How can I assign a quality to a regression based on the number of data points? Let's say I want to create a line of best fit to approximate the relationship between years of golf experience, and average golf score.  
If I have only 4 data points, my line of best fit will have a lot of noise.  Is there an equation I can use to say how good the line of best fit is based on the number of data points are used to create it? 
I guess we could say quality = theNumberOfDataPoints, but it doesn't seem like a linear relationship to me...  Is it maybe the square root of the number of data points?
 A: You mention your line of best fit, so you are thinking graphically.  You could also show the "quality" graphically.
In that case I would suggest plotting, along with the line of best fit itself, the upper and lower bounds of:


*

*the 95 % confidence interval (of the mean DV for different values of IV), and

*the 95 % prediction interval (of DVs predicted by the model from different values of IV).


There are some examples here:  http://www.medcalc.org/manual/scatter_diagram_regression_line.php
...and here is a simple one for data just like yours, with


*

*95 % confidence interval bounds in red

*95 % prediction interval bounds in orange



R code:
(
a <- c(5,10,15,20)
score <- c(95,82,75,69)
plot(a,score)
model.lm <- lm(score ~ a)
abline(model.lm,col="grey30")
frame = data.frame(a,score)
newx <- seq(0,25)
prdConf <- predict(model.lm, newdata=data.frame(a=newx), interval = c("confidence"), level = 0.95, type="response")
prdPred <- predict(model.lm, newdata=data.frame(a=newx), interval = c("prediction"), level = 0.95, type="response")
lines(newx,prdConf[,2],col="red",lty=2)
lines(newx,prdConf[,3],col="red",lty=2)
lines(newx,prdPred[,2],col="orange",lty=2)
lines(newx,prdPred[,3],col="orange",lty=2)
# with help from [https://stat.ethz.ch/pipermail/r-help/2007-November/146285.html][3]

)
In my view plots like this should be actually be standard practice (especially the 95 % prediction interval) since it communicates the predictions made by the model so clearly, but I have only seen it rarely.
A: You could look at the variance in your residuals and see how long it takes for that to begin to converge:
x=NULL; y=NULL; N=1e2; v=NULL
for(i in 1:N){
  new.x=runif(1)
  x=c(x,new.x)
  y=c(y,jitter(5*new.x))

  m=lm(y~x)      
  v=c(v, var(m$residuals))
}

plot(v, type='l', xlab='sample size', ylab='var(residuals)')


This isn't a measure of the quality of your model as much as it is a way of evaluating if you should expect your model to improve with more data. If you're just interested in model quality, for linear models the go-to evaluation of fit is generally the $R^2$ statistic, but there are certainly others. As Justin mentioned, you can reference the F statistic and p-value.
A: When you run your model you should get an F statistic and p-value for the model overall (standard significance guidelines apply) and those also appear for each coefficient. They should take sample size into account.
Here's some more good information:
http://blog.yhathq.com/posts/r-lm-summary.html
