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, SS

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

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Khoii Minh 5 years 2021-08-14T10:15:21+00:00 1 Answers 157 views 0

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  1. trungdung22
    0
    2021-08-14T10:16:23+00:00
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    Answer:

    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.

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