12 Polynomials

Associations in the social world are not necessarily linear. The graph below shows this quite clearly for the case of life expectancy at birth and health expenditures per capita. OLS regression assumes a linear relationship between the dependent variable and the independent variables. However, if the relationship is nonlinear, then OLS regression will produce biased estimates of the coefficients.

There are two ways to address this problem: polynomial regression and transformations of variables.Polynomial regression involves adding polynomial terms to the regression model. For example, if the relationship between life expectancy and health expenditures is quadratic, then we could add a term for the square of health expenditures to the model. Transformations of variables involve transforming the independent or dependent variables (or both) before running the regression. For example, if the relationship between life expectancy and health expenditures is logarithmic, then we could take the logarithm of both variables before running the regression.

Today, we will learn about both of these methods. We will also discuss the pros and cons of each method.

Lecture slides.