Least-squares fitting of a straight line

1968 ◽  
Vol 46 (16) ◽  
pp. 1845-1847 ◽  
Author(s):  
J. H. Williamson
Keyword(s):  
Least Squares ◽  
Efficient Method ◽  
Least Squares Fitting ◽  
Statistical Errors ◽  
Straight Line

An efficient method is given for computing the best straight line by least squares when there are statistical errors in both coordinates. Exact expressions are obtained for the variances of the slope and intercept.

LEAST-SQUARES FITTING OF A STRAIGHT LINE

1966 ◽  
Vol 44 (5) ◽  
pp. 1079-1086 ◽  
Author(s):  
Derek York
Keyword(s):  
General Solution ◽  
Least Squares ◽  
Method Of Least Squares ◽  
Least Squares Fitting ◽  
Straight Line ◽  
Special Solutions

A detailed discussion of the calculation of the "best straight line" by the method of least squares is given. The most general solution is found and the conditions under which certain previously derived special solutions are valid are clearly stated. The "best" slope is shown to be given by the solution of the "Least-Squares Cubic". An example is given to illustrate the method. It is shown that the best slope is not necessarily bounded by values found from the regressions of x on y and y on x.

Theoretical accuracy of the last squares method in the isotope dilution analysis

1984 ◽  
Vol 49 (4) ◽  
pp. 805-820
Author(s):  
Ján Klas
Keyword(s):  
Least Squares ◽  
Isotope Dilution ◽  
Least Squares Method ◽  
Isotope Dilution Analysis ◽  
Straight Line ◽  
The One ◽  
Two Parameter ◽  
Theoretical Accuracy

The accuracy of the least squares method in the isotope dilution analysis is studied using two models, viz a model of a two-parameter straight line and a model of a one-parameter straight line.The equations for the direct and the inverse isotope dilution methods are transformed into linear coordinates, and the intercept and slope of the two-parameter straight line and the slope of the one-parameter straight line are evaluated and treated.

scholarly journals An Error-Reduction Method for Temporal Phase Unwrapping Based on Double Three-Step Phase-Shifting and Least-Squares Fitting

2012 ◽  
Vol 6-7 ◽  
pp. 76-81
Author(s):  
Yong Liu ◽  
Ding Fa Huang ◽  
Yong Jiang
Keyword(s):  
Least Squares ◽  
Reduction Method ◽  
Intermediate Phase ◽  
Error Reduction ◽  
Phase Unwrapping ◽  
Phase Shifting ◽  
Surface Measurement ◽  
Acquisition Time ◽  
Least Squares Fitting ◽  
Temporal Phase

Phase-shifting interferometry on structured light projection is widely used in 3-D surface measurement. An investigation shows that least-squares fitting can significantly decrease random error by incorporating data from the intermediate phase values, but it cannot completely eliminate nonlinear error. This paper proposes an error-reduction method based on double three-step phase-shifting algorithm and least-squares fitting, and applies it on the temporal phase unwrapping algorithm using three-frequency heterodyne principle. Theoretical analyses and experiment results show that this method can greatly save data acquisition time and improve the precision.

A modified tangent-gas approximation for two-dimensional steady flow

1958 ◽  
Vol 4 (6) ◽  
pp. 600-606 ◽  
Author(s):  
G. Power ◽  
P. Smith
Keyword(s):  
Least Squares ◽  
Steady Flow ◽  
Variational Approach ◽  
Least Squares Method ◽  
Two Dimensional ◽  
Subsonic Flows ◽  
Von Karman ◽  
Straight Line ◽  
Volume Relationship ◽  
Pressure Volume Relationship

A set of two-dimensional subsonic flows past certain cylinders is obtained using hodograph methods, in which the true pressure-volume relationship is replaced by various straight-line approximations. It is found that the approximation obtained by a least-squares method possibly gives best results. Comparison is made with values obtained by using the von Kármán-Tsien approximation and also with results obtained by the variational approach of Lush & Cherry (1956).

Sign in / Sign up

Export Citation Format

Share Document