Curve Fitting

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Curve Fitting
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Fitting a Curve to Data

• Done to find a mathematical function that
  represents a real behavior
• Must include a thorough understanding of the
  system
• Potential for erroneous forecasts
• An example

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Measuring a Fit

• Correlation
• Statistical relationship between two variables
• Goes between -1.0 and 1.0
• Zero means no relationship
• http//argyll.epsb.ca/jreed/math9/strand4/scatterP
  lot.htm

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Linear Regression

• Assumes a cause and effect between one dependent
  variable and one or more independent variables
• Solution of the linear equation with a best fit
  to data
• Y aX b 
• where 
• Y the dependent variable
• a a coefficient equivalent to the slope of the
  line
• b the Y intercept of the line (the place where
  it crosses the Y axis)
• Y a1X1 a2X2 a3X3 b for multiple causes

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• Use the vertical offsets to estimate Y for a
  given X
• Square the differences so all numbers are
  positive
• Sum of the squared offsets or deviations is a
  measure of the goodness of fit
• R2 or coefficient of determination (0 to 1.0)

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Fitting Non-linear Data

• Same principle and measurement of the deviations
• Choice of curve to fit not automatic
• Individual choice with possibility of error
• Real relationship may not be fully represented by
  experimental data

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Potential Errors

• Chose the wrong function
• Experiments did not measure all possible
  circumstances
• Behavior may change in areas outside the sample
  data
• E.G. physical limitations of system lead to
  failure

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Exercise

• Use MATLAB curve fitting tool to fit a non-linear
  curve
• Interpret the output
• Discuss the potential failure of the model when
  it reaches the limits