In the model Y_i = ?₀ + ?₁X₁+ ?₂X₂ + ?₃(X₁ × X₂)+ u_i, the expected effect $\frac { \Delta Y } { \Delta X _ { 1 } }$ is A)?₁+ ?₃X₂. B)?₁. C)?₁+ ?₃. D)?₁+ ?₃X₁.

Question

Quizplus · Accepted Answer

The expected effect $\frac { \Delta Y } { \Delta X _ { 1 } }$ includes the direct effect of $X_1$ on $Y$ and the interaction effect of $X_1$ with $X_2$. Therefore, it includes both the coefficient of $X_1$ and the coefficient of the interaction term $X_1 \times X_2$, which are represented by ?₁ and ?₃X₂, respectively.

In the Model Yi = ?0 + ?1X1 + ?2X2 ΔYΔX1\frac { \Delta Y } { \Delta X _ { 1 } }ΔX1​ΔY​

In the Model Y_i = ?₀ + ?₁X₁+ ?₂X₂ $\frac { \Delta Y } { \Delta X _ { 1 } }$