59. Explain the concept of curvilinear regression model.
Answer: Linear regression models are not appropriate for every situation. A scatter chart of the data might show a nonlinear relationship, or the residuals for a linear fit might result in a nonlinear pattern. In such cases, a nonlinear model is proposed to explain the relationship. For instance, a second-order polynomial model would be:
Y = β0 + β1X + β 2X2 + ε
Sometimes this is called a curvilinear regression model. In this model, β
1 represents the linear
effect of X on Y, and β
2 represents the curvilinear effect. However, although this model appears
to be quite different from ordinary linear regression models, it is still linear in the parameters. In other words, all terms are a product of a beta coefficient and some function of the data, which are simply numerical values. In such cases least squares can still be applied to estimate the