rregressionlinear-regressionlm

How to obtain RMSE out of lm result?

I know there is a small difference between $sigma and the concept of root mean squared error. So, i am wondering what is the easiest way to obtain RMSE out of lm function in R?

randomData = ggplot2::diamonds

res <- lm(randomData$price ~ randomData$carat +
                         randomData$cut + randomData$color +
                         randomData$clarity + randomData$depth +
                         randomData$table + randomData$x +
                         randomData$y + randomData$z)

length(coefficients(res))
## [1] 24

The lm object contains 24 coefficients, and I cannot make my model manually anymore. So, how can I evaluate the RMSE based on coefficients derived from lm?

Solution

  • Residual sum of squares:

    RSS <- c(crossprod(res$residuals))

    Mean squared error:

    MSE <- RSS / length(res$residuals)

    Root MSE:

    RMSE <- sqrt(MSE)

    Pearson estimated residual variance (as returned by summary.lm):

    sig2 <- RSS / res$df.residual

    Statistically, MSE is the maximum likelihood estimator of residual variance, but is biased (downward). The Pearson one is the restricted maximum likelihood estimator of residual variance, which is unbiased.

    Remark