In a multiple regression analysis involving 6 independent variables and a sample of 19 data points the total variation in y is SST = 900 and the amount of variation in y that is explained by the variations in the independent variables is SSR = 600. The value of the F-test statistic for this model is:
A)4.0.
B)4.3.
C)4.8.
D)6.3.

Question

Quizplus · Accepted Answer

The F-test statistic in a multiple regression analysis is calculated using the formula $F = \frac{MSR}{MSE}$, where $MSR = \frac{SSR}{df_{regression}}$ and $MSE = \frac{SSE}{df_{error}}$. Here, $SSR = 600$, $SST = 900$, so $SSE = SST - SSR = 900 - 600 = 300$. With 6 independent variables, $df_{regression} = 6$, and with 19 data points, $df_{total} = 19 - 1 = 18$, so $df_{error} = df_{total} - df_{regression} = 18 - 6 = 12$. Thus, $MSR = \frac{600}{6} = 100$ and $MSE = \frac{300}{12} = 25$, leading to $F = \frac{100}{25} = 4.0$.

In a Multiple Regression Analysis Involving 6 Independent Variables and a Sample