# How to know the original values of my data from the contour plot of copula

Suppose I have a data with Gaussian copula with ($$\rho =0.8$$). Suppose further the contour plot is as follows:

My question is:

How can I interpret the result with respect to my original values? For example, suppose that the first variable is the temperature and the second one is the bike rental. Suppose that I would like to explain at what values these variables become independent, from the plot. For example, I can say that these two variables are positively correlated at the interval $$[0.4,0.6]$$ (for example).

Now I would like to know if there is a way that I can say what is the corresponding temperature? That is, what is the corresponding temperature for $$[0.4,0.6]$$?

• You don't have the information to do this. You need the maps from your original variables to the $(u_1,u_2)$ coordinates in the image. – whuber Jun 30 at 13:27
• @whuber Thank you so much for your comment. Is there a way to do so? Thanks. – Maryam Jun 30 at 13:32
• Yes: review the process you used to produce the copula. The initial step must construct those two maps. There's no other way. – whuber Jun 30 at 13:36
• @whuber thank you again. I really appreciate your help. However, I really do not get your comment. I just use pobs to get copula data and then I plot the contour. If I plot my original data then, it is not helpful. – Maryam Jun 30 at 13:58
• You will need to consult your software documentation to learn how to extract this information. – whuber Jun 30 at 14:16