I need help with this for my numerical analysis class! Consider the following data set: (1,2.2), (3,5), (5,5.5),(7,6.1), (10,6.6
). Use least squares to determine the constants m and b in the function y = mx/(b+x).
1 answer:
Answer:
- m ≈ 8.165
- b ≈ 2.299
Step-by-step explanation:
It is convenient to let technology help out. Some graphing calculators will accommodate a model of your choice. Others are restricted to particular models, of which yours may not be one.
A spreadsheet solver may also offer the ability to optimize two variables at once. For that, you would write a function that gives the sum of the squares of the differences between your data points and those predicted by the model. You would ask the solver to minimize that sum.
If you want to do this "the old-fashioned way," you would write the same "sum of squares" function and differentiate it with respect to m and b. Solve the simultaneous equations that make those derivatives zero. (My solver finds multiple solutions, so the neighborhood needs to be restricted in some way. For example m > 0, b > 0, or sum of squares < 1.)
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