An economist estimated a linear relationship between the daily consumption of electricity for a region in megawatt-hours and the maximum daily temperature in degrees Celsius using daily data for December 2004 and January and February 2005 (n = 90). If the sums of squares of regression and the standard error of the estimate were found to be 918.13 and 3.17, respectively, determine the coefficient of determination. Answer as percentage correct to two decimal places.

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Sol:- Given data is,Standard error (\hat{\sigma})=3.17Error of the estimate (S S R)=918.13n=90Here,\begin{array}{l} \text { Standard error }(\hat{\sigma})=\sqrt{\frac{S S E}{n-2}} \\\Rightarrow \begin{aligned}(\hat{\sigma})^{2} & =\frac{S S E}{n-2} \\\Rightarrow S S E & =(\hat{\sigma})^{2} *(n-2) \\& =(3.17)^{2} *(90-2) \\& =10.0489 * 88 \\& =884.3032 \\\Rightarrow \text { SST }= & \text { SSR+SSE } \\= & 918.13+884.3032 \\= & 1802.4332\end{aligned}\end{array}\Rightarrow Coefficient of determination R^{2}=\frac{S S R}{S S T}\begin{aligned}\Rightarrow R^{2}=\frac{918.13}{1802.4332} & =0.5093836487 \\& =50.94 \%\end{aligned}\therefore Coefficient of determination R^{2}=50.94 \% Please like  ...