Question

Explain the difference between the meaning of r² and the meaning of the adjusted r² in a multiple regression model. Would it be permissible to eliminate any or all “outliers” to increase the value of the adjusted r²? Why or why not?

Answer 1

Solution

The R-square measures the percentage of variation explained by the model. It help s to decide whether fitted model is good or not. If value of R-square near to 1 then we say that model is good or 100% variation is explain by model.

Now for Adjusted R-Square

Suppose we have 10 independent variables the importance these indepndent variable decided by the Adjusted R-Square at the time of model building. For example if we remove one of the independent variable from the model if our Adjusted R-Square is decreased then we say that we should not remove that variable or if  Adjusted R-Square is increased then we will remove that variable.

Would it be permissible to eliminate any or all “outliers” to increase the value of the adjusted r2? Why or why not?

Ans : If your data contain outliers then first we need to check that whether these outlier points affecting the value of Adjusted R-Square . If we remove the outlier points and our Adjusted R-Square decrease significantly then we have to keep these outliers in the model we can not remove them from the model.