Summation and coefficient of determination

Question

Hi Support,

I recently started the AI course, and while going through the learning paths, I came across the regression and couldn't understand the given formula. How it is calculated and from where ȳ is came from in the given formula R2 = 1- ∑(y-ŷ)2 ÷ ∑(y-ȳ)2.

Can the support team help to understand the above formula and how could that calculated in ice cream example.

Thanks in advance.

Answer 1

Hi 999,

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

From your question we understand that you are in the following

Learn path: Microsoft Azure AI Fundamentals: AI Overview

The formula is from the following module: Fundamentals of machine learning.

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

R2 = 1- ∑(y-ŷ)2 ÷ ∑(y-ȳ)2

R2 = 1- 36 / 740.8336

R2 = 1-0.04859391

R2= 0.951

As given in the Learn Path document, R2 value is 0.95.

I hope you understand!

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