How to calculate the deviation of points from a curve?

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SUMMARY

This discussion focuses on calculating the deviation of points from a modeled curve, specifically addressing quadratic curves and Cartesian forms of polar equations. The recommended method for evaluating the proximity of points to the curve is to calculate the root mean square distance, which serves as an effective measure of standard deviation. Additionally, employing a chi-square test is suggested for statistical validation of the fit between the points and the curve.

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  • Understanding of quadratic equations and their properties
  • Familiarity with polar equations and their Cartesian conversions
  • Knowledge of statistical measures, specifically standard deviation and root mean square
  • Experience with chi-square tests for statistical analysis
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  • Research methods for calculating root mean square distance in data sets
  • Explore the application of chi-square tests in curve fitting
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  • Investigate the conversion process between polar and Cartesian coordinates
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MelanieBrett
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Hi,
I'm working on some coursework for which I have been modelling a curve to a set of points, and for the final section I am wanting to calculate how close each point is to the curve as a method of comparison between the curves I have calculated. Some of the curves are quadratic, and others are the Cartesian form of some Polar equations. If anyone could offer any help or advice, it would be much appreciated :)
 
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You could try calculating the average distance of each set of points from the curve - perhaps better to look at the root mean square distance. Essentialy the standard deviation of the points from the curve.
 

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