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A primer for biomedical scientists on how to execute Model II linear regression analysis
Author(s) -
Ludbrook John
Publication year - 2012
Publication title -
clinical and experimental pharmacology and physiology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.752
H-Index - 103
eISSN - 1440-1681
pISSN - 0305-1870
DOI - 10.1111/j.1440-1681.2011.05643.x
Subject(s) - linear regression , regression analysis , bootstrapping (finance) , calculator , computer science , linear model , statistics , regression , confidence interval , data mining , mathematics , econometrics , machine learning , operating system
Summary 1. There are two very different ways of executing linear regression analysis. One is Model I, when the x ‐values are fixed by the experimenter. The other is Model II, in which the x ‐values are free to vary and are subject to error. 2. I have received numerous complaints from biomedical scientists that they have great difficulty in executing Model II linear regression analysis. This may explain the results of a Google Scholar search, which showed that the authors of articles in journals of physiology, pharmacology and biochemistry rarely use Model II regression analysis. 3. I repeat my previous arguments in favour of using least products linear regression analysis for Model II regressions. I review three methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis: (i) scientific calculator and/or computer spreadsheet; (ii) specific purpose computer programs; and (iii) general purpose computer programs. 4. Using a scientific calculator and/or computer spreadsheet, it is easy to obtain correct values for OLP slope and intercept, but the corresponding 95% confidence intervals (CI) are inaccurate. 5. Using specific purpose computer programs, the freeware computer program smatr gives the correct OLP regression coefficients and obtains 95% CI by bootstrapping. In addition, smatr can be used to compare the slopes of OLP lines. 6. When using general purpose computer programs, I recommend the commercial programs systat and Statistica for those who regularly undertake linear regression analysis and I give step‐by‐step instructions in the Supplementary Information as to how to use loss functions.