Variance-covariance matrix

vcov() gives the variance-covariance matrix for a regression model. Confusingly (to me) there is a seemingly similar matrix if you use summary()$cov, I’m not exactly sure what this matrix is. It’s very easy to verify the vcov() matrix is right since you just need to square the standard errors for the estimates of b0 and b1.

extrapolating values in R from a standard curve

perdict can be used.

extrapolating values, in general, from a standard curve

The following works provided X is known without error:

Var{Y} = Var{mX + b} = Var{mX} + Var{b} + 2 Cov{Xm,b}
Var{Y} = X^2 * Var{m} + Var{b} + 2 * X * Cov{m,b}

If X is a random variable with it’s own mean E{X} and variance Var{X} then the the Var{Y} is given by:

Var{Y} = Var{mX + b}
Var{Y} = Var{b} + 2 * E{X} * Cov{m,b} + Var{X} * (E{m})^2 + Var{m} * (E{X})^2 + Var{m} * Var{x}