 + .9x. Compute SSE, SST, and SSR (to 1 decimal). SSE SST SSR What percentage of the total sum of squares can be accounted for by the estimated regression equation (to 1 decimal)? % What is the value of the sample correlation coefficient (to 3 decimals)? Check My Work

Answer 1

SSE = 127.3

SST= 281.2

SSR = 153.9

R² = 0.5473

% = 54.73%

r= +0.7398

Explanation:

xi yi Y^ (Yi-Y^)² (Yi-Y`)²

2 7 7.6 + 0.9(2) (7-9.4)² (7-16.6)²

= 9.4 = 5.76 92.16

6 18 7.6 + 0.9(6) (18-13)² (18-16.6)²

= 13 =25 1.96

9 9 7.6 + 0.9(9) (9-15.7)² (18-16.6)²

= 15.7 =44.89 57.76

13 26 7.6 + 0.9(13) (26-19.3)² (18-16.6)²

= 19.3 = 44.89 88.36

20 23 7.6 + 0.9(20) (23-25.6)² (18-16.6)²

= 25.6 = 6.76 40.96

∑50 83 83 127.3 281.2

Y~= ∑yi/n= 83/5= 16.6

SSE = ∑ (Yi-Y^)² = 127.3

SST= ∑(Yi-Y`)²=281.2

SST = SSR + SSE

SSR = SST- SSE

= 281.2- 127.3= 153.9

Co -efficient of determination= R² = SSR/ SST= 153.9/ 281.2= 0.5473

The regression equation is explained by 54.73 % of the total sum of squares.

The linear correlation coefficient is the square root of the co -efficient of determination

r= ±√r²= √0.5473= +0.7398

We only consider the positive value for the linear correlation coefficient to be positive.