Negative values in covariance matrix

In summary, a user had measured a luminescence decay profile and wanted to fit a function to approximate their experimental data. They used a program in LabView, but encountered a problem where the program gave them negative values in the covariance matrix. They were concerned about this and questioned why it was happening. The response explained that negative covariance can still be acceptable and provided an example. The user also shared that the problem was specifically with the diagonal elements of the covariance matrix, which could result in imaginary errors for the function coefficients.
  • #1
latvietis
2
0
Hello

I had measured luminescence decay profile. Then I want to fit a function which would approximate my experimental date. For that I make a simple program in LabWiev. The problem is that, that program give me out a negative values in covariance matrix. Why that?


P.S.
Sorry for my English
 
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  • #2
Negative covariance is OK. It means that higher-than-average results from one variable will happen at the same time as lower-than-average results from the other variable.

For example, the covariance between how cold it is out and much people get sunburned is probably negative.

If you have more intuition for correlation, this may help: the covariance between 2 variables is just the correlation between the variables, scaled by the standard deviations.
 
  • #3
Ok

But problem is that the negative values is in diagonal elements. Diagonals elements of covariance matrix is [tex]\sigma^2[/tex]. So I get that errors of functions coefficients [tex]\sigma[/tex] is imaginary.
 

FAQ: Negative values in covariance matrix

1. What is a covariance matrix?

A covariance matrix is a mathematical tool used in statistics to measure the relationship between two or more variables. It is a square matrix that contains the variances of each variable on the diagonal and the covariances between each pair of variables on the off-diagonal elements.

2. What do negative values in a covariance matrix indicate?

Negative values in a covariance matrix indicate that the variables have a negative relationship, meaning that as one variable increases, the other variable decreases. This is also known as an inverse relationship.

3. Can a covariance matrix have only negative values?

Yes, a covariance matrix can have only negative values if all variables in the dataset have a negative relationship with one another. This is possible, but rare to see in real-world data.

4. How do negative values in a covariance matrix affect data analysis?

Negative values in a covariance matrix can affect data analysis by showing a negative correlation between variables. This information can be useful in understanding the relationship between variables and making predictions or decisions based on the data.

5. Are negative values in a covariance matrix always a cause for concern?

No, negative values in a covariance matrix are not always a cause for concern. They simply indicate a negative relationship between variables, which may or may not be relevant to the research or analysis being conducted. It is important to consider the context and purpose of the analysis when interpreting the values in a covariance matrix.

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