Coefficient of Determination \(R^2\) (from \(ESS\))

Source: R/R2.R

Calculates the coefficient of determination using $$ R^2 = \frac{\textrm{Explained sum of squares}} {\textrm{Total sum of squares}} . $$

.R2fromESS(ESS = NULL, TSS = NULL, X, y)

Arguments

ESS

Numeric. Explained sum of squares.
TSS

Numeric. Total sum of squares.
X

n by k numeric matrix. The data matrix \(\mathbf{X}\) (also known as design matrix, model matrix or regressor matrix) is an \(n \times k\) matrix of \(n\) observations of \(k\) regressors, which includes a regressor whose value is 1 for each observation on the first column.
y

Numeric vector of length n or n by 1 matrix. The vector \(\mathbf{y}\) is an \(n \times 1\) vector of observations on the regressand variable.

Value

Returns the coefficient of determination \(R^2\) .

Details

If ESS = NULL, ESS is computed using ESS() with X and y as required arguments. If TSS = NULL, TSS is computed using TSS() with y as a required argument. If ESS and TSS are provided, yhat, ybar, betahat, X, and y are not needed.

References

Wikipedia: Residual Sum of Squares

Wikipedia: Explained Sum of Squares

Wikipedia: Total Sum of Squares

Wikipedia: Coefficient of Determination

See also

Other assessment of model quality functions: .MSE(), .R2fromRSS(), .RMSE(), .Rbar2(), .model(), MSE(), R2(), RMSE(), Rbar2(), model()

Author

Ivan Jacob Agaloos Pesigan