Determining the goodness of an R fit using lm()

Question

I learned to get a linear fit with some points using lm in my R script. So, I did that (which worked nice), and printed out the fit:

lm(formula = y2 ~ x2)

Residuals:
         1          2          3          4 
 5.000e+00 -1.000e+01  5.000e+00  7.327e-15 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)   
(Intercept)   70.000     17.958   3.898  0.05996 . 
x2            85.000      3.873  21.947  0.00207 **
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 

Residual standard error: 8.66 on 2 degrees of freedom
Multiple R-squared: 0.9959, Adjusted R-squared: 0.9938 
F-statistic: 481.7 on 1 and 2 DF,  p-value: 0.00207 

I'm trying to determine the best way to judge how great this fit is. I need to compare this fit with a few others (which are also linear using lm() function). What value from this summary would be the best way to judge how good this fit is? I was thinking to use the residual standard error. Any suggestions. Also, how do I extract that value from the fit variable?

Answer 1

If you want to access the pieces produced by summary directly, you can just call summary and store the result in a variable and then inspect the resulting object:

rs <- summary(lm1)
names(rs)

Perhaps rs$sigma is what you're looking for?

EDIT

Before someone chides me, I should point out that for some of this information, this is not the recommended way to access it. Rather you should use the designated extractors like residuals() or coef.

Answer 2

This code would do something similar:

 y2 <- seq(1, 11, by=2)+rnorm(6)  # six data points to your four points
 x2=1:6
 lm(y2 ~ x2)
 summary(lm(y2 ~ x2))

The adjusted R^2 is the "goodness of fit" measure. It is saying that 99% of the variance in y2 can be "explained" by a straight line fit of y2 to x2. Whether you want to interpret your model with only 4 data points on the basis of that result is a matter of judgment. It would seem to somewhat dangerous to me.

To extract the residual sum of squares you use:

summary(lm(y2~x2))$sigma

See this for further details:

?summary.lm

Answer 3

There are some nice regression diagnostic plots you can look at with

plot(YourRegression, which=1:6)

where which=1:6 give you all six plots. The RESET test and bptest will test for misspecification and heteroskedasticity:

resettest(...)
bptest(...)

There are a lot of resources out there to think about this sort of thing. Fitting Distributions in R is one of them, and Faraway's "Practical Regression and Anova" is an R classic. I basically learned econometrics in R from Farnsworth's paper/book, although I don't recall if he has anything about goodness of fit.

If you are going to do a lot of econometrics in R, Applied Econometrics in R is a great pay-for book. And I've used the R for Economists webpage a lot.

Those are the first ones that pop to mind. I will mull a little more.