Consider the scenario where a practical problem is tackled utilizing the method of least squares. Upon each iteration, an estimation of the parameter $\theta$ is derived via $\hat{\theta} = (X^\top X)^{-1}X^\top Y$, where $X$ and $Y$ denote arrays of $x_i$ and $y_i$ for $i$ ranging from 1 to $n$. However, it is pertinent to acknowledge the result may differ in each estimation. Let's say N values of $\hat{\theta}$ are derived from N estimations, each of which is an outcome obtained using arrays of $x$ and $y$. Is there a methodology to assess the confidence associated with $\hat{\theta}$ procured from each least squares estimation?

  • $\begingroup$ Confidence intervals for the coefficients? $\endgroup$
    – Dave
    Commented Nov 2, 2023 at 2:31
  • $\begingroup$ @Dave could you please be more specific? $\endgroup$
    – yangtzech
    Commented Nov 2, 2023 at 14:05
  • $\begingroup$ I'd encourage you to read about regression confidence intervals. Perhaps these lecture slides from a Georgia Tech course could be a starting point. $\endgroup$
    – Dave
    Commented Nov 2, 2023 at 14:11
  • $\begingroup$ @Dave Sorry for the late reply. Great attitude to your kind help, and I'll try to look into it first. $\endgroup$
    – yangtzech
    Commented Nov 8, 2023 at 1:59


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