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Applied Calculus
Fall 2008
Module 3: Curve Fitting
Problem 1: Root Growth, a One Parameter Linear
Model
Problem 2: Development Test Results, Two
Parameter Linear Model
Problem 3: Concentration of Chemical, Two
Parameter Non-linear Model
Introduction
In Module 1 we dealt with situation where a model could be fitted exactly to the
data. It is always possible to find a model that fits the data exactly. This is not,
however, the most appropiate way of modeling the data, especially if want to use the
model to make predictions about future events. It is also inefficient, since there are as
many parameters to calculate as there are data points. An efficient model is one with
the fewest parameters that still manages to describe the behaviour of the data. The
disadvantage of using a model with fewer parameters than data points is that it will
not pass through all the data points, and so we find the model that is the 'best fit' for
the data.
The first problem shows you have to fit the 'best' model of...

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