Question

  Education Level. Age. Female

Education level. 1   

Age -0.780841825. 1.

Female. -0.055985622 0.051903605 1

1. Using the correlation matrix above, do you believe there might be a problem with multi-collinearity in the multiple regression model in Activity One? If so, with which variables?

2. b) What would happen to the R-squared if you now took “gender” out of the model?

3. c) If you now removed “education level” and “gender”, what type of regression analysis

   would you now have?

Answer 1

Given Correlation Matrix:

(A) Yes,there is a problem with multi-collinearity in the multiple regression model.

   From the correlation matrix,we can say that there is a fairly strong correlation (-0.78081825) between Age and Education_Level.This is the sign of Multicollinearity

(B)

• R² = 1-(Residual sum of squares/Total sum of squares). Therefore whenever Residual sum of squares increases R² increases.
• In this case,the variable Female has no correlation with any other 2 variables Education_Level and Age.From this we can conclude that R² may increase if we remove Gender out of the model.

(C)

If the 2 Variables Education_Level and Age are removed,then the regression analysis with one variable will be SIMPLE LINEAR REGRESSION MODEL.