# Coefficient of Determination - Meaning & Definition

Published by MBA Skool Team in Statistics Last Updated: October 03, 2023Read time:

## What is Coefficient of Determination?

A statistical measure to assess how well a model explains and predicts future outcomes.  Co-efficient of determination is commonly known as R-square.

Mathematical representation

 The simple linear regression equation is E(Y) = a + bX Where, a is the Y intercept of the regression line and b is the slope of the regression line. E(Y) is expected value for given X. Now, for linear regression SSR, SSE and SST are defined as, SST = total sum of squares = ∑(yi – ӯ)2 SSR = sum of squares due to regression= ∑ (ŷi – ӯ)2 SSE = sum of squares due to error = ∑ (yi – ŷi)2 SST = SSR +SSE The coefficient of determination is r2 = SSR/SST Where, SSR = sum of squares due to regression SST = total sum of squares

The value of co-efficient of determination varies between 0 and 1. The correlation is very strong the value of co-efficient will be near to one. If the value is near to zero, the regression model isn’t good enough to describe the data set.

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