I have some data, with known error, and have used a linear regression algorithm to make a fit of this data and plot it. I have also used the algorithm to calculate an associated covariance. How would I combine this covariance with the errors from the original data to find the standard error of say the intercepts or gradients?

  • $\begingroup$ Please explain what "associated covariance" means and what you mean by "combining" it with the errors. Are you just asking how to compute the standard errors of the parameter estimates? That's answered in many of our posts: search for "regression formulas." What does your title phrase "covariance of graph" mean? $\endgroup$
    – whuber
    Jan 14 at 21:37
  • $\begingroup$ When I used my linear regression algorithm on the parameters, I'm given a covariance for the fit, and want to use this value with the errors in the parameters to find the overall error. By associated I just mean associated with the estimated parameters. I could not find anything useful when I searched "regression formulas" $\endgroup$
    – Tom888
    Jan 14 at 21:39
  • $\begingroup$ I get several hundred hits at stats.stackexchange.com/search?q=regression+covariance+formula. Many look useful. It's unclear what you are asking, though: the diagonal entries of the covariance matrix for the fit are the squares of the standard errors (by definition). What would it mean to "use this value with the errors in the parameters"? What is the "overall error"?? $\endgroup$
    – whuber
    Jan 14 at 21:40

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