Coefficient of Determination

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Definition: 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


The coefficient of determination is r2 = SSR/SST


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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