Coefficient of determination (R2) - Fundamentals of Machine Learning

Question

Hello

I would like to understand from where this ȳ is coming from in the R2 formula.(R2 = 1- ∑(y-ŷ)2 ÷ ∑(y-ȳ)2)

In the example of ice cream selling, I understood that it corresponds to the mean of actual label values (= the mean of the actual sales). So is it 121/6 = 20.16666? is this the right calculation?

Cause on my calculations, I found 0.96 whereas you stated 0.95 (In the case of the ice cream regression model, the R2 calculated from the validation data is 0.95.)

Thanks

Christophe Ristevski

Answer 1

Hi Chris,

Thanks for reaching out to us on Microsoft Q&A forum.

From the given formula R2 = 1- ∑(y-ŷ)2 ÷ ∑(y-ȳ)2

Where y = actual values, ŷ= predicted values, ȳ= mean of actual values = 121/6 = 20.16666 (Yes, you calculated correctly).

R2 = 1- ∑(y-ŷ)2 ÷ ∑(y-ȳ)2

R2 = 1- 36 / 740.8336

R2 = 1-0.04859391

R2= 0.951

So, R2 = 0.95 the validation value was correct as per the Learn Path document.

I hope you understand! Thank you.

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