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.

Hence, this concludes the definition of Coefficient of Determination along with its overview.


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