When assumptions are violated, several strategies can be employed: 1. Transformations: Applying transformations like log or square root can address non-linearity and non-normality. 2. Robust Regression: This method reduces the influence of outliers. 3. Multivariate Techniques: Techniques like principal component analysis can address multicollinearity. 4. Advanced Models: Use more complex models like generalized linear models (GLMs) or mixed-effects models.