# Covariance in fitting function

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Hello! I have to calculate the covariance between 2 parameters from a fit function. I found this package in Python called iminuit that did a good fit and also calculate the covariance matrix of the parameters. I tested the package on a simple function and I am not sure I understand the result. When the function I put is x^2+y^2, which has the minimum for x=y=0, I obtain ((1.0, 0.0), (0.0, 1.0)), as a covariance matrix. When I use (x-y)^2 I obtain ((250.24975024975475, 249.75024975025426), (249.75024975025426, 250.24975024975475)), as a covariance matrix. I don't understand why do I get value of covariance greater than 1 and why in the first case I get 0 on the sides and 1 on the main diagonal? It is the first time I encounter covariance so I am not sure I got it right. Thank you!

## Answers and Replies

gleem
Science Advisor
Education Advisor
The definition of covariance is If two variable are independent we would expect in the limit of large n that the covariance would be 0. If they are dependent the covariance is not limited to 1.

Perhaps you are thinking of the correlation matrix call it Σ where the diagonal elements ∑II are always 1 and the off diagonal elements are -1 ≤ Σij ≤ 1

Your second function does not have an unique minimum but an infinitely long trough for values x=y.

mathman
Science Advisor
covariance is not limited to 1. Correlation, the ratio of the covariance to the square root of the product of the variances, is limited (in magnitude) to 1.