kth term. Each term can be a single predictor, a polynomial term, or an interaction term.
estimate of kth regression coefficient
Standard error of fitted value (SE Fit)
The standard error of the fitted value in a regression model with one
The standard error of the fitted value in a regression model with more than
one predictor is:
For weighted regression, include the weight matrix in the equation:
When the data have a test data set or K-fold cross validation, the formulas
are the same. The value of
s2 is from the training data. The design matrix and the
weight matrix are also from the training data.
value of the predictor
mean of the predictor
ith predictor value
vector of values
that produce the fitted values, one for each column in the design matrix,
beginning with a 1 for the constant term
transpose of the new vector of predictor
ith observed response value
ith fitted response
Standardized residual (Std Resid)
Standardized residuals are also called "internally Studentized residuals."
ith diagonal element of X(X'X)–1X'
mean square error
transpose of the design matrix
Deleted (Studentized) residuals
Also called the externally Studentized residuals. The formula is:
Another presentation of this formula is:
The model that estimates the ith observation omits the ith observation from the data set. Therefore, the ith observation cannot influence the estimate. Each deleted residual has a student's t-distribution with degrees of freedom.
mean square error calculated without the ith observation