Question

What is the coefficient of determination? how is it calculated? what does it measure? what values does it take on?

Answer 1

The coefficient of determination (denoted by $R^{2}$) is a key output of regression analysis.

It is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.

The coefficient of determination (R2) for a linear regression model with one independent variable is:

$R^{2}$ = { ${ (\frac{1}{N}) *$ Σ $[ ( x_{i} - x) *( y_{i} -y) /$ (σx * σy )] }^2

where N is the number of observations used to fit the model, Σ is the summation symbol, $x_{i}$ is the x value for observation i, x is the mean x value, $y_{i}$ is the y value for observation i, y is the mean y value, σx is the standard deviation of x, and σy is the standard deviation of y.