Recall that R² is the multiple coefficient of determination and is an indication of the goodness of fit for an estimated multiple regression equation. That is, it is the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation. Since it is a proportion, it will only take on values between 0 and 1. It is calculated as follows where SSR is the sum of squares due to regression and SST is the total sum of squares. SSR R2 = SST We are given that SST = 1,808 and SSR = 1,778. Use these values to find the value of R2, rounding the result to three decimal places. SSR R2 SST 1,778

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Author:Amos Gilat
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The following estimated regression equation based on 30 observations was presented.
ý = 17.6 + 3.8x, – 2.3x2 + 7.6x3 + 2.7x4
The values of SST and SSR are 1,808 and 1,778, respectively.
(a) Compute R2.
(b) Compute R,.
a
(c) Comment on the goodness of fit.
Step 1
(a) Compute R?.
Recall that R is the multiple coefficient of determination and is an indication of the goodness of fit for an
estimated multiple regression equation. That is, it is the proportion of the variability in the dependent variable
that can be explained by the estimated multiple regression equation. Since it is a proportion, it will only take
on values between 0 and 1. It is calculated as follows where SSR is the sum of squares due to regression and
SST is the total sum of squares.
SSR
R2 .
SST
1,808 and SSR = 1,778. Use these values to find the value of R2, rounding the result
We are given that SST =
to three decimal places.
%3D
SSR
R2
%3D
SST
1,778
%D
Transcribed Image Text:The following estimated regression equation based on 30 observations was presented. ý = 17.6 + 3.8x, – 2.3x2 + 7.6x3 + 2.7x4 The values of SST and SSR are 1,808 and 1,778, respectively. (a) Compute R2. (b) Compute R,. a (c) Comment on the goodness of fit. Step 1 (a) Compute R?. Recall that R is the multiple coefficient of determination and is an indication of the goodness of fit for an estimated multiple regression equation. That is, it is the proportion of the variability in the dependent variable that can be explained by the estimated multiple regression equation. Since it is a proportion, it will only take on values between 0 and 1. It is calculated as follows where SSR is the sum of squares due to regression and SST is the total sum of squares. SSR R2 . SST 1,808 and SSR = 1,778. Use these values to find the value of R2, rounding the result We are given that SST = to three decimal places. %3D SSR R2 %3D SST 1,778 %D
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