What is the difference between linear and curvilinear regression?

What is the difference between linear and curvilinear regression?

• A. Curvilinear fits a curved line
• B. Linear fits a curved line
• C. Linear fits a straight line
• D. Curvilinear is non-parametric

Answer: (C)

The main idea is the shape of the relationship between the predictor and the outcome. Linear regression assumes a straight-line relationship, described by y = β0 + β1x, and finds the best-fitting straight line. Curvilinear regression, on the other hand, allows curvature in the relationship (for example, using x^2 terms or splines) to capture a bending pattern in the data. So the simplest, most direct way to state the difference is that linear regression fits a straight line, while curvilinear regression fits a curved line. Note that curvilinear models can be either parametric (like polynomials) or non-parametric (like splines), so the idea of non-parametric isn’t inherently tied to curvilinear.

The main idea is the shape of the relationship between the predictor and the outcome. Linear regression assumes a straight-line relationship, described by y = β0 + β1x, and finds the best-fitting straight line. Curvilinear regression, on the other hand, allows curvature in the relationship (for example, using x^2 terms or splines) to capture a bending pattern in the data. So the simplest, most direct way to state the difference is that linear regression fits a straight line, while curvilinear regression fits a curved line. Note that curvilinear models can be either parametric (like polynomials) or non-parametric (like splines), so the idea of non-parametric isn’t inherently tied to curvilinear.