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I had to use the LOGEST function in Excel to obtain parameters of an exp. equation for regression. I thought the returns will just be "a" and "b" for the following equation.

  1. $ y=bx^{a} $

The values turn out to be for the following instead.

  1. $ y=be^{x(a-1)} $

Can anyone explain how to rewrite the 1. equation in to the 2. equation? Thanks!

Blue
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уве вонг
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1 Answers1

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This is simply not true!

Since $e^x$ and $ln(x)$ are inverse functions, $\alpha= e^{ln(\alpha)}$ for any number $\alpha$. In particular, with $\alpha= x^a$, $x^a= e^{ln(x^a)}= e^{a ln(x)}$.

If $y= bx^a$ then $y= be^{ln(x^a)}= be^{aln(x)}$. That is not anything like "$y= be^{x(a- 1)}$!

George Ivey
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  • How about $ y=be^{xln(a)} $ ? Is this possible if my starting equation is $ y=ba^{x} $? I just know what the return values of the LOGEST function in excel are representing.... – уве вонг Jul 07 '22 at 12:07