Question

Which of the following statement is wrong about multiple linear regression?

a.Adding more predictors will give larger or equal R² on the training set.
b.Adding more predictors will give larger or equal R² on the test set.
c.Adding more predictors may give lower adjusted R² on the training set.
d.Using R² on the test set is a generic approach for assessing the performance of a regression.

Answer 1

The correct statement about multiple linear regression is option d. Using R² on the test set is not a generic approach for assessing the performance of a regression. Adding more predictors can increase R² on the training set, but may lower the adjusted R².

Step-by-step explanation:

The correct statement about multiple linear regression is option d. Using R² on the test set is not a generic approach for assessing the performance of a regression.

When it comes to multiple linear regression, adding more predictors will give a larger or equal R² on the training set (option a) because more predictors can increase the amount of explained variation in the dependent variable.

However, adding more predictors may give a lower adjusted R² on the training set (option c) as the adjusted R² accounts for the number of predictors used, and adding more predictors can potentially introduce noise or unimportant variables.

Using R² on the test set is not a generic approach for assessing the performance of a regression (option d) because the test set is typically used to evaluate how well the model generalizes to new, unseen data.

Other metrics like mean squared error (MSE) or cross-validation techniques are commonly used to assess the performance of a regression on the test set.