2.2 The Statistical Sommelier: An Introduction to Linear Regression

2.2 The Statistical Sommelier: An Introduction to Linear Regression

Quick Question

Suppose we add another variable, Average Winter Temperature, to our model to predict wine price. Is it possible for the model’s R² value to go down from 0.83 to 0.80?

 No, the model's R² value can only decrease to 0.81 by adding new variables.  close
 No, the model's R² value can not decrease at all by adding new variables.   check
 Yes, the R² value could decrease to 0.80.  close
Check Show Solution

Explanation The model's R² value can never decrease from adding new variables to the model. This is due to the fact that it is always possible to set the coefficient for the new variable to zero in the new model. However, this would be the same as the old model. So the only reason to make the coefficient non-zero is if it improves the R² value of the model, since linear regression picks the coefficients to minimize the error terms, which is the same as maximizing the R².

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