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Regression Error Metrics
In Simple Linear Regression, the objective is to determine the optimal line that predicts the dependent variable Y based on the independent variable X.
To assess the effectiveness of the regression model, we rely on error metrics to measure the accuracy of the model’s predictions against the actual data.
Understanding these metrics is essential for evaluating the performance of the model and pinpointing opportunities for refinement.
1. Mean Absolute Error (MAE)
The Mean Absolute Error (MAE) calculates the average of the absolute differences between predicted and actual values. It is easy to understand and interpret.
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2. Mean Squared Error (MSE)
The Mean Squared Error (MSE) calculates the average of the squared differences between actual and predicted values. Squaring the errors penalizes larger mistakes more than smaller ones.
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3. Root Mean Squared Error (RMSE)
The Root Mean Squared Error (RMSE) is the square root of the MSE. It gives the error in the same units as the dependent variable, making it easier to interpret.
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4. R-squared (R²)
The R-squared (R²) metric measures how well the regression model fits the data. It indicates the proportion of variance in the dependent variable that is explained by the independent variables. An R² of 1 indicates a perfect fit, while 0 indicates no explanatory power.
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5. Mean Absolute Percentage Error (MAPE)
The Mean Absolute Percentage Error (MAPE) calculates the average of the absolute percentage differences between actual and predicted values. It is often used when we want to express errors in percentage terms.
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Conclusion
Each of these metrics—MAE, MSE, RMSE, R², and MAPE—gives different insights into how well a regression model is performing. The choice of which error metric to use depends on the problem and how you want to interpret the performance:
- MAE is easy to understand and works well when the scale of errors is important.
- MSE and RMSE penalize large errors more, which can be useful when large errors are especially undesirable.
- R² is a good measure of model fit.
- MAPE is useful when you want to express errors as percentages.