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Machine learning : R Squared mathod Archive - helpcode.me

Machine learning : R Squared Regression Archive

The R Square is Used to Decide the Linear Regression is fitted or not or giving best Predictions.
Actually in Linear Regression Graph , we find the Line which has less distance from the Data Points. You Can view in The Diagram below .





Formula Of R square is 
R^2 = 1 - SSres / SStot

SSres = SUM ( Yi - Yi^)^2 

SStot = SUM ( Yi - Yavg)^2 

 


if  Y = b0 + b1 * X1  when having the only one dependent term in Linear equation R square will Goodness of fit hence greater the prediction .

 Y = b0 + b1 * X1 +  b2 * X2 , when new variable add to the Linear regression i.e. X2 and b2 then value of R square will not decrease because the value of SSres remain minimum so that the R square is increasing when added new term so that we get new term i.e. Adjusted R square . 


 Adjust R Square 


Adj R ^2 = 1 - ( 1 - R ^2 ) (n - 1) / ( n - p - 1)

P = No of regressor ( independent variable )

n =  sample size 


when P is increase the ( adding new variable ) the ( n - p -1 ) this part will be decrease so that ration increase mean the , ( 1 - R ^2 ) (n - 1) / ( n - p - 1) this part will increase so that hole term 1 - ( 1 - R ^2 ) (n - 1) / ( n - p - 1) i.e. 1- increasing term = Decrease .so the value of Adj R square will Decreasing when adding the new variable which in only R square will increase the R square . So that the prediction will work fine in Linear Regression .The Model become Robust . 



  

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