What type of regression model is represented by the equation y=B0+B1x1+B2x1^2+e?

The equation y = B0 + B1x1 + B2x1^2 + e represents a second-order regression model due to the inclusion of the x1 squared term (x1^2) in the equation. In regression analysis, a second-order model is characterized by having a quadratic term, which allows the relationship between the independent variable (x1) and the dependent variable (y) to be represented as a parabola rather than a straight line.

This quadratic term enables the model to capture more complex relationships, such as when the effect of x1 on y may increase or decrease at different levels of x1. The presence of both the linear term (B1x1) and the quadratic term (B2x1^2) means that the model can account for curvature in the data, which is a crucial aspect of non-linear modeling.

In contrast, a first-order model only includes linear terms, while a linear model typically refers to models that do not include any polynomial terms greater than one. A logistic model is designed for binary outcomes and uses an S-shaped curve; therefore, it does not apply here. The presence of the squared term clearly indicates that this is a second-order model, which is why this option