Consider the first-order regression model $\hat{ y } $ = 15 + 6x₁+ 5x₂ + 4x₁x₂. A unit increase in x1 increases the value of y on average by: A) 5. B) 30. C) 26. D) an amount that depends on the value of x₂.

Question

Quizplus · Accepted Answer

The correct answer is D because the model includes an interaction term between $x_1$ and $x_2$ ($4x_1x_2$). This means the effect of a unit increase in $x_1$ on $\hat{y}$ is not constant but depends on the value of $x_2$. Specifically, the effect of $x_1$ is $6 + 4x_2$, which varies with $x_2$.

Consider the First-Order Regression Model y^\hat{ y } y^​ = 15 + 6x1 + 5x2 + 4x1x2

Consider the First-Order Regression Model $\hat{ y }$ = 15 + 6x₁+ 5x₂ + 4x₁x₂