The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant? A) Only x₁ _B)Only x₃ _C)_x₁ and x₂ _D)_x₂ and x₃

Question

Quizplus · Accepted Answer

In order to determine whether an explanatory variable is individually significant, we need to look at its coefficient's p-value. If the p-value is less than 0.05, then we can reject the null hypothesis that the coefficient is zero and conclude that the explanatory variable is significant at the 5% level. Looking at the table, we can see that the p-values for , _{, x₁, x₂, and x₃ are all less than 0.05. Therefore, these explanatory variables are individually significant at the 5% level.

Option A is incorrect because x₁ has a significant coefficient, while _{is not significant.

Option B is incorrect because x₃ has a significant coefficient, while} is not significant.

Option D is incorrect because x₃ has a significant coefficient, but _x₂ does not.

Therefore, the best choice is C because it includes all individually significant explanatory variables.}

The Accompanying Table Shows the Regression Results When Estimating Y