# Regression, extrapolating, and R functions

### 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}
```