# Simple regression question

#### kvd

##### New Member
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

#### Attachments

• 41.5 KB Views: 6

#### Dason

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

#### Dason

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

#### kvd

##### New Member
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

##### New Member
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.

#### Attachments

• 902.3 KB Views: 2