scholarly journals POLYANOVA: A general-purpose FORTRAN IV program for trend analysis with equally or unequally spaced levels of the independent variable

1976 ◽  
Vol 8 (3) ◽  
pp. 315-316
Author(s):  
David Brian Williams
Keyword(s):  
Trend Analysis ◽  
General Purpose ◽  
Unequally Spaced ◽  
Independent Variable

scholarly journals On the Standard Errors in the Fitting of Polynomials to Unequally Spaced Observations

1953 ◽  
Vol 6 (2) ◽  
pp. 131 ◽  
Author(s):  
PG Guest
Keyword(s):  
Least Squares ◽  
Standard Errors ◽  
The Third ◽  
Unequally Spaced ◽  
Uniform Spacing ◽  
Independent Variable ◽  
Two Parameters ◽  
Second Degree

From the observed values of the independent variable two parameters are derived which specify the departure from uniform spacing. Expressions are obtained for the standard errors of the coefficients and fitted values in terms of these parameters, and numerical tables for the estimation of the errors are given. It is shown that the errors calculated in this way lie within a few per cent. of the exact least squares values for polynomials of the first and second degree, but when the polynomial is of the third degree the deviations may be much greater.

Failure to Make Orthogonal Polynomial Adjustments for Unequally Spaced Intervals Yields Inaccurate F Values in Trend Tests

1971 ◽  
Vol 33 (3_suppl) ◽  
pp. 1179-1183 ◽  
Author(s):  
Jon E. Roeckelein
Keyword(s):  
Orthogonal Polynomial ◽  
Linear Component ◽  
Major Result ◽  
Quadratic Regression ◽  
Trend Analyses ◽  
Quadratic Component ◽  
Unequally Spaced ◽  
Independent Variable ◽  
Made In

Trend tests on the same sets of data having unequally spaced intervals of the independent variable were conducted under conditions of adjustment and non-adjustment of the orthogonal coefficients for linear and quadratic regression. The major result was an inflated F value for the linear component and potentially spurious values for the quadratic component. It was recommended that authors explicitly cite procedures when adjustments of orthogonal coefficients have been made in trend analyses for unevenly spaced levels of the independent variable.

174: Heat as an Independent Variable in the Development of Rat Testicles During Different Stages of Life

2004 ◽  
Vol 171 (4S) ◽  
pp. 46-46
Author(s):  
Andy Yu-How Chang ◽  
Andrew Hwang ◽  
Hei Wen Xie ◽  
Jie Cai ◽  
Susan Groshen ◽  
...  
Keyword(s):  
Independent Variable
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