In the quadratic regression model, y = α + β₁x + β₂x² + e, β₂ can be interpreted as the amount that y will be expected to change when the value of x is increased by one unit.

Question

Quizplus · Accepted Answer

In the quadratic regression model, $y = \alpha + \beta_1x + \beta_2x^2 + e$, the term $\beta_2$ (which corresponds to $\beta_{12}$ in the question) represents the change in the slope of the relationship between $y$ and $x$ for a one-unit change in $x$, not the change in $y$ itself. This is because $\beta_2$ is the coefficient of the quadratic term ($x^2$), indicating it affects the curvature of the model, not the linear change in $y$.

In the Quadratic Regression Model, Y = α + β1x

In the Quadratic Regression Model, Y = α + β₁x