What I want is the uncertainty in the coefficients

[Winzer]

Homework Statement

I was given a set of data from a Ion engine experiment. I fitted the data with an 8th order polynomial that seems pretty reasonable. What I want is the uncertainty in the coefficients.
One way I read was through the design matrix.

Homework Equations

$$C_{ij}=(A^T A)^{-1}$$

The Attempt at a Solution

The square root of the diagonals give the uncertainties. But my matrix in not invertible since its not square.
What am I missing?

 

[The Electrician]

Homework Statement

I was given a set of data from a Ion engine experiment. I fitted the data with an 8th order polynomial that seems pretty reasonable. What I want is the uncertainty in the coefficients.
One way I read was through the design matrix.

Homework Equations

$$C_{ij}=(A^T A)^{-1}$$

The Attempt at a Solution

The square root of the diagonals give the uncertainties. But my matrix in not invertible since its not square.
What am I missing?

The matrix A may not be square, but

$$(A^T A)$$

is square, so it's invertible.

 

[Winzer]

The matrix A may not be square, but

$$(A^T A)$$

is square, so it's invertible.

Thank you. Yes it turns out square but the inverse gives me problems.
Maybe I am using the command wrong.
Here are the results of a test.

I threw in .1 just for error sake. My model is a+bx+cx^2. The uncertainties are suppose to be given by the square root of the diagonals of
$$(A^T A)^{-1}$$ A being the design matrix.

 

[Winzer]

Never mind I got it.
I was able to find the covariance matrix and the associated uncertainties. I feel stupid.