Compute Y on X regression. Assumes y(i) = slope*x(i) +error(i) (all the error is in y.)
This program calculates a Y on X regression. The x values are considered exact. Only the Y values contain error (noise). The added noise can be proportional, i.e., y=Yexact*(1+Fraction*Noise), where Fraction is usually chosen 0<=Fraction<=0.25, or additive y=Yexact+Fraction*Noise, where Noise is either Gaussian or Uniform with mean 0 and variance 1.
Yexact is the dashed blue line. It graphs the exact relationship between x and Yexact.
y are the circles connected by black lines. These are the Yexact values perturbed by noise (error). The noise is proportional Gaussian noise, i.e. y = Yexact*(1+Fraction*G(0,1)) where G(0,1) is Gaussian noise with mean 0 and variance 1. Fraction scales the noise and gives it a variance of Fraction*Fraction. Fraction is usually chosen to be greater than 0 and less than 0.25.
Yfit is the red line. This is a plot of the regression.
The equations for this model may be viewed by running the JSim model applet and clicking on the Source tab at the bottom left of JSim's Run Time graphical user interface. The equations are written in JSim's Mathematical Modeling Language (MML). See the Introduction to MML and the MML Reference Manual. Additional documentation for MML can be found by using the search option at the Physiome home page.
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Please cite https://www.imagwiki.nibib.nih.gov/physiome in any publication for which this software is used and send one reprint to the address given below:
The National Simulation Resource, Director J. B. Bassingthwaighte, Department of Bioengineering, University of Washington, Seattle WA 98195-5061.
Model development and archiving support at https://www.imagwiki.nibib.nih.gov/physiome provided by the following grants: NIH U01HL122199 Analyzing the Cardiac Power Grid, 09/15/2015 - 05/31/2020, NIH/NIBIB BE08407 Software Integration, JSim and SBW 6/1/09-5/31/13; NIH/NHLBI T15 HL88516-01 Modeling for Heart, Lung and Blood: From Cell to Organ, 4/1/07-3/31/11; NSF BES-0506477 Adaptive Multi-Scale Model Simulation, 8/15/05-7/31/08; NIH/NHLBI R01 HL073598 Core 3: 3D Imaging and Computer Modeling of the Respiratory Tract, 9/1/04-8/31/09; as well as prior support from NIH/NCRR P41 RR01243 Simulation Resource in Circulatory Mass Transport and Exchange, 12/1/1980-11/30/01 and NIH/NIBIB R01 EB001973 JSim: A Simulation Analysis Platform, 3/1/02-2/28/07.