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I have a simple question for data transformation for fitting my dataset to a negative exponential graph. There are negative values on my dataset which hinder fitting a negative exponential curve. How can I successfully transform my data in statistical way? My data is about Mantel correlation coefficients with distance. Here is my data.

Distance   Coefficients
    1       0.7241232
    2       0.19643728
    3      -0.06509062
    4      -0.16492022
    5      -0.39367865
    6      -0.50758682

What is the best way to transform this data?

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  • $\begingroup$ You could add a constant to the coefficients, but that destroys the meaning of it as a correlation; why do you need a negative exponential function? Would some other function be OK? $\endgroup$ – Peter Flom Nov 10 '13 at 12:54
  • $\begingroup$ @PeterFlom I was suddently curious about finding the best way to make a exponential curve without destroying the meaning of the correlation. Thank you! $\endgroup$ – Kangmin Nov 10 '13 at 13:04
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Short answer: No transformation at all.

Here is a plot of your results. They don't match exponential decline at all, as that implies decay towards zero. Quite possibly you might regard small negative coefficients as compatible with that, but you have some quite large negative coefficients too.

enter image description here

For guidance I have superimposed a token curve $\exp(-\text{Distance})$. The arbitrary constant $k = 1$ in $\exp(-k\,\text{Distance})$ is plucked out of the air and not a fit to your data, but neither steeper curves nor gentler curves with different $k$ could offer much improvement. (I have assumed that zero distance defines an origin.)

It appears that you might need a different functional form, or perhaps none at all. If exponential decline is a hypothesis you are testing, you could proceed to a formal test of the hypothesis, but scientifically it appears contradicted by these results.

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