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.

S_b₁= 3
S_b₂= 6
S_b₃= 7
SST = 4900
SSE = 1296

The p-value for testing the significance of the regression model is

Question

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.

S_b₁= 3
S_b₂= 6
S_b₃= 7
SST = 4900
SSE = 1296

The p-value for testing the significance of the regression model is

Quizplus · Accepted Answer

To test the significance of the regression model, we use the F-test, where the null hypothesis is that all regression coefficients are equal to zero, and the alternative hypothesis is that at least one regression coefficient is not equal to zero. Based on the provided sum of squares, we can calculate the F-statistic as (4900-1296)/3 / (25-4) = 63.33, which corresponds to a p-value less than .01. Therefore, we reject the null hypothesis and conclude that the regression model is significant at the .01 level of significance.

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