Question

Which of the following statements is true?

1. When we add a new variable to a linear regression, as long as the R-squared increases by at least a tiny decimal, we should keep that variable
2. We use variable selection techniques to help remove unnecessary variables in our model and reduce overfitting
3. Backward stepwise regression is a technique where we start with no variables and we choose the next best addition at each step
4. Forward stepwise regression is a technique where you start with all the variables in the model and slowly remove one variable at a time, stopping whenever you have removed all variables that are not contributing substantially

Answer 1

The true statement is that we use variable selection techniques to remove unnecessary variables and reduce overfitting.

Step-by-step explanation:

The true statement from the given options is: 2. We use variable selection techniques to help remove unnecessary variables in our model and reduce overfitting.

Variable selection techniques are used in regression analysis to identify the most important variables that contribute significantly to the model. This helps to simplify the model and prevent overfitting.

Examples of variable selection techniques include stepwise regression, which can be both forward (starting with all variables and removing them one by one) or backward (starting with no variables and adding them one by one) and best subset selection which evaluates all possible combinations of variables to find the best one. These techniques aim to find the best subset of variables that improve the model's performance.