The following estimated regression equation based on 10 observations was presented. ý = 29.1270 + 0.5106Xq + 0.4980X, The values of SST and SSR are 6,714.125 and 6,225.375, respectively. (a) Find SSE. SSE= 488.75 (b) Compute R2. (Round your answer to three decimal places.) R² = 0.927 (c) Compute R₂². (Round your answer to three decimal places.) R₁₂²= 0.906 (d) Comment on the goodness of fit. (For purposes of this exercise, consider a proportion large if it is at least 0.55.) O The estimated regression equation provided a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. O The estimated regression equation did not provide a good fit as a small proportion of the variability in y has been explained by the estimated regression equation. O The estimated regression equation did not provide a good fit as a large proportion of the variability in y has been explained by the estimated regression equation. O The estimated regression equation provided a good fit as a large proportion of the variability in v has been explained by the estimated regression equation.

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The following estimated regression equation based on 10 observations was presented:

\[
\hat{y} = 29.1270 + 0.5106x_1 + 0.4980x_2
\]

The values of SST and SSR are 6,714.125 and 6,225.375, respectively.

(a) **Find SSE.**
   - **SSE** = 488.75

(b) **Compute \( R^2 \).** (Round your answer to three decimal places.)

   \[
   R^2 = 0.927
   \]

(c) **Compute \( R^2_a \).** (Round your answer to three decimal places.)

   \[
   R^2_a = 0.906
   \]

(d) **Comment on the goodness of fit.** (For purposes of this exercise, consider a proportion large if it is at least 0.55.)
   - The estimated regression equation provided a good fit as a large proportion of the variability in \( y \) has been explained by the estimated regression equation.
Transcribed Image Text:The following estimated regression equation based on 10 observations was presented: \[ \hat{y} = 29.1270 + 0.5106x_1 + 0.4980x_2 \] The values of SST and SSR are 6,714.125 and 6,225.375, respectively. (a) **Find SSE.** - **SSE** = 488.75 (b) **Compute \( R^2 \).** (Round your answer to three decimal places.) \[ R^2 = 0.927 \] (c) **Compute \( R^2_a \).** (Round your answer to three decimal places.) \[ R^2_a = 0.906 \] (d) **Comment on the goodness of fit.** (For purposes of this exercise, consider a proportion large if it is at least 0.55.) - The estimated regression equation provided a good fit as a large proportion of the variability in \( y \) has been explained by the estimated regression equation.
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