Question

Consider the multiple regression model E(Y|X₁ X₂) = β₀ + β₁X₁ + β₂X₂ + β₃X₁X₂

Can we interpret β₁ as the change in the conditional mean response for a unit change in X₁ holding all the other predictors in the model fixed?

Group of answer choices

a. Yes, because that is the traditional way of interpreting a regression coefficient.

b. Yes, because the response variable is quantitative and thus the partial slopes are interpreted exactly in that manner.

c. No, because the error term is absent in the specification of the model.

d. No, because an interaction term is present, and the interaction involves X₁

Answer 1

Solution:

Consider the multiple regression model E(Y|X₁ X₂) = β₀ + β₁X₁ + β₂X₂ + β₃X₁X₂

Can we interpret β₁ as the change in the conditional mean response for a unit change in X₁ holding all the other predictors in the model fixed?

Ans:

b. Yes, because the response variable is quantitative and thus the partial slopes are interpreted exactly in that manner.

because β₁ is a coefficient of X1 which can represent the slope of regression line it means that β₁ is the value which make change Y when the value of x is one unit .

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