error from a relationship

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Mary292 on 21 Feb 2015
Commented: Star Strider on 4 Mar 2015
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Star Strider
Star Strider on 4 Mar 2015
Context: ‘Mary292’ originally asked how to determine the error with respect to a linear regression applied to perturbed data with a model derived from unperturbed data on the same system. The system was initially unperturbed (the first 2000 data pairs, on which the regression was performed), then perturbed.

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Accepted Answer

Star Strider
Star Strider on 21 Feb 2015
Your model is the linear regression of the first 2000 points. To get the model predictions for the rest of the data, ‘plug in’ the values for your independent variable for the rest of your data in your model. The output of your model are the predictions for those values. To get the error, subtract your predictions from the dependent variable data for those same values of the independent variable.
To illustrate:
x = linspace(0,200); % Create Data
y1 = 0.5*x(1:50) + 0.1*randn(1,50) + 1.2; % Create Data To Fit
y2 = 0.6*x(51:100) + 0.1*randn(1,50) + 1.5; % Create Data To Evaluate Error
b = polyfit(x(1:50), y1, 1); % Parameter Estimates
yfit = polyval(b, x); % Predict Entire Data Set
model_error = yfit - [y1 y2]; % Calculate Error
plot(x, [y1 y2], 'xr')
hold on
plot(x, yfit, '-b')
hold off
legend('Data', 'Model Fit', 'Location','SE')
Star Strider
Star Strider on 22 Feb 2015
My pleasure! And thank you for the compliment!

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