Which of the following statement(s) can be true post adding a variable in a linear regression model? 1. R-Squared and Adjusted R-squared both increase 2. R-Squared increases and Adjusted R-squared decreases 3. R-Squared decreases and Adjusted R-squared decreases 4. R-Squared decreases and Adjusted R-squared increases

The correct answer is: D. None of the above

R-squared is a measure of how well the data fits the model. Adjusted R-squared is a measure of how well the data fits the model, taking into account the number of variables in the model.

If we add a variable to a linear regression model, R-squared can either increase or decrease. It will increase if the new variable is correlated with the response variable and not correlated with the other variables in the model. It will decrease if the new variable is not correlated with the response variable or is correlated with the other variables in the model.

Adjusted R-squared will always decrease when we add a variable to a linear regression model. This is because adjusted R-squared takes into account the number of variables in the model. When we add a variable, we are increasing the number of parameters in the model, which will decrease the adjusted R-squared.

Therefore, none of the statements in the question can be true post adding a variable in a linear regression model.