How do you handle non-linearity in a multiple regression context?

3 Add Polynomials

Polynomial regression is another technique to handle non-linearity. By adding polynomial terms (like squared or cubed terms) to your model, you can fit a wider range of curves. For example, if you suspect a quadratic relationship, you can include a squared term of the predictor in your model using predictor^2 . This approach can provide a better fit but beware of overfitting—where your model is too tailored to the sample data and may not generalize well to new data.

4 Consider Splines

Splines introduce flexibility by dividing the data into pieces and fitting a separate line or polynomial to each segment. They can adapt to the data's form and are particularly useful when the relationship changes at certain points. Implementing splines involves selecting knots, which are the points where the pieces join. You'll need to balance having enough knots to fit the data well without having so many that the model becomes overly complex.

5 Use Nonlinear Models

Sometimes, a linear model just won't do. In such cases, consider switching to a nonlinear model that can naturally handle curvilinear relationships. Nonlinear models are designed for specific types of non-linearity and can be more theoretically appropriate for certain datasets. However, they often require more complex estimation techniques and a deeper understanding of the underlying relationships in your data.

6 Regularize Carefully

Regularization techniques like Ridge or Lasso regression can help when dealing with non-linearity by penalizing large coefficients in your model. This can prevent overfitting to the training data and improve the model's performance on new data. Regularization can be particularly helpful when you've added polynomial terms or interaction effects to capture non-linearity. Just remember to tune the regularization parameter carefully using cross-validation to find the right balance between bias and variance.

7 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?