In a regression analysis of a first-order model involving 3 predictor variables and 25 observations, the following estimated regression equation was developed. = 12 - 18x₁ + 4x₂ + 15x₃ Also, the following standard errors and the sum of squares were obtained. If we are interested in testing for the significance of the relationship among the variables (i.e., significance of the model), the critical value of F at α = .05 is A) 2.76. B) 4.87. C) 3.10. D) 3.07.

Question

Quizplus · Accepted Answer

To test the significance of the relationship among the variables or the overall model, we need to perform an F-test. The null hypothesis for the F-test is that all the regression coefficients are equal to zero or that there is no significant relationship among the predictor variables and the dependent variable.

The test statistic for the F-test is calculated as:

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

where SSR is the regression sum of squares, SSE is the error sum of squares, k is the number of predictor variables, and n is the sample size.

From the output, we have the following information:

SSR = 1518.68
SSE = 642.02
k = 3
n = 25

Substituting these values into the formula, we get:

F = (1518.68 / 3) / (642.02 / 21) = 11.77

To find the critical value of F at α = .05, we need to look up the F-distribution table with degrees of freedom (k, n - k - 1) = (3, 21). The critical value is found to be 3.10.

Since 11.77 > 3.10, we can reject the null hypothesis and conclude that the model is significant at α = .05 level. Therefore, the best choice is B.

In a Regression Analysis of a First-Order Model Involving 3