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Related Concept Videos

Regression Analysis01:11

Regression Analysis

Regression analysis is a statistical tool that describes a mathematical relationship between a dependent variable and one or more independent variables.
In regression analysis, a regression equation is determined based on the line of best fit– a line that best fits the data points plotted in a graph. This line is also called the regression line. The algebraic equation for the regression line is called the regression equation. It is represented as:
Calibration Curves: Linear Least Squares01:20

Calibration Curves: Linear Least Squares

A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the instrument response levels, using the substance and its concentrations as standards. Alternatively, or additionally, an equation is fitted to the calibration curve plot and subsequently used to calculate the unknown concentrations of other samples reliably.
For data that follow a straight line, the standard method for fitting is the linear...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least squares (OLS)...
Multiple Regression01:25

Multiple Regression

Multiple regression assesses a linear relationship between one response or dependent variable and two or more independent variables. It has many practical applications.
Farmers can use multiple regression to determine the crop yield based on more than one factor, such as water availability, fertilizer, soil properties, etc. Here, the crop yield is the response or dependent variable as it depends on the other independent variables. The analysis requires the construction of a scatter plot...
Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
In individual population analyses, different algorithms are employed, such as Cauchy's method, which uses a...
Calculating and Interpreting the Linear Correlation Coefficient01:11

Calculating and Interpreting the Linear Correlation Coefficient

The correlation coefficient, r, developed by Karl Pearson in the early 1900s, is numerical and provides a measure of strength and direction of the linear association between the independent variable, x, and the dependent variable, y. Hence, it is also known as the Pearson product-moment correlation coefficient. It can be calculated using the following equation:

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Related Experiment Video

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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
04:35

Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach

Published on: July 3, 2020

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

John Ludbrook1

  • 1The University of Melbourne, Parkville, Victoria, Australia. ludbrook@bigpond.net.au

Clinical and Experimental Pharmacology & Physiology
|November 15, 2011
PubMed
Summary

Model II linear regression analysis, crucial for data with variability, is often challenging for scientists. This study advocates for least products regression and reviews accessible computational methods for accurate analysis.

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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.