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

SSE =  127.3

SST= 281.2

SSR = 153.9

R² = 0.5473

% = 54.73%

r=  +0.7398

Step-by-step 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.

the 8 in 8,420 is in the thousands place so it's value is 8 thousand.

the 8 in 6,870 is in the hundreds place so it's value is 8 hundred.

divide 8000 by 800 to find the answer:

8000 / 800 = 10

the 8 in 8,420 is 10 times greater than the 8 in 6,870

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