There are several appropriate evaluation methods for regression models. Let's discuss a few commonly used ones:

  1. Mean Squared Error (MSE): MSE measures the average squared difference between the predicted and actual values. It calculates the average error for all the data points, giving more weight to larger errors. Lower values indicate better model performance.

  2. Root Mean Squared Error (RMSE): RMSE is the square root of the MSE and provides an interpretable scale as it is in the same units as the dependent variable. It has the same interpretation as MSE, with lower values indicating better model performance.

  3. Mean Absolute Error (MAE): MAE measures the average absolute difference between the predicted and actual values. It calculates the average error for all the data points, irrespective of the direction of errors. Like MSE, lower values of MAE indicate better model performance.

  4. R-squared (R²) or Coefficient of Determination: R-squared measures the proportion of the variance in the dependent variable that is predictable from the independent variables. It ranges from 0 to 1, where 0 indicates the model does not explain the variance at all, and 1 indicates a perfect fit. However, R-squared may not be reliable when dealing with complex models or overfitting.

  5. Adjusted R-squared: Adjusted R-squared penalizes complexity in regression models by adjusting for the number of predictors. It takes into account the increase in explained variance associated with the addition of each predictor. Higher values generally indicate better model fit.

  6. Cross-Validation: Cross-validation techniques such as k-fold or leave-one-out cross-validation can be used to assess the performance of regression models. These methods help evaluate how well the model performs on unseen data by splitting the available data into training and testing subsets.

  It is generally recommended to use a combination of evaluation methods to get a comprehensive understanding of the model's performance and choose the one most relevant to the specific problem at hand.