109k views
5 votes
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

User Vhs
by
6.0k points

1 Answer

5 votes

Answer:

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.

User Piraba
by
6.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.