Coefficient of Determination \(R^2\)

Calculates the coefficient of determination using $$ R^2 = 1 - \frac{\textrm{Residual sum of squares}} {\textrm{Total sum of squares}} $$ or $$ R^2 = \frac{\textrm{Explained sum of squares}} {\textrm{Total sum of squares}} . $$

R2(X, y, fromRSS = TRUE)

Arguments

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.
fromRSS	Logical. If TRUE, calculates the coefficient of determination from RSS. If FALSE, calculates the coefficient of determination from ESS.

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(), .R2fromESS(), .R2fromRSS(), .RMSE(), .Rbar2(), .model(), MSE(), RMSE(), Rbar2(), model()

Author

Ivan Jacob Agaloos Pesigan

Examples

# Simple regression------------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
X <- X[, c(1, ncol(X))]
y <- jeksterslabRdatarepo::wages.matrix[["y"]]
R2(X = X, y = y)
#> [1] 0.08263864

# Multiple regression----------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, -ncol(X)]
R2(X = X, y = y)
#> [1] 0.3233388