How to obtain RMSE out of lm result?

Question

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?

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))

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

Answer 1

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.

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Remark

• Given two vectors x and y, c(crossprod(x, y)) is equivalent to sum(x * y) but much faster. c(crossprod(x)) is likewise faster than sum(x ^ 2).
• sum(x) / length(x) is also faster than mean(x).