Adjusted R-squared \(\bar{R}^{2}\)

Source: R/R2.R

Calculates the adjusted coefficient of determination $$ \bar{R}^{2} = 1 - \left(\frac{RSS / \left( n - k \right)} {TSS / \left( n - 1 \right)} \right) = 1 - \left( 1 - R^2 \right) \frac{n - 1}{n - k} . $$

Rbar2(X, y)

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.

Value

Returns the adjusted coefficient of determination \(\bar{R}^{2}\) .

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(), R2(), RMSE(), 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"]]
Rbar2(X = X, y = y)

#> [1] 0.08192585

# Multiple regression----------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, -ncol(X)]
Rbar2(X = X, y = y)

#> [1] 0.3207018