Metrics for Assessing Linear Regression

What does R^2 measure in a regression model?

• The average size of prediction errors.

• The proportion of variance in the dependent variable explained by the independent variables.

• The total error in the model.

• The sensitivity of the model to changes in the training data.

Which metric penalizes the addition of irrelevant predictors in a regression model?

• R^2

• Adjusted R^2

• Mean Absolute Error (MAE)

• Mean Squared Error (MSE)

How is Mean Absolute Error (MAE) calculated?

• By squaring the residuals, averaging them, and taking the square root.

• By dividing the sum of absolute value of the residuals by the number of data points.

• By dividing the total error by the number of predictors.

• By dividing the total error by the mean of observed values.

What does a high standard deviation of residuals indicate?

• The model is underfitting the data.

• The model's predictions are consistently close to the observed values.

• The model’s predictions have large errors on average.

• The independent variables are uncorrelated.

When is the Adjusted R^2 value likely to decrease?

• When a useful predictor is added to the model.

• When an irrelevant predictor is added to the model.

• When the total sum of squares (SST) decreases.

• When the number of observations increases.

Which metric is expressed as a percentage and helps compare models across datasets with different scales?

• MSE

• MAPE

• RMSE

• R^2

Why could RMSE be preferred over MSE?

• Because RMSE is easier to calculate by hand.

• Because RMSE penalizes large errors less than MSE.

• Because RMSE is in the same units as the dependent variable, making it more interpretable.

• Because RMSE gives a lower error value than MSE.

What is the key limitation of R^2?

• It cannot be used for evaluating regression models.

• It decreases when more predictors are added to the model.

• It does not account for the number of predictors, potentially encouraging overfitting.

• It is not affected by changes in the training data.

What does the MSE metric do?

• It calculates the average absolute difference between predicted and actual values.

• It measures the average squared difference between predicted and actual values, penalizing large errors more heavily.

• It calculates the percentage of variance explained by the model.

• It calculates the sum of residuals.

Which of the following is true about the standard deviation of residuals?

• It is always larger than R^2.

• It is expressed as a percentage.

• It provides the average distance between actual and predicted values, in the same units as the dependent variable.

• It decreases as the model complexity increases.