# Explanation of covariance matrix of polynomial parameters [duplicate]

I'm asked to find the covariance matrix of $$\alpha$$, $$\beta$$, and $$\gamma$$ for:

$$y_i=\alpha+\beta(x_i-\bar{x})+\gamma[(x_i-\bar{x})^2-\zeta^2]+\epsilon_i$$

where all the errors have equal variance $$\sigma^2$$.

I haven't had a probability class before, and none of my current course material gives me any idea how to find a covariance matrix in the context of these parameters.

Could someone please show me the steps to work this out, and explain in beginners terms what you're doing? I would really appreciate the help.

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