# Quadratic Functions Offer Flexibility in Econometrics

Because economic relationships are rarely linear, you may want to allow your econometric model to have some flexibility. With a quadratic function, you allow the effect of the independent variable (*X*) on the dependent variable to change. As the value of *X* increases, the impact of the dependent variable increases or decreases.

The mathematical representation of an econometric model with a quadratic function is

If you estimate this type of regression, several outcomes are possible for your coefficients. However, the two most common results are as follows:

In the estimated regression

if both

are positive, then your estimated regression line looks like the one shown in part (a). If

then part (b) is an approximate depiction of the regression curve.

A total variable cost (TVC) or total cost (TC) curve may display the shape shown in part (a), whereas a short-run total product (TP) curve is likely to display the sort of behavior shown in part (b) if marginal product is diminishing at any level of input. (These concepts were covered in your microeconomics course.)