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Roly
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Searching for the equation for the confidence lines for a nonlinear fitted curve

I have been playing around with the nonlinear fit tool, and am having a lot of fun with the individual confidence limits that it can generate. I want to be able to perform the same work using column formulas rather than pulling up the nonlinear tool (I am adjusting the section of the data to perform the fit on using variables). I have a way to perform the nonlinear fit using column formula, but I do not know the equations used to calculate the confidence limits. I know that the individual confidence limits for a linear fit has the equation;

 

Yc = Yp +/- t(n-2.alpha/2) * Sqrt( Sum( ( Yi - Yip )^2) / ( n-2 ) ) * Sqrt( 1 + 1/n + ( Xp - Xbar )^2 / Sum( ( Xi - Xbar ) ^2 ) )

 

Yc = the confidence limit

Yp = the predicted value of y from the fitted line

t(n-2.alpha/2) = the t statistic for n-2 degrees of freedom and alpha/2 confidence

Yi = the ith y value

Yip = the predicted ith y value

n = number of data points

Xp = the x value for which Yp is predicted

Xbar = the average x value

Xi = the ith x value

 

Can anyone tell me the similar equation for the confidence line for a fitted 3 parameter exponential (ie a fitted curve with the equation y = Exp ( m * x + b ) + c)?

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