Given the following regression equation ( Ŷ = 3.5 X ₁ + 2 X ₂ + 12), the coefficient for X ₁ would mean that A) two people who differ by one point on X ₁ would differ by 3.5 points on Ŷ . B) two people who differ by one point on X ₁ would differ by 3.5 points on Ŷ , assuming that they did not differ on X ₂. C) X ₁ causes a 3.5 unit change in the dependent variable. D) X ₁ is more important than X ₂.

Question

Quizplus · Accepted Answer

The coefficient of 3.5 for $X_1$ in the regression equation indicates the expected change in the dependent variable ($\hat{Y}$) for a one-unit change in $X_1$, assuming all other variables in the model are held constant. This means that if two individuals differ by one unit on $X_1$, their predicted values on $\hat{Y}$ would differ by 3.5 units, assuming no difference in $X_2$.

Given the Following Regression Equation ( Ŷ = 3