(r7) DataFitting < OpsRes

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CaseStudyForm
Title	DataFitting
DateSubmitted	19 Feb 2008
CaseStudyType	DIYCaseStudy
OperationsResearchTopics	NonlinearProgramming
ApplicationAreas	Data Analysis
ProblemDescription	Also known as The Least Squares Problem When modelling data, scientists often want to fit an analytical model to their experimental data. In this case an experiment has provided some -coordinates that have a growth curve shape, i.e., initially increases quickly with , thens tails off to some maximum value. The scientists in this study have suggested three possible functions to model this behaviour: $y = f(x) \equiv \displaystyle\frac{1}{a x^2 + b x + c}$ $y = f(x) \equiv a\log(x - b) + c$ $y = f(x) \equiv a\sqrt{x - b} + c$ Given one of the possible functions and the data points $(x_i, y_i), i=1, \ldots, n$ they want to find , and to minimize the squared distance between the data points and the estimates, i.e., $\begin{equation} \min_{a, b, c} \sum_{i=1}^n \left(y_i - f(x_i) \right)^2 \end{equation}$ The scientists have specified the number of data points and their coordinates in an AMPL data file `regression.dat`. The scientists want to know which of the suggested functions provides the best fit to the data.
ProblemFormulation	The formulation...
ComputationalModel	The computational model...
Results	The results...
Conclusions	In conclusion...
ExtraForExperts
StudentTasks	Write AMPL files `regression.mod` and `regression.run` that use `regression.dat` to solve The Data Fitting Problem. Write a management summary of your solution. Be sure to indicate which of the functions fits the data best. What to hand in Your new AMPL files `regression.mod` and `regression.run`. Your management summary.