Given the regression model y = $\beta$₀ + $\beta$₁X₁ + $\beta$₂X₂ + $\beta$₃X₁² + $\beta$₄X₂² + $\varepsilon$,if we wish to test the significance of the independent variable X₂,the appropriate null hypothesis is: A)H₀: X₂ = 0 B)H₀: $\beta$₂ $\neq$ 0 C)H₀: $\beta$₂ $\neq$ X₂ D)H₀: $\beta$₂ = 0 E)H₀: $\beta$₂ - X₂ = 0

Question

Quizplus · Accepted Answer

The appropriate null hypothesis to test the significance of the independent variable X₂ is H₀: F1F1F1S1F1F1F10₂ = 0. This is because we want to test if there is a significant relationship between X₂ and the dependent variable, while holding all other independent variables constant. Therefore, we set the coefficient for X₂ equal to zero, implying that X₂ has no effect on the dependent variable, and compare the resulting model to the original model using an appropriate statistical test.

Given the Regression Model Y = β\betaβ 0 β\betaβ 1X1 β\betaβ

Given the Regression Model Y = $\beta$ ₀ $\beta$ ₁X₁ $\beta$