In this assignment, you must use variables, loops, if statements, your own function definitions and function calls to write the required functions. For now, you may not use any of the powerful functions available in python modules, with a few exceptions: You may import functions from the math, copy, matplotlib.plot and numpy. You may NOT use numpy.linalg.lstsq(). You may use fsolve() and quad() from scipy, but nothing else.

a) Write a program that demonstrates the Least Squares Curve Fitting method. You must write and call at least the following 3 functions def LeastSquares(x,y,power): # which calculates and returns an array containing the coefficients of the least squares polynomial def PlotLeastSquares(x,y,power): # which calls LeastSquares, generates datapoints and plots the least squares curve along with the original data def main() A main program that uses the data given below to 1. Call LeastSquares to generate and print the coefficients of a linear fit 2. Call PlotLeastSqares to display a plot for the linear fit 3. Call LeastSquares to generate and print the coefficients of a Cubic fit 4. Call PlotLeastSqares to display a plot for the Cubic fit 956 1.09 1.332 05 .15 .31 .46 .7 74 .82 98 1.17 y539 .378 .370 306 242 .104