A multiple regression analysis includes 25 data points and 4 independent variables produces SST = 400 and SSR = 300. Then, the multiple standard error of estimate is 5.

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Michaela Farrell · Accepted Answer

Final Answer : False, Explanation :   The multiple standard error of estimate (also known as the standard error of the estimate) is calculated using the formula   S S E n − k − 1 \sqrt{\frac{SSE}{n-k-1}} n − k − 1 SSE ​ ​  , where SSE is the sum of squares due to error (SST - SSR),   n n n   is the number of observations, and   k k k   is the number of independent variables. Given SST = 400 and SSR = 300, SSE = 400 - 300 = 100. With 25 data points (n = 25) and 4 independent variables (k = 4), the formula becomes   100 25 − 4 − 1 = 100 20 = 5 \sqrt{\frac{100}{25-4-1}} = \sqrt{\frac{100}{20}} = \sqrt{5} 25 − 4 − 1 100 ​ ​ = 20 100 ​ ​ = 5 ​  , which does not equal 5.

A multiple regression analysis includes 25 data points and 4 independent variables produces SST = 400 and SSR = 300. Then, the multiple standard error of estimate is 5.

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