Curve Fitting with multiple Y data point for each X

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

Answer 1

[Pat]

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

Answer 2

[Matt J]

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.

[Matt J]

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.