Let say you have three variables
X1, X2, and Y, all normally distributed, zero mean, unit variance.
When you build a simple linear regression using:
Y ~ X1, the R-Squared is
Y ~ X2, the R-Squared is
So my question is: what are the bounds on R-squared when you use both variables? (
Y ~ X1 + X2)
My gut instinct is that you can roughly say
- The max bound would exist if the features are orthogonal, so
0.03is the max
- The min bound would exist if
X2contains all the information of
0.02is the min
Is this correct? What is the mathematical proof for the bounds?