Curve Fitting with multiple Y data point for each X

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Pat
Pat 2013-3-28
Hi I would like to fit a Gaussian curve to some data. The data are from 3 subjects and there are 7 x data points.
x = [-90 -45 -22.5 - 22.5 45 90] y = [0.3099 0.4806 0.5899 0.6836 0.6635 0.5841 0.2969; 0.2096 0.5600 0.2403 0.7877 0.8406 0.6927 0.2095; 0.1274 0.1973 0.1632 0.5383 0.6522 0.4410 0.1696];
I think I can do the fitting if I average across subjects first but I want to do the fit across all subjects 'at the same time'.
How can I do that??
Thanks for you help,
Pat

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Pat
Pat 2013-3-28
Hi
1- You mean the fitted curve would look the same?
2- But what if I need to run some stats as I have another group of data that I need to compare it with?
I though I'd have more info if I run it at the same time across all the subjects!
Thanks

更多回答（1 个）

Matt J
Matt J 2013-3-28
I think I can do the fitting if I average across subjects first but I want to do the fit across all subjects 'at the same time'
The 2 results would be equivalent.
  1 个评论
Matt J
Matt J 2013-3-28
编辑：Matt J 2013-3-28
The fitted curve would be the same. If you fit "all the data" you are minimizing the following cost function with respect to x
sum_{i=[1,2,3]} [norm(F(x,xdata)-y_i)^2]/3
= sum_i [norm(F(x,xdata))^2 + 2*dot(F(x,xdata),y_i)]/3 + constant
= norm(F(x,xdata))^2 + 2*dot(F(x,xdata), sum_i y_i/3) + constant
= norm(F(x,xdata)-sum_i y_i/3)^2 +constant
This shows that minimizing the original curve fitting function is equivalent to minimizing
norm(F(x,xdata)-sum_i y_i/3)^2
which is the same as fitting the average of the data sum_i y_i/3.
I though I'd have more info if I run it at the same time across all the subjects!
You will have more info. The average over y_i will reflect that additional information.

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