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 = ax + b describing the trend of data. In your answer include the following: 1) n=1 xn, where N is a total number of measurements. (2 points) 1n, where N is a total number of measurements. (2 points) 1(x), where N is a total number of measurements. (2 points) 1n yn, where N is a total number of measurements. (2 points) 2) 3) 4) 5) Determinant of the matrix A = 6) Elements of the inverse matrix =1 A-1 = Xn =1 =1 1 (2 points) (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) Problem 2 (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 1 2 3 4 5 Vn 5.3 6.3 4.8 3.8 3.3 Using the method of least squares determine the linear equation y = ax + b describing the trend of data. In your answer include the following: 1) n=1 xn, where N is a total number of measurements. (2 points) 2) n=1 Yn, where N is a total number of measurements. (2 points) 3) E-1(x), where N is a total number of measurements. (2 points) N 4) En=1 Xn Yn, where N is a total number of measurements. (2 points) 5) Determinant of the matrix A = 6) Elements of the inverse matrix N =1()2 N =1 A- = 2n=1 xn -1 1 (2 points) = [3]. (10 points) 7) Coefficients a and b in y = a x + 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) 1