How to interpret the covariance matrix from a curve fit?
How do I interpret the covariance matrix from a curve fit? I’m not too great at statistics, so apologies if this is a simplistic question. I am fitting a curve to some data, and sometimes my data best fits a negative exponential in the form a ∗ e ( − b ∗ x) + c, and sometimes the fit is closer to a ∗ e ( − b ∗ x 2) + c.
How to calculate the transformed data from the covariance matrix?
The transformed data is then calculated by Y = T X or Y = R S X. This leads to the question how to decompose the covariance matrix C into a rotation matrix R and a scaling matrix S. Eigen Decomposition is one connection between a linear transformation and the covariance matrix.
Is the covariance matrix of a data set well approximated?
The covariance matrix of a data set is known to be well approximated by the classical maximum likelihood estimator (or “empirical covariance”), provided the number of observations is large enough compared to the number of features (the variables describing the observations).
How to extract scaling matrix from covariance matrix?
What we expect is that the covariance matrix C of our transformed data set will simply be which means that we can extract the scaling matrix from our covariance matrix by calculating S = C and the data is transformed by Y = S X.
Can a variance-covariance matrix Tell Me which model to use?
UPDATE: Based on a similar question, I’m hoping that the variance-covariance matrix can tell me which of the three models I am attempting best fits the data (I am trying to fit many datasets to one of these three models).
When is the covariance of two features not equal to zero?
If two features are not independent (like age and size might be), the covariance won’t be equal to zero. if two features and dependent and “moves together” on the same direction (i.e. if X increase, Y increases too), then C o v ( X, Y) will be strictly positive.
Is the variance of the estimator independent of the underlying coefficient?
Intuitively, the variance of the estimator is independent of the value of true underlying coefficient, as this is not a random variable per se. The result is valid for all individual elements in the variance covariance matrix as shown in the book thus also valid for the off diagonal elements as well with β0β1 to cancel out respectively.
What are the criteria to use in comparison of different models?
So the criteria to use in comparison of different models depends on what you want to achieve. For instance, if you want a curve that is the “close as possible” to the data, you could select a model which gives the smallest residual. In your case it would be the model func and the estimated parameters popt that has the lowest value when computing