When a linear regression models shows bad fit due to nonlinearity, one option is to add polynomial terms for one or more covariates. For example, with one covariate $X_1$ $Y_i = \beta_0 + \beta_1X_{i,1} + \beta_2X^2_{i,1} + \dots + \beta_dX_{i,1}^d$ Heuristics for how to fit the model include: - add terms of higher order until they are no longer statistically significant - start with some high guess and remove terms until all are statistically significant Note that these heuristics will not always produce equivalent results. In general, it is considered a bad idea to include a higher order term without also including all lower order terms. In [[R]] ```R lm_mod <- lm(y ~ x + I(x^2) + ..., data=data) ```