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KonstantinChe [14]
3 years ago
10

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

Mathematics
1 answer:
Evgen [1.6K]3 years ago
4 0
The coefficient of determination (denoted by R^{2}<span>) is a key output of </span>regression<span> analysis.

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

</span>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}<span> is the x value for observation i, </span>x<span> is the mean x value, </span>y_{i}<span> is the y value for observation i, </span>y<span> is the mean y value, σ</span>x<span> is the standard deviation of x, and σ</span>y <span>is the standard deviation of y.</span>
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