4
$\begingroup$

I had a recent question which I probably should re-formulate to a more general one.

I came across this: Using scatter plots to understand multiple values of Y for a given X and thought the accepted answer was very good, but what's unclear to me is: given a nasty scatter plot, how would you visually get the idea what sort of relationship the x:es and y:s have? In my mind, there's no way of telling if a linear, quadratic, etc regression is appropriate.

If we look at the plot that is currently confounding me: scatterplot

My idea was to somehow plot the AVERAGE of f(x), with x clumped together in intervals, instead of each observation. Is this how you would go about it? If not, what other way do you visually make sense of this data?

$\endgroup$
1
  • $\begingroup$ Just an observation on your particular plot, but the y values appear to fixed at integer intervals. If the y values are known to be accurate you only need regression on the x values. Or to look at it another way, as in Glen_b's bins example, you already have bins. I'm no expert on this stuff though. $\endgroup$
    – Jaydee
    Jul 31, 2014 at 15:27

2 Answers 2

4
$\begingroup$

You might want to consider a lowess (/loess) or similar local smooth.

consider:

enter image description here

This one was generated in R with scatter.smooth. It's an estimate of the local mean, but in a way that they vary smoothly; directly akin to using a kernel density estimate instead of a histogram.

If you must have bins, see here which describes how to do something like this regressogram (bin smoother):

regressogram of mcycle data

$\endgroup$
4
  • $\begingroup$ Very interesting! I think your answer in the other question was what I was looking for here aswell though. $\endgroup$ Jul 31, 2014 at 12:30
  • 1
    $\begingroup$ +1 - a slight amount of jitter and making the points smaller and semi-transparent in the original plot would make it more informative as well (which takes minimal data manipulation). I can't figure out the precision of the values on the x-axis - but they already appear to be "clumped together" as the circles overlap exactly. $\endgroup$
    – Andy W
    Jul 31, 2014 at 16:24
  • $\begingroup$ @AndyW By 'original plot', I presume you mean the one in the question (I didn't attempt to reproduce that aspect of the x-variable); I agree completely with your thoughts about making the plot more informative. $\endgroup$
    – Glen_b
    Jul 31, 2014 at 16:54
  • $\begingroup$ Yes I meant the plot in Benjamin's question. $\endgroup$
    – Andy W
    Jul 31, 2014 at 17:15
0
$\begingroup$

Your idea is called 2d density. Here are some examples in R and ggplot. Contouring in ggplot. I recently needed contouring including expected joint distribution so here is example code in R.

 ggplot(mtcars, aes(x = hp, y = wt)) + stat_density2d () + 
stat_density_2d(mapping = aes(x = mtcars$hp[sample(1:length(mtcars$hp))], y = mtcars$wt), color = "green",
geom = "density_2d", position = "identity" , contour = TRUE, n = 100, h = NULL, na.rm = FALSE, show.legend = F, inherit.aes = F)
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.