plotting a curvilinear line of best fit

Question

What is the correct way to plot a curvilinear line of best fit on a graph? I am trying to provide a regression model as a parameter to the line- not specific points. In the model below the correct line should be a perfect fit (because there is no noise in the data). How do I plot the line of best fit from a linear model?

library(lattice)
vals<-data.frame(x=1:10,y=(1:10)^2)

xyplot(x~y,data=vals)
line(lm(x~y,data=vals)) #doesnt work
abline(vals$x,vals$y) #doesnt work

Answer 1

I'm thinking you may be reversing the order of the arguments in the formula, since the conventional plot of y versus x would be returned from xyplot( y ~ x ). But if you really do want a linear regression with a second-degree polynomial fit, then use the poly function in the formula and the predict function to get the fitted values:

xyplot(x~y,data=vals)
plot(vals$y, predict( lm(x~poly(y, 2), data=vals)) ) 

It's not an exact fit since you are plotting the square root of x against x.

resid(  lm(x~poly(y, 2),data=vals)) 
#------------------------------
          1           2           3           4           5           6           7 
-0.57799840 -0.01438720  0.28444720  0.35772841  0.26036947  0.06297286 -0.14816950 
          8           9          10 
-0.27107622 -0.18807651  0.23418989 

Another way (which does give an exact fit) is to use the I function inside the formula:

 plot(vals$y, fitted( lm(x~I(y^(1/2) ), data=vals)) )
 points(vals, pch="x", col='red')
 points(vals$y, vals$x, pch="x", col='red')

Answer 2

To get a regression using the lattice library, you need to include a type parameter in the xyplot function. To get a linear regression use "r" and to get a non-linear regression (which is what you want here) use "smooth". So this is what your code should look like

library(lattice)
vals<-data.frame(x=1:10,y=(1:10)^2)
xyplot(x~y,data=vals,type=c("p","smooth"))

The "p" is for the points and the "smooth" is for the smooth regression. This will result in a graph that looks like this

Alternative, if you, for some reason, did want a linear regression on this your code would look like this

library(lattice)
vals<-data.frame(x=1:10,y=(1:10)^2)
xyplot(x~y,data=vals,type=c("p","r"))

and your graph would look like this