# [R] bowed linear approximations

Fox, John jfox at mcmaster.ca
Mon Sep 25 22:36:00 CEST 2017

```Dear Rich,

Assuming that I understand what you want to do, try adding the following to your script (which, by the way, is more complicated that it needs to be):

xx <- 10:50
m <- lm(y ~ x)
yy <- predict(m, data.frame(x=xx))
lines(spline(xx, yy), col="blue")

m <- lm(y ~ log(x))
yy <- predict(m, data.frame(x=xx))
points(xx, yy, col="magenta")

The first set of commands adds a line corresponding to the points that you plotted, which if I understand right, is *not* what you want. The second set of commands shows how to find points along the diagonal straight line that you plotted, given their x-values, which is what I think you want.

If you examine the linear models fit, you'll see that they just interpolate between the two points, albeit differently.

I hope this helps,
John

-----------------------------
John Fox, Professor Emeritus
McMaster University
Web: socserv.mcmaster.ca/jfox

> -----Original Message-----
> From: R-help [mailto:r-help-bounces at r-project.org] On Behalf Of Evans,
> Richard K. (GRC-H000)
> Sent: Monday, September 25, 2017 3:28 PM
> To: r-help at r-project.org
> Subject: [R] bowed linear approximations
>
> Hello,
>
> Please run the following code snippet and note the resulting plot:
>
> x <- c(10, 50)
> y <- c(0.9444483, 0.7680123)
> plot(x,y,type="b",log="x")
> for(i in 1:50){
>  xx <- exp(runif(1,log(min(x)),log(max(x)) )) yy <- approx(x,y,xout=xx, method =
> "linear")
> points(xx,yy\$y)
> }
>
> notice the "log=x" plot parameter and the resulting "bow" in the linear
> approximation.
>
> This makes sense when I realized that the plot command is first making the
> plot and then drawing straight lines between points on a log plot AFTER the
> plot is generated and that that's why the line is straight. I get that.
> .. and it also makes sense that the bowed points are a result of the linear
> approximations being made BEFORE plotted in a logarithmic plot. I get that..
>
> My goal is to make approximations that lie on the line produced on the plot as
> shown, so I realize that what I want to do is NOT linear approximations, but
> maybe "log" approximations?
> However, the approximation methods are only "linear" and "constant" .. there
> isn't a "log" method to approximate with.
>
> So can anyone tell me how to fix the code such that he approximated points
> DO lie on the line as plotted with the "log=x" plot parameter?
> Oh, and they have to be uniformly distributed along the Log=x axis.. I think
> that's the tricky part.
>
> Any help and/or insight would be greatly appreciated.
>
> Thank you!
> -Rich
>
>
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