Write a MatLab user-defined function that determines the coefficients of a cubic polynomial, ƒ(x)=a₂x³ + a₂x² + a₁x + a that best fits a given set of data points. The function should also calculate the overall error E. Name the function [a,Er] = CubPolFit(x,y), where the input arguments x and y are vectors with the coordinates of the data points, and the output argument a is a four-element vector with the values of the coefficients a3, a₂, a₁, a. The output argument Er is the value of the overall error. (a) Use CubPolFit to find the cubic polynomial that best fits the data in the rubber tension tests (see lecture slides): Curve fitting - polynomial regression - Example A tension test is conducted for determining the stress-strain be- havior of rubber. The data points from the test are shown in the figure, and their values are given below. Determine the fourth order polynomial that best fits the data points. Make a plot of the data points and the curve that corresponds to the polynomial. Strain € Stress o (MPa) Strain € Stress o (MPa) 0 0.4 0.8 1.2 1.6 2.0 2.4 0 3.0 4.5 5.8 5.9 5.8 6.2 2.8 3.2 3.6 4.0 4.4 4.8 5.2 5.6 6.0 7.4 9.6 15.6 20.7 26.7 31.1 35.6 39.3 41.5 40 36 Strain 6 6 2 (b) Write a program in a script file that plots the data points and the curve of the cubic polynomial that best fits the data.

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Use of XOR function

XOR function or exclusive OR function was introduced in Excel 2013. This function is available under excel logical functions. For the given statement, the XOR function will return true only when either of the statements is true. It returns false when both the statements are true or when both the statements are false.