Root Mean Squared Error

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(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 root mean squared error.

References

Wikipedia: Root-mean-square deviation

See also

Other assessment of model quality functions: .MSE(), .R2fromESS(), .R2fromRSS(), .RMSE(), .Rbar2(), .model(), MSE(), R2(), 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"]]
RMSE(X = X, y = y)
#> [1] 7.56011

# Multiple regression----------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, -ncol(X)]
RMSE(X = X, y = y)
#> [1] 6.492972