Learn about the key metrics, RMSE and R2, used to evaluate regression models in the Azure AI Fundamentals certification exam. Understand how these metrics assess model performance and help in making informed decisions.
Table of Contents
Question
What metrics you can use to evaluate a regression model? Select two correct options.
A. F1 score
B. root mean squared error (RMSE)
C. coefficient of determination (R2)
D. area under curve (AUC)
Answer
B. root mean squared error (RMSE)
C. coefficient of determination (R2)
Explanation
To evaluate a regression model, two widely used metrics are:
1. Root Mean Squared Error (RMSE):
RMSE is a popular metric for measuring the accuracy of a regression model. It calculates the average magnitude of the residuals (prediction errors) by taking the square root of the mean of the squared differences between the predicted and actual values. The formula for RMSE is:
RMSE = sqrt(mean((y_pred – y_actual)^2))
where y_pred represents the predicted values and y_actual represents the actual values.
RMSE provides a measure of how much the predicted values deviate from the actual values, with lower values indicating better model performance. It is sensitive to outliers and gives higher weight to larger errors due to the squaring operation.
2. Coefficient of Determination (R2):
R2, also known as R-squared, is another commonly used metric for evaluating regression models. It represents the proportion of variance in the dependent variable that can be explained by the independent variables in the model. R2 ranges from 0 to 1, with higher values indicating a better fit.
The formula for R2 is:
R2 = 1 – (SSR / SST)
where SSR is the sum of squared residuals and SST is the total sum of squares.
An R2 value of 1 indicates that the model perfectly explains all the variability in the dependent variable, while a value of 0 suggests that the model does not explain any of the variability. In practice, R2 values closer to 1 are desirable, but it’s important to consider other factors such as the complexity of the model and the interpretability of the coefficients.
Both RMSE and R2 provide valuable insights into the performance of a regression model. RMSE quantifies the average magnitude of the prediction errors, while R2 measures the proportion of variance explained by the model. By considering both metrics, you can assess how well the model fits the data and make informed decisions about model selection and refinement.
To evaluate a regression model, you can use: Root Mean Squared Error (RMSE) – This measures the average magnitude of the errors between predicted and actual values. A lower RMSE indicates a better fit. Coefficient of Determination (R²) – This indicates the proportion of variance in the dependent variable that is predictable from the independent variables. A higher R² value indicates a better fit.
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