Here's a couple of links about curve fitting.
Curve fitting made easy - The Industrial Physicist
Wikipedia Entry on Curve Fitting
Curve Fitting in Microsoft Excel
One of the important things about curve fitting that is mentioned, briefly, in the first link, is that properly using the curve fitting technique requires some background knowledge and assumptions. It is always possible to find a curve that will match the data to some degree. In many cases, it is always possible to create a curve that fits better than the one produced by your own theory or the theory of anyone else. This is because if we are willing to consider more parameters to our theories, more aspects where we can identify a different value, we have more power over the shape of our curve. With one parameter, we have a straight line on our graph, with two parameters we have a single "bend" in our curve, and with each additional parameter we have the potential for another "bend" somewhere in our graph to turn our curve towards a data point.
However, curve fitting is not supposed to be some sort of mathematical exercise, but a means of determining the which theory of a pre-selected group of theories is the best. This means that curve fitting cannot stand on its own as a theory selection method.
Curve fitting is a good metaphor for scientific reasoning in general. If we look at theory selection from only one direction, we may be basing our scientific beliefs on something pathological.
Curve fitting made easy - The Industrial Physicist
Wikipedia Entry on Curve Fitting
Curve Fitting in Microsoft Excel
One of the important things about curve fitting that is mentioned, briefly, in the first link, is that properly using the curve fitting technique requires some background knowledge and assumptions. It is always possible to find a curve that will match the data to some degree. In many cases, it is always possible to create a curve that fits better than the one produced by your own theory or the theory of anyone else. This is because if we are willing to consider more parameters to our theories, more aspects where we can identify a different value, we have more power over the shape of our curve. With one parameter, we have a straight line on our graph, with two parameters we have a single "bend" in our curve, and with each additional parameter we have the potential for another "bend" somewhere in our graph to turn our curve towards a data point.
However, curve fitting is not supposed to be some sort of mathematical exercise, but a means of determining the which theory of a pre-selected group of theories is the best. This means that curve fitting cannot stand on its own as a theory selection method.
Curve fitting is a good metaphor for scientific reasoning in general. If we look at theory selection from only one direction, we may be basing our scientific beliefs on something pathological.
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