A primer for biomedical scientists on how to execute model II linear regression analysis.

Area of Science:

• Statistics
• Biomedical Science
• Data Analysis

Background:

• Linear regression analysis is performed using two distinct models: Model I (fixed x-values) and Model II (variable x-values with error).
• Biomedical scientists frequently report difficulties with Model II linear regression, potentially explaining its infrequent use in physiological, pharmacological, and biochemical research.

Purpose of the Study:

• To advocate for the use of least products linear regression analysis for Model II regressions.
• To review and compare three computational methods for executing ordinary least products (OLP) and weighted least products (WLP) regression analysis.

Main Methods:

• Review of three approaches for OLP and WLP regression: scientific calculators/spreadsheets, specific-purpose software, and general-purpose software.
• Evaluation of the accuracy of slope, intercept, and confidence intervals (CI) obtained from each method.
• Demonstration of using specific programs like 'smatr' for accurate OLP regression coefficients and bootstrapping for CIs.

Main Results:

• Scientific calculators/spreadsheets provide accurate OLP slope and intercept but inaccurate 95% confidence intervals.
• The freeware program 'smatr' accurately calculates OLP regression coefficients and obtains 95% CIs using bootstrapping, also enabling slope comparisons.
• General-purpose programs like Systat and Statistica are recommended for regular users, with detailed instructions provided for using loss functions.

Conclusions:

• Least products linear regression analysis is recommended for Model II regressions.
• Specific-purpose programs like 'smatr' offer accurate results and are accessible for biomedical scientists.
• General-purpose statistical software provides robust options for advanced users performing frequent linear regression analyses.