We would always use a quadratic term in a regression when we think there is a nonlinear relationship between the dependent and independent variable.

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Including a quadratic term in a regression model is one way to capture a nonlinear relationship, but it's not always used. Other methods, such as transformation of variables or using more complex models like polynomial regression with higher degrees, splines, or non-parametric models, might be more appropriate depending on the specific nature of the nonlinearity.

We Would Always Use a Quadratic Term in a Regression