Curve FittingCurve Fitting

Discovering RelationshipsDiscovering Relationships

Purpose of Curve FittingPurpose of Curve Fitting Effectively communicate (describe) informationEffectively communicate (describe) information

Help make predictionsHelp make predictionsIf you have an equation that describes the relationship If you have an equation that describes the relationship between two variables, then you can predict the between two variables, then you can predict the dependent value for each independent value.dependent value for each independent value.

Help us to select from among two or more possible Help us to select from among two or more possible hypotheseshypothesesIf there is more than one possible way to interpret your If there is more than one possible way to interpret your data, sometimes knowing which type of equation better data, sometimes knowing which type of equation better describes the data (linear, log, power, describes the data (linear, log, power, etcetc.) will help you .) will help you decide which interpretation makes more sense.decide which interpretation makes more sense.

rr22 = correlation coefficient = correlation coefficient“goodness of fit”“goodness of fit”

The correlation coefficient tells you the The correlation coefficient tells you the percentage of the variability in the data that percentage of the variability in the data that may be attributed to the proposed equation.may be attributed to the proposed equation.

““What percentage of the ‘ups’ and ‘downs’ in What percentage of the ‘ups’ and ‘downs’ in the data are accounted for by the equation?”the data are accounted for by the equation?”

Lab RulesLab 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.

Metabolic Rate of Goldfish Metabolic Rate of Goldfish at Various Temperaturesat Various Temperatures

•Independent variable?

•Dependent variable?

•General trends?

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."

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.