The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | }
\hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \
\hline \text { Repression } & & 700 & & & \
\hline \text { Error } & & & & & \
\hline \text { Total } & & 1000 & & & \
\hline
\end{array}$$ The observed F value is __________.
A)17.50
B)2.33
C)0.70
D)0.43
E)0.50

Question

The following ANOVA table is from a multiple regression analysis with n = 35 and four independent variables. $$\begin{array} { | c | c | c | c | c | c | } 
\hline \text { Source } & \mathrm { df } & \mathrm { SS } & \mathrm { MS } & F & p \
\hline \text { Repression } & & 700 & & & \
\hline \text { Error } & & & & & \
\hline \text { Total } & & 1000 & & & \
\hline
\end{array}$$ The observed F value is __________.
A)17.50
B)2.33
C)0.70
D)0.43
E)0.50

Quizplus · Accepted Answer

The observed F value is calculated as the ratio of the mean square due to regression (MSR) to the mean square due to error (MSE). Given that there are four independent variables, the degrees of freedom (df) for regression is 4. The total df is n - 1 = 35 - 1 = 34, and thus the df for error is 34 - 4 = 30. The sum of squares due to error (SSE) is the total sum of squares (SST) minus the sum of squares due to regression (SSR), which is 1000 - 700 = 300. The mean square due to regression (MSR) is SSR/df for regression = 700/4 = 175. The mean square due to error (MSE) is SSE/df for error = 300/30 = 10. Therefore, the observed F value is MSR/MSE = 175/10 = 17.50.

The Following ANOVA Table Is from a Multiple Regression Analysis