A least-squares algorithm for fitting data points with mutually correlated coordinates to a straight line

2011 ◽  
Vol 22 (3) ◽  
pp. 035101 ◽  
Author(s):  
Michael Krystek ◽  
Mathias Anton
Keyword(s):  
Least Squares ◽  
Straight Line ◽  
Data Points ◽  
Least Squares Algorithm

A least squares algorithm for fitting data points to a circular arc cam

Measurement ◽  
2017 ◽  
Vol 102 ◽  
pp. 170-178 ◽  
Author(s):  
Shan Lin ◽  
Otto Jusko ◽  
Frank Härtig ◽  
Jörg Seewig
Keyword(s):  
Least Squares ◽  
Circular Arc ◽  
Data Points ◽  
Least Squares Algorithm

Reply by authors to Discussion by Yoich Ohta and Masanori Saito.

Geophysics ◽  
1979 ◽  
Vol 44 (9) ◽  
pp. 1589-1591
Author(s):  
A. F. Gangi ◽  
J. N. Shapiro
Keyword(s):  
Least Squares ◽  
Odd Order ◽  
Data Points ◽  
Independent Variable ◽  
Least Squares Algorithm

We are pleased to hear that Ohta and Saito found our “Propagating‐least‐Squares” algorithm (PROLSQ) for fitting polynomials, [Formula: see text], (1) simple to use and efficient in execution. We appreciate their pointing out that there can be a difficulty with the algorithm under very special (but easily determined) circumstances; that is, when the independent‐variable values [Formula: see text] at the data points are so distributed that the odd‐order moments [Formula: see text] are zero. We did not experience this difficulty because we never treated a case in which all these odd moments were zero.

A Note on Patterns of Wear Within the Tread Area

1979 ◽  
Vol 7 (1) ◽  
pp. 3-13
Author(s):  
F. C. Brenner ◽  
A. Kondo
Keyword(s):  
Content Analysis ◽  
Groove Depth ◽  
Climatic Data ◽  
Periodic Behavior ◽  
Harmonic Content ◽  
Straight Line ◽  
Data Points

Abstract Tread wear data are frequently fitted by a straight line having average groove depth as the ordinate and mileage as the abscissa. The authors have observed that the data points are not randomly scattered about the line but exist in runs of six or seven points above the line followed by the same number below the line. Attempts to correlate these cyclic deviations with climatic data failed. Harmonic content analysis of the data for each individual groove showed strong periodic behavior. Groove 1, a shoulder groove, had two important frequencies at 40 960 and 20 480 km (25 600 and 12 800 miles); Grooves 2 and 3, the inside grooves, had important frequencies at 10 240, 13 760, and 20 480 km (6400, 8600, and 12 800 miles), with Groove 4 being similar. A hypothesis is offered as a possible explanation for the phenomenon.

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.

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