Negative values in covariance matrix

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SUMMARY

The discussion centers on the issue of negative values appearing in the covariance matrix generated by a LabVIEW program used to fit a function to luminescence decay profile data. The user notes that while negative covariance between variables can be expected, the presence of negative values in the diagonal elements of the covariance matrix indicates that the variance (σ²) is negative, leading to imaginary errors in the function's coefficients. This suggests a fundamental problem in the fitting process or the data being analyzed.

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  • Understanding of covariance matrices and their properties
  • Familiarity with LabVIEW programming for data analysis
  • Knowledge of statistical concepts such as variance and correlation
  • Experience with luminescence decay profile measurement techniques
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  • Investigate the mathematical foundations of covariance matrices and their diagonal elements
  • Learn about proper data fitting techniques in LabVIEW
  • Explore methods for handling negative variance in statistical models
  • Study the implications of covariance in experimental data analysis
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Researchers and data analysts working with experimental data, particularly in fields involving luminescence measurements, as well as LabVIEW users seeking to improve their understanding of statistical analysis and data fitting techniques.

latvietis
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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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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.
 
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.
 

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