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Problem 4 (20 points) - Least-Squares Fitting with Higher-Order Polynomials In the linear least-squares regression, we are aiming at minimizing the error of the fit defined as the sum of the squares of all the residuals ry's: E(a, , d, , a ,do) = > =[[x- f(x,)]' =[[x-(atax tax tax) 1-1 where a is the number of data points, x and y are associated with / data point, and do, al, az, and, as are the four unknown coefficients to be determined. Derive the four equations that could be used to solve for the four unknown coefficients ao, al, az, and, a3. Note that you need to provide step-by-step & detailed derivations. NO partial credit will be given if you simply write down the four equations.Assignment 5: Introduction to MATLAB Calculations & Plotting 1. The surface to volume ratio of the earth is 7.5753 x 10" miles . Determine an approximate diameter for the earth. 2. The length L of a belt that traverses two pulley wheels, one of radius R and one of radius r and whose centers are distance S apart is given by L = 25cosB + n(R + r) + 20(R - r) where 0 = sin '[(R -r)/S) Determine L when R = 30 cm, r =12 cm, and $ =50 cm. (Remember MATLAB likes angles in radians). 3. A geometric series is defined as the sequence 1, x x, x". . . in which the powers of x range over the integers from 0 to infinity. The sum of the terms in a geometric series converges to the limiting value of 1/ (1 -x) if |x|