In testing the significance of a multiple regression model in which there are three independent variables,the null hypothesis is:
A)$H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 1$
B) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 }$
C) $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$
D) $H _ { 0 } : \beta _ { 0 } = \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } \neq 0$

Question

Quizplus · Accepted Answer

The null hypothesis for testing the significance of a multiple regression model is that all the regression coefficients (β's) are equal to 0, which means that none of the independent variables have a significant effect on the dependent variable. Therefore, the correct null hypothesis in this case is $H _ { 0 } : \beta _ { 1 } = \beta _ { 2 } = \beta _ { 3 } = 0$. Choice A and B are incorrect because they assume that the regression coefficients are equal to 1, which may not be the case. Choice D is also incorrect because it assumes that the coefficients are not equal to 0, which is not the null hypothesis for testing the significance of the model.

In Testing the Significance of a Multiple Regression Model in Which