67.1k views
0 votes
For the multiple regression Y=β₀+β₁X+β₂X² +u,β₁ can be interpreted as the effect of one unit increase in X on Y.

a. True
b. False

User Nalina
by
8.6k points

1 Answer

3 votes

Final answer:

The statement that \u03b21 in the equation Y=\u03b20+\u03b21X+\u03b22X2 +u can be interpreted as the effect of a one unit increase in X on Y is false because the presence of the X squared term means that \u03b21 cannot be interpreted in isolation.

Step-by-step explanation:

In the context of the multiple regression equation Y=\u03b20+\u03b21X+\u03b22X2 +u, \u03b21 does not solely represent the effect of a one unit increase in X on Y when X is squared in the model. This is because \u03b21 only indicates the immediate effect of a one unit change in X when \u03b22 equal to zero.

However, when considering the full equation, \u03b21 is complicated by the presence of the \u03b22 term, which alters the relationship between X and Y non-linearly. Therefore, the statement is False since in the presence of the \u03b22X2 term, \u03b21 can't be interpreted in isolation as the change in Y for a one unit increase in X.

In multiple regression, the coefficient β1 represents the effect of a one unit increase in the independent variable (X) on the dependent variable (Y), holding other variables constant. Therefore, it can be interpreted as the effect of a one unit increase in X on Y.

User Gcastro
by
9.4k points