= Fixed-phase sinusoidal least squares
{title2=$y_i=Ks_i+V_0,\quad s_i=\sin(\omega t_i+\phi_0)$}
When <frequency> and phase are known, sinusoidal <amplitude> and offset fitting is a two-parameter <linear regression>. For equal known errors $\sigma$, profiling out the offset gives $K=\sum(s_i-\bar s)(y_i-\bar y)/\sum(s_i-\bar s)^2$ and $\operatorname{Var}(K)=\sigma^2/\sum(s_i-\bar s)^2$. Identical phases cannot separate <amplitude> from offset. Unknown phase instead requires independent sine and cosine coefficients.
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