Simple regression question

[kvd]

Hi all,

This is my first post on this forum. My area of studies is electronics, and I came across a situation where I have some (6) measured values y, a model, and need to find some (2) values β for a best fit of the model to the measured values. The model can be described as follows:

y = β X

so:
y is a 6-dimensional vector, with known, measured values
X a 2x6 matrix with fixed values
β a. 2-dimensional vector, for which I want to find the best fitting values.

(see attached image)

My statistics skills are very rusty, but to me it looks like a very simple linear regression problem, only in higher dimensions.
What method should I use to solve this? Are there any online calculators for this?

I have done some investigations myself, and I think it is a multivariate regression problem, but then I get stuck in a bewildering number of different methods. I may, and probably will, be wrong on this however.

For the curious, the area of interest is of signal strengths of mixing products in a JFET mixer.

Thanks, ciao,
Koen

 

[Dason]

Just so we are clear - you don't want any intercept term in your regression?

 

[kvd]

No, there is no intercept. The actual, complete model is in the attached image.
The values to be calculated are the VLO and VRF values. The measured values are the S, IDSS and VP values.

I feel like I am making a very stupid mistake, or that the solution may be very simple....

 

[Dason]

You are dictation what the epsilon terms are. That's... Unusual. Are those quantities that are impossible to measure?

 

[kvd]

All the measured values values are encapsulated in y. So the epsilon terms are measured values as well. I just brought them to the y to make the equation simpler. X is part of the model, and β is the unknown. For β I want to calculate a best fit.

 

[kvd]

I have found the solution, with help from the website

.

I have tested this regression model to find best estimates for β, compared these with crudely measured values for β. These fit very good.
Also entered the estimates for β in the model equations to compare the measured values to the calculated values, they fit excellent. See attached file for explanation/derivation.