R Squared Complete

README.md

@@ -13,6 +13,24 @@ Random Forest is a team of Decision Trees.
 
 # Evaluation Regression Models
 
-## R-Squared Intitution
+## R-Squared
 
-SS<sub>res</sub> = SUM (y<sub>i</sub> - y<sub>pred<sub>i</sub></sub>)<sup>2</sup>
+SS<sub>res</sub> = SUM (y<sub>i</sub> - y<sub>pred<sub>i</sub></sub>)<sup>2</sup>
+SS<sub>tot</sub> = SUM (y<sub>i</sub> - y<sub>avg<sub>i</sub></sub>)<sup>2</sup>
+
+R<sup>2</sup> = 1 - (SS<sub>res</sub>/SS<sub>tot</sub>)
+
+It tells how good is our best fit line compared to average line
+Ideal: R<sup>2</sup> = 1
+R<sup>2</sup> can be negative when SS<sub>res</sub> fits daughter worse than the average line. It means model is completely broken
+
+## Adjusted R-Squared
+
+Whenever a third variable or more variable is added to the regression model, SS<sub>res</sub> keeps minimizing and R<sup>2</sup> will never decrease, even if the third variable does not affect the prediction or negatively affect the prediction as there is always a co-relation between data. So problem is we can add variable and we will not know if it helped our model or not.
+
+Adjusted R<sup>2</sup> = 1 - (1 - R<sup>2</sup>)((n-1)/(n-p-1))
+
+ p = number of regressors
+ n = sample size
+
+ Adjusted R<sup>2</sup> has a penalizing factor, it penalizes for adding a factor that dont help the model