I am currently writing a report for one of my engineering labs, and have the distinct pleasure of trying to put together a statistical analysis of all of my gathered data. For each data point I've found the standard error of the x and y values.
My data fit to a power-law curve pretty nicely:
y = A*x^b
but I'm having trouble finding the standard deviations of A and b.
For one, I have not found any data analysis tool in my Excel math pack to do a power-law regression (all I can find is linear regressions), so I've been regressing the logarithmic form of the equation below.
Problem #2 is that I know my standard deviation I'm getting from Excel is not taking the standard errors of each individual data point into account. We've been given an excerpt from a textbook about how to find the standard error of a linear regression based on each data point's error, but I'm not sure how to take it from the linear function
log(y) = log(Aħσa) + (bħσb)*log(x)
to the power function
y = (Aħσa)*x^(Bħσb)
Any thoughts? Thanks!