HW 7: Data Fit (100 points) Problem 1 (50 points) Experimental data for force versus displacement is indicated in the table below. n=1 n=2 n=3 n=4 n=5 Xn 0 1 2 4 5 Yn 2.1 2.4 2.6 2.8 3.0 Using the method of least squares determine the linear equation y = a x + b describing the trend of data. In your answer include the following: 1) 1 xn, where N is a total number of measurements. (2 points) 2) En=1 Yn, where N is a total number of measurements. (2 points) 3) 1(x), where N is a total number of measurements. (2 points) 4) 1xn yn, where N is a total number of measurements. (2 points) 5) Determinant of the matrix A = 6) Elements of the inverse matrix C^=1(xn) ^=1xn] Zn=1 xn 1xn]. (2 points) Zn=1 A- = [] (10 points) 7) Coefficients a and b in y = ax + b and the equation for the trend line. (10 points) 8) Plot experimental data and the trend line. Include appropriate labels for the plot. (10 points) 9) A Matlab code for questions (1) to (8). (10 points)