Curve Fitting Discovering Relationships. Purpose of Curve Fitting Effectively communicate (describe) information Effectively communicate (describe) information.

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Presentation transcript:

Curve Fitting Discovering Relationships

Purpose of Curve Fitting Effectively communicate (describe) information Effectively communicate (describe) information Help make predictions If you have an equation that describes the relationship between two variables, then you can predict the dependent value for each independent value. Help make predictions If 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 hypotheses If 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. Help us to select from among two or more possible hypotheses If 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.

r 2 = correlation coefficient “goodness 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?”

Lab Rules For this course, a r 2 value which is less than 0.8 will not be considered acceptable. If no equation produces a r 2 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 r 2 values for the equations must differ by at least For example, if one equation had a r 2 value of 0.85 and another equation had a r 2 value of 0.89, you would have to accept both as reasonable descriptions of the data.

Metabolic Rate of Goldfish at 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 + cX 2...). 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.