A Note on Pure Error and Its Effect on Regression Model Significance

We extend the concept of maximum coefficient of determination \operatorname{Max}R^{2} caused by repeat runs to ideas about a maximum test statistic F_{0} and a minimum p-value Min P for regression

Estimating the variance in coordinate measuring for binary orbit

The variance of a purely random error - “pure error” - in measuring the relative coordinates during the calculation of the orbits of binary stars, (its "unbiased estimate"), is necessary for each test used in the orbit calculation for double stars, such as the adequacy test for the orbit model, gross-error tests and the like. Since this variance is unknown, in this paper we present the robust PEROBEPE1 method which provides an unbiased variance estimate for the pure error in the coordinate measurements concerning the orbits of double stars. This estimate is independent of the model adequacy for a double-star orbit and thus can be used in any test concerning double stars.