Curve Fitting

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Curve Fitting

• Discovering Relationships

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Purpose of Curve Fitting

• Effectively communicate (describe) information
• Help make predictionsIf you have an equation
  that describes the relationship between two
  variables, then you can predict the dependent
  value for each independent value.
• Help us to select from among two or more possible
  hypothesesIf there is more than one possible way
  to interpret your data, sometimes knowing which
  type of equation better describes the data
  (linear, log, power, etc.) will help you decide
  which interpretation makes more sense.

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r2 correlation coefficientgoodness of fit

• The correlation coefficient tells you the
  percentage of the variability in the data that
  may be attributed to the proposed equation.
• What percentage of the ups and downs in the
  data are accounted for by the equation?

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Lab Rules

• For this course, a r2 value which is less than
  0.8 will not be considered acceptable. If no
  equation produces a r2 value of at least 0.8, you
  should state that no acceptable regression
  equation could be found.
• In order for one equation to be chosen over
  another, the r2 values for the equations must
  differ by at least 0.05. For example, if one
  equation had a r2 value of 0.85 and another
  equation had a r2 value of 0.89, you would have
  to accept both as reasonable descriptions of the
  data.

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Metabolic Rate of Goldfish at Various
Temperatures

• Independent variable?
• Dependent variable?
• General trends?

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A WORD OF CAUTION Just because you have found
an equation that "fits" your data, it does not
mean that you have actually found the "right"
relationship. Sometimes the "fit" between data
and an equation is the result of two or more
simultaneous events or even the result of your
experimental protocol. It is essential that you
remember "data may provide evidence in support
of a hypothesis, but it does not prove your
hypothesis."
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• PRESENTING RESULTS OF CURVE FITTING
• When you prepare a lab report or article, you
  should inform the reader about all types of
  equations which you attempted to fit to your
  data.
• You should also present the corresponding
  equations and r2 values for any curve fitting
  that you may have done.
• Do not attempt a curve fit with a polynomial
  equation ( Y a bX cX2 . . .). Polynomial
  equations will always fit but they do not provide
  any useful information about your data unless you
  can propose a reasonable hypothesis which fits a
  polynomial equation. Generally linear, log and
  exponential and power equations will suffice for
  this class.