R-square, Adjusted R-square

R-square

- Increasing the number of X-variables, increases R-square.

- Varies from 0 to 1

- Proportion of variation in the Y variable explained  by the regression model.

- Values closer to 1 indicate a good fit.

 

‘Overall’ variation in Y variable : ‘Total’ Sum of Squares

‘Explained’ variation in Y variable : ‘Regression’ Sum of Squares

‘Unexplained’ variation in Y variable : ‘Residual’ Sum of Squares

 

 The regression model can explain about 47.45% variation in the House Prices.

 The remaining variation goes unexplained.

Adjusted R-square

 Mere addition of X variables always increases R-square.

 Adj. R-square adjusts the R-square for the number of X variables in the model.

 Better to use the Adj. R-square.

 

Importance of the Normality assumption about errors

- Errors are equally distributed with the mean of zero (constant std).