Q. Model with better fit. In the estimation of a multiple regression model with two explanatory variables and 20 observations, SSE = 550 and SST = 1000. Which of the following is the correct value of R2?
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Step 1: Calculate the sum of squares regression (SSR) using the formula SSR = SST - SSE. Show more…
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In exercise I, the following estimated regression equation based on 10 observations was presented. $$\hat{y}=29.1270+.5906 x_{1}+.4980 x_{2}$$ $$\begin{array}{l}{\text { The values of SST and SSR are } 6724.125 \text { and } 6216.375, \text { respectively. }} \\ {\text { a. Find SSE. }} \\ {\text { b. Compute } R^{2} \text { . }} \\ {\text { c. Compute } R_{\text { a. }}^{2}} \\ {\text { d. Comment on the goodness of fit. }}\end{array}$$
In exercise $4,$ the following estimated regression equation relating sales to inventory investment and advertising expenditures was given. $$\hat{y}=25+10 x_{1}+8 x_{2}$$ The data used to develop the model came from a survey of 10 stores; for these data $\mathrm{SST}=16,000$ and $\mathrm{SSR}=12,000 .$ $\begin{array}{l}{\text { a. Compute SSE, MSE, and MSR. }} \\ {\text { b. Use an } F \text { test and a } .05 \text { level of significance to determine whether there is a relation }} \\ {\text { ship among the variables, }}\end{array}$
In exercise $4,$ the following estimated regression equation relating sales to inventor investment and advertising expenditures was given. $$\hat{y}=25+10 x_{1}+8 x_{2}$$ $\begin{array}{l}{\text { The data used to develop the model came from a survey of } 10 \text { stores; for those data }} \\ {\text { SST }=16,000 \text { and } S S R=12,000 \text { . }} \\ {\text { a. For the estimated regression equation given, compute } R^{2} \text { . }} \\ {\text { b. Compute } R_{\text { a. }}^{2} \text { . }} \\ {\text { c. Does the model appear to explain a large amount of variability in the data? Explain. }}\end{array}$
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