# CONDITIONS FOR THE COINCIDENCE OF THE LS AND AITKEN ESTIMATIONS OF THE HIGHER COEFFICIENT OF THE QUADRATIC REGRESSION MODEL

### Abstract

In the paper in the case of heteroscedastic independent deviations a regression model whose function has the form $ f (x) = ax^2 + bx + c$, where $a$, $b$, and $c$ are unknown parameters, is studied. Approximate values (observations) of functions $f (x)$ are registered at equidistant points of a line segment. The theorem proved in the paper states that Aitken estimation of the higher coefficient of the quadratic model in the case of odd the number of observation points coincides with its estimation of LS iff values of the variances satisfy a certain system of nonlinear equations. Under these conditions, the Aitken and LS estimations of $b$ and $c$ will not coincide. The application of the theorem for some cases of a specific quantity of observation points and the same values of the variances at nodes symmetric about the point $\frac{1}{2}$ is considered. In all these cases it is obtained that the LS estimation will be coincide Aitken estimation if the variance in two points accepts arbitrary values, and at all others does certain values that are expressed through the values of variances in these two points.

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