# Is there anyway to evaluate the estimation results of least square

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?

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