# how is the logistic regression scatter plot created

I have a newbie question about logistic regression fit plots. I'm fitting a very simple binary output based on a simple continuous input

X   Y
0.1 0
0.1 0
0.1 0
0.1 1
0.5 0
0.5 0
0.5 1
0.5 1
0.9 0
0.9 1
0.9 1
0.9 1

when using JMP, the fitting model is logistic. I understand the fitted line, but what are the points plotted on the chart? I only have 0,1 in the output, but why does the logistic plot show values of Y that are not 0,1?

Thanks for any help with this.

## 2 Answers

The plot that JMP uses for logistic fits is described on page 2-79 (page 93 of the PDF) in this demo document produced by JMP.

http://www.jmp.com/training/scripting_workshop/2004/concepts_using_jmp_handout.pdf

This platform features a new kind of scatter plot. The data points are plotted according to their real abscissa and a dummy random ordinate. It organizes the points so that you can see how they fall into one of the categories.

So for each point, the $X$ coordinate is the position that is in the data, and the $Y$ coordinate is just randomly placed above or below the blue line so you can see where the points fall.

• Thanks for the explanation but what is the purpose of plotting a random value as the y axis? Is it completely random or some weighed random number based on the fitted model? – Jonjilla Sep 28 '14 at 5:44
• @Jonjilla The point is probably to just jitter the data so that you can get a sense of where the data lies relative to the logistic curve. It doesn't look completely random, but the JMP guide still uses the word "random." – Blue Marker Sep 28 '14 at 21:04

The left y-axis location of these dots is meaningless as the location is completed random within the region above or under the curve. Also, the left y-axis reading is NOT the fitted probability of Y=1, rather it is of Y=0! What a confusing plot!

• Think it might be worth emphasising, for clarity, that the left y-axis refers to the blue curve. I was also surprised by the fact this seems to show P(Y=0)! – Silverfish Jul 2 '16 at 19:39