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R-Squared Intuition

R Squared

• SS_res = SUM(y_i - y^_i)²

• SS_tot = SUM(y_i - y_avg)²

• R² = 1 - SS_res/SS_tot
  R2 - Goodness of fit (greater is better)

• NOTE:-

  If the value of R is:-

    1.0 = Perfect fit (suspicious)
    ~0.9 = Very good
    <0.7 = Not great model
    <0.4 = Terrible
    <0 = Model makes no sense for this data
  

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Adjusted R-Squared Intuition

Adjusted R Squared

• Note:- R2 - Goodness of fit (greater is better)

Problem:

 y^ = b0 + b1X1 + b2X2

SStot doesn’t change

SSres will decrease or stay the same (This is because of Ordinary Least Squares: SSres-> Min)

Solution:

 Adj R2 = 1 - (1 - R2) * (n - 1)/(n - k - 1)

k - number of independent variables
n - sample size

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