When estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,you wish to test H₀: β₁ = β₂ = 0 versus H_A: At least one β_i= 0.The value of the test statistic is F_(2,20) = 2.50 and its associated p-value is 0.1073.At the 5% significance level,the conclusion is to ____________________________________________________________. A) reject the null hypothesis and conclude that x₁ and x₂ are jointly significant B) reject the null hypothesis and conclude that x₁ and x₂ are not jointly significant C) not reject the null hypothesis and conclude that x₁ and x₂ are jointly significant D) not reject the null hypothesis and conclude that x₁ and x₂ are not jointly significant

Question

Quizplus · Accepted Answer

Since the p-value is greater than the significance level of 5%, we fail to reject the null hypothesis. Therefore, we conclude that there is not sufficient evidence to suggest that at least one of the coefficients is not zero, and thus we cannot conclude that x₁ and x₂ are jointly significant. Option D reflects this conclusion.

When Estimating Y = β0 + β1x1 + β2x2

When Estimating Y = β₀ + β₁x₁ + β₂x₂