R-squared calculation?

acarruthers

In Notebook 4, R² is calculated using cor(test_dat$default_rate, pred_deg5) ^ 2. Is this not squaring the correlation between y and y-hat, which is potentially different than R²?

ivonnem10

@acarruthers Great question! This is only true for a simple linear regression. When there's only one independent variable, squaring the correlation coefficient gives you the coefficient of determination, which is R²

dylarm

This is something I've wondered off and on again for some time and it appears that, while there might be some cases where the square of the correlation coefficient isn't necessarily the coefficient of determination, this case does seem to keep that true.

Edit: and I see @ivonnem10 answered at the same time.

ivonnem10

Here is a YouTube video in case you want to see the mathematical proof: https://www.youtube.com/watch?v=_pw6SDHOvkA