Calculating R Square of an Exponential Function

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To calculate R-squared for an exponential function, a dataset is required alongside the function itself. R-squared measures how well the data fits the chosen model, calculated as one minus the ratio of the sum of squared errors to the total sum of squares around the mean. An example dataset is provided, and the user seeks a manual method for calculation without software. Additionally, the Pearson product moment correlation coefficient can be squared to obtain R-squared. Understanding these concepts is essential for accurately assessing the fit of an exponential model to data.
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Hi there,

I have googled for the R square formula, but it's very confusing, so I need some help. Please come up with an example on how to use it, if I have a exponential function on how i want to calculate its R square.

Thanks:cry:
 
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R^2 is used to gauge the "goodness" of "fit" of a data set to some known function. So you need a data set and a function, you cannot meaningfully speak of R^2[/itex] of a function by itself.
 
If I then have a table of data:

0 2
40 6
80 8
120 12
160 18
200 24
240 42
280 82
320 110
360 190
400 300
440 500
480 800

... and I want to find the R^2, what should I do (I don't want to use software)?
 
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google: "Pearson product moment correlation coefficient"

multiply PPMCC by itself for R^2

http://mathbits.com/Mathbits/TISection/Statistics2/correlation.htm

sorry it's 4 years late...
 
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I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks

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