In a multiple regression analysis involving 25 data points and 5 independent variables, the sum of squares terms are calculated as: total variation in y = SSY = 500, SSR = 300, and SSE = 200. In testing the validity of the regression model, the F-value of the test statistic will be:
A) 5.70.
B) 2.50.
C) 1.50.
D) 0.176.

Question

Quizplus · Accepted Answer

The F-value of the test statistic is calculated as:

F = (SSR / k) / (SSE / (n - k - 1))

where k is the number of independent variables and n is the number of data points.

In this case, k = 5 and n = 25. Plugging in the given values, we get:

F = (300 / 5) / (200 / 19) = 15 / 10 = 1.5

Therefore, the F-value of the test statistic is 1.5.

Comparing this value to the F-distribution table with degrees of freedom (k, n - k - 1) = (5, 19) at α = 0.05, we find that the critical F-value is 2.45. Since 1.5 < 2.45, we fail to reject the null hypothesis that all of the regression coefficients are equal to 0. Therefore, the regression model is not significant.

In a Multiple Regression Analysis Involving 25 Data Points and 5