# [R] Estimate of variance and prediction for multiple linear regression

Gavin Simpson gavin.simpson at ucl.ac.uk
Wed Jun 23 09:57:56 CEST 2010

```On Tue, 2010-06-22 at 23:11 -0700, cc super wrote:
> Hi, everyone,
>
> Night. I have three questions about multiple linear regression in R.
>
> Q1:
>
> y=rnorm(10,mean=5)
> x1=rnorm(10,mean=2)
> x2=rnorm(10)
> lin=lm(y~x1+x2)
> summary(lin)
>
> ## In the summary, 'Residual standard error: 1.017 on 7 degrees of freedom',
> 1.017 is the estimate of the constance variance?

Yes, it is sigma.

Just a note, in order for the above code to yield the same results as
you quote, you need a call to set.seed() to fix the pseudo random number
generator.

> Q2:
>
> beta0=lin\$coefficients[1]
> beta1=lin\$coefficients[2]
> beta2=lin\$coefficients[3]
>
> y_hat=beta0+beta1*x1+beta2*x2
>
> ## Is there any built-in function in R to obtain y_hat directly?

fitted(lin)

Note that there are quite a few standard extractor functions like fitted
available for modelling functions in R. coef() for example should be
used to extract the coefficients, resid() will extract residuals etc.

> Q3:
>
> If I want to apply this regression result to another dataset, that is, new
> x1 and x2. Is the built-in function in 2 still available?

It is called predict() (although if you called predict(lin) above
fitted values for the observations).

One gotcha that catches people out is that in the new dataset, the
variables (used in the model) must have the same names as the data frame
used to fit it. So we could do:

pdat <- data.frame(x1 = rnorm(10, 2), x2 = rnorm(10))
predict(lin, pdat)

to get predictions at the new values of x1 an x2.

HTH

G

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```