The following ANOVA table is from a multiple regression analysis. $$\begin{array} { | c | c | c | c | c | c | } \hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \ \hline \text { Repression } & 3 & 1500 & & & \ \hline \text { Error } & 26 & & & & \ \hline \text { Total } & & 2300 & & & \ \hline \end{array}$$ The value of the standard error of the estimate s_e is __________. A)30.77 B)5.55 C)4.03 D)3.20 E)0.73

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Quizplus · Accepted Answer

The standard error of the estimate, denoted as $s_{e}$, is calculated using the formula $s_{e} = \sqrt{\frac{SSE}{n - k - 1}}$, where $SSE$ is the sum of squares due to error, $n$ is the sample size, and $k$ is the number of predictors. From the ANOVA table, the total sum of squares (SST) is 2300, and the sum of squares due to regression (SSR) is 1500. The sum of squares due to error (SSE) can be found by subtracting SSR from SST, which gives $SSE = 2300 - 1500 = 800$. The degrees of freedom for error (dfE) is 26, which corresponds to $n - k - 1$. Thus, $s_{e} = \sqrt{\frac{800}{26}} \approx 5.55$.

The Following ANOVA Table Is from a Multiple Regression Analysis