# Statistical Advisor, Polynomial Multiple Regression

Use GENERAL REGRESSION MODELS(GRM), GENERAL LINEAR MODELS (GLM), or MULTIPLE REGRESSION. These chapters discuss various techniques for polynomial regression analysis. Other transformations of independent variables are also supported.

Polynomial (or 'fixed nonlinear') regression computes the relationship between a dependent variable with one or more independent (predictor) variables, and those independent variables squared, cubed, etc. For example, for one independent variable one could estimate the regression equation:

**y ^{2} = a + b_{1}*x +b_{2}*x^{2}**

Here, the dependent variable y is a linear function of x and x^{2}. Polynomial regression is common in cases when one wants to detect some curvilinearity in a relationship. For example, stress (the independent variable) may have a curvilinear relationship to performance on a complex task (dependent variable). For low to moderate stress, performance may increase, but as stress increases beyond moderate stress, performance may deteriorate. If so, the nonlinear (quadratic) component or regression coefficient in the regression equation would be significant.