Root Mean Squared Error (from \(\mathrm{RSS}\))

Source: R/MSE.R

Calculates the root mean squared error \(\left( \mathrm{RMSE} \right)\) using $$ \mathrm{RMSE} = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} \left( \mathbf{y} - \mathbf{X} \boldsymbol{\hat{\beta}} \right)^{2}} \\ = \sqrt{\frac{1}{n} \sum_{i = 1}^{n} \left( \mathbf{y} - \mathbf{\hat{y}} \right)^{2}} \\ = \sqrt{\frac{\mathrm{RSS}}{n}} . $$

.RMSE(MSE = NULL, X, y)

Arguments

MSE

Numeric. Mean square error.
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 root mean squared error.

Details

If MSE = NULL, MSE is computed using MSE() with X and y as required arguments. If MSE is provided, X, and y are not needed.

References

Wikipedia: Root-mean-square deviation

See also

Other assessment of model quality functions: .MSE(), .R2fromESS(), .R2fromRSS(), .Rbar2(), .model(), MSE(), R2(), RMSE(), Rbar2(), model()

Author

Ivan Jacob Agaloos Pesigan