Use Least Squares to fit the points (8, -2), (1.1, - 1.6), (1.48, 6.3), (1.75, 1

Question

Use Least Squares to fit the points (8, -2), (1.1, - 1.6), (1.48, 6.3), (1.75, 15), (2.25), (2.25, 48), (2.5, 70), (2.75, 110) to the equation y = ax^3.5 + e^bx - c sin(x)/x^2. Find the constants a, b, c. Show all of your work. Include a plot with the data points and curve of the equation. Include your Matlab code. Use Least Squares to fit the points (.5, 8.9), (1, 2.9), (2, 2.5)(2.5, 2.3), (3, 2).(3.4, 1.7), (4, 1.3), (4.5, 1), (5, 8), (5.5, 66), (6.5, .63), (8., 9) To the equation ae^x + bx - c log(x)/x. Do this by setting up and minimizing the equation phi(a, b, c). Show all of your work. Include a plot with the data points and curve included. Include your Matlab code. Fit the same data point to the equation ae^x + bx - c log(x)/x - x^d. Do this by setting up an minimizing the equation phi(a, b, c, d) Show all of your work. Include a plot with the data points and curve included. Included your Matlab code.

Explanation / Answer

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Short Description Of The Method of Least Squares
The Method of Least Squares is a procedure to determine the best fit line to data; the
proof uses simple calculus and linear algebra. The basic problem is to find the best fit
straight line y = ax + b given that, for n Belongs To{ 1, ........... ,N} the pairs (xn, yn) are observed.
The method easily generalizes to finding the best fit of the form
y = a1f1(x) + ......... + cKfK(x);

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