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I was putzing around with Excel and the LOGEST function. This fits your data to $y=ab^x$. It does this by linearizing the data, and doing a least-squares fit to $\log(y) = \log(a) + \log(b) x.$ It then transforms the parameters back. However, I noticed that when the "Additional regression parameters" are returned, they are exactly the same as if I had done a linear fit on $\log(y)$ vs $x$, including the Sum Of Squares and standard error of the parameters. The list is stand_err_a, stand_err_b, standard_err_y, r², degree_freedom, F, SSreg, SSres.

The only values that are any different are the $a$ and $b$ parameters.

Is this the expected result? Should the standard errors be transformed back to the log form or not? What about the sum of squares?

Additionally, maybe the bigger question is...is there a better procedure (numeric, or matrix) to fit log data?

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    $\begingroup$ I voted to leave this open, on the grounds that it's not about doing something with Excel, but rather about understanding the statistical operation that Excel is doing.... $\endgroup$ – Matt Krause Jul 27 '16 at 15:29
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    $\begingroup$ Thanks, that's exactly right. Know how to do this in excel, and could do it in R with a little Google-fu, but I don't understand why the regression statistics are not scaled back like the parameters. $\endgroup$ – Kevin Nowaczyk Jul 27 '16 at 16:44

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