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The problems is

Suppose that E(Y_i|X)=$\beta_0+\beta_1\sin(2 \pi \theta_1 i/n)+\beta_2\cos(2\pi\theta_2i/n)$, i=1,...n, where positive integers $\theta_1$ and $\theta_2 $ are given.

I want to find least squares estimates of $\beta_0,\beta_1,\beta_2$ and the variance.

firstly, I tried that partially differentiate SSE and then solve normal equation. But it is hard to solve. I think other method exist.. Can you help me?

GGyu
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  • The normal equation is just a linear equation. Where is difficulty? Are you expecting that the inverse of the coefficient matrix has some particular closed form? – user251257 Oct 14 '17 at 13:31
  • yes.. I tried to find the inverse but can't calculate it. – GGyu Oct 14 '17 at 17:15

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