How to do multiple linear regression in different combination of numbers?

Good day everyone! This is what I'm trying to code: I have to analyze several mobility profiles from ion mobility spectrometry experiments. I do that by fitting gaussian curves to several data files I obtained. After the fitting, I get the position of the peaks (in the X-axis) in arrays like this:

a = [a1,a2,a3,...,an]

b = [b1,b2,b3,...,bn] and so on.

What I need is a way to do a linear regression on all the combinations of the numbers in the matrices:

e.g.

reg1 = [a1,b2,c3,...]

reg2 = [a2,b1,c1,...] to obtain the intercept of each one and select only one with the highest R^2 value.

I thought about nesting for loops, but the problem that I encounter is that I can have multiple arrays of data (from 5 to 20) with an unknown number of positions on each array. The linear regressions can have only one number from each array.

Currently I'm not using any toolbox.

Thanks in advance for you help!

[Star Strider]

What is your regression model?

In a multiple linear regression such as yours, the model is usually:

x = A*b

where x is the independent variable, A is the data matrix, and b is a vector of coefficients to be estimated (slope, intercept, etc.). I understand that a, b, and the rest are vectors of positions of the peaks.

I have no idea how reg1, reg2, etc. relate to what you are doing. How does the permutation of the elements of a, b, c, and the rest to get reg1, reg2, etc. apply to your problem?

[Camilo]

Hi, thanks for your answer. When I run the IMS experiments, I do it for different mobility times of the ions in the quadrupole. Sometimes I get the same number of peaks with the same intensity for each one, and in this case is easy to determine the best fit, because the position of the most intense peak is used (is usually in the same position for each time). However, this is not always the case. Sometimes I get different number of peaks, and their stability varies with time. In order to calibrate the experiment (for later calculations) I need the best fit for a combination of peak positions (one from each time). Right now I am doing it manually in OriginLab, but I know there must be a way to automate the process using Matlab.

reg1, reg2, etc, are just examples of matrices I should get with the different combinations of the peak positions.

[Matt J]

The different notation used is not clear to me. What does [a1...an] signify? How is it different from [b1..bn] and [c1...cn]?

[Star Strider]

Please describe in detail, ideally with data (real or simulated), and what you want to do with it.

It’s quite likely you can do what you want in MATLAB. We can’t help you if you don’t tell us what your data are and what you want to do with them.

I still don’t understand the permutations involved in getting reg1, reg2, and the rest. What’s the pattern? Why?

[Camilo]

ok, I have the following (simulated) values that correspond to peak positions. Each array corresponds to a gaussian fit of data obtained experimentally:

a = [12,25,36,75]

b = [6,36,81]

c = [14,23,38,79]

d = [7,20,31,74,92]

I need the best linear regression between values of different gaussian fits.

12,6,14,7

12,36,14,7

12,81,14,7

12,6,23,7

    and so on...

In each linear regression I can have only one value from each experiment. So, I can't have something like

12,25,6,36,14,23

The problem is that the number of experiments can vary. In this case I have 4, but sometimes I need to run 5 or 20.

finally, what I really need is the intercept of the best linear regression.