A New Method For Point Estimating Parameters Of Simple Regression

Abstract

A new method is described for finding parameters of univariate regression model: the greatest cosine method. Implementation of the method involves division of regression model parameters into two groups. The first group of parameters responsible for the angle between the experimental data vector and the regression model vector are defined by the maximum of the cosine of the angle between these vectors. The second group includes the scale factor. It is determined by means of "straightening" the relationship between the experimental data vector and the regression model vector. The interrelation of the greatest cosine method with the method of least squares is examined. Efficiency of the method is illustrated by examples.

Keywords

• simple regression
• point estimation
• method of least squares
• two-exponential luminescence decay
• boiling point of water
• electrical resistivity
• Bloch–Gruneisen function