Thread: Empirical data
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Sep23-09, 02:45 PM
HW Helper
P: 925
Sort of. Need to be careful of terminology: tk is an experimentally determined data point. Equation 1 is the idealized function that is suppose to represent the data, but doesn't precisely do so because of experimental error associated with the data points. The method to estimate the parameters a & b is least squares. Equation 2 is the least squares problem to solve based on the desired fitting function (i.e. equation 1).

Thus, if you have a bunch of experimentally determined data points tk, estimates of the parameters a & b can be found by minimizing equation 2. I hope this helps explain the situation.

One thing that seems odd is the use of k in equation 2. The index k is meant to represent the index of data points, but k is also used within the fitting function itself (i.e. equation 1). Either that's a typo or the "x" values associated with the data points is really 0,1,2...n.