Abstract [ Reference]

In regression-based supervised machine learning, the label predicted by the model is a numeric value.

Training Regression Models

1. Split the data (randomly) to create a training dataset and a validation dataset.
2. Use a regression algorithm (perhaps linear regression) to fit the training data to a model.
3. Use the validation dataset to test the model by predicting labels for the features.
4. Evaluate the model’s performance by comparing the known actual labels in the validation dataset to the labels that the model predicted.
5. Repeat with different algorithms and/or parameters.

Regression Model Evaluation Metrics

Mean Absolute Error (MAE)

The level by which the prediction varied from the actual.

Mean Squared Error (MSE)

Squares the individual errors to “amplify” larger errors.

• Useful for determining, along with the MAE, if the model makes many—but smaller—errors or fewer—but larger—errors.
• Because it squares the errors, it does not represent variance.

Root Mean Squared Error (RMSE)

The square root of the MSE (to get back to variance).

Coefficient of Determination ($R^2$)

Measures the proportion of variance in the validation results that can be explained by the model as opposed to some anomalous aspect of the validation data.

• It determines how fit the model is to the data.
• It is the sum of squared differences between predicted and actual labels with the sum of squared differences between the actual label values and the mean of actual label values:
• $R^2=1-\sum_{} {(y -\hat{y})^2} / \sum_{} {(y-\hat{y})^2}$
• The resulting value between 0 and 1 describes the proportion of the variance explained by the model.
• The closer the value is to $1$, the better the model fits the data.