Estimated error of prediction, assuming multivariate normality.
Computes the estimated mean square error of prediction assuming that both independent and dependent variables are multivariate normal.
$$MSE(n + 1)(n - 2) / n(n - p - 1)$$
where \(MSE = SSE / (n - p)\), n is the sample size and p is the number of predictors including the intercept
Stein, C. (1960). “Multiple Regression.” In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, edited by I. Olkin, S. G. Ghurye, W. Hoeffding, W. G. Madow, and H. B. Mann, 264–305. Stanford, CA: Stanford University Press.
Darlington, R. B. (1968). “Multiple Regression in Psychological Research and Practice.” Psychological Bulletin 69:161–182.
model <- lm(mpg ~ disp + hp + wt + qsec, data = mtcars) ols_msep(model) #>  220.8882