2. (6 marks) Find the best line y = c+dt to fit y = 1, 1, 2, 2 at times t = -1, 0, 1, 2. (Use the least squares approximation.)
LINEAR ALGEBRA 2. (6 marks) Find the best line y=c+dt to fit y=1, 1, 2, 2 at times t=-1, 0, 1, 2. (Use the least squares approximation.)
1. (4 marks) Show that the set of vectors {7: = (1,1,1,1), 7x = (1,0,−1,0), 7: = (0,1,0, -1)} is orthogonal. Use those vectors in the set to get an orthonormal set {to, to, s}. 2. (6 marks) Find the best line y =c+dt to fit y=1, 1, 2, 2 at times t = -1, 0, 1, 2. (Use the least squares approximation.)
3. Find the best straight-line fit (least squares) to the measurements t -2, b 4 at at t =-1 b 1 at t0 b 0 at t = 2. Then find the projection p of 3 b 0 onto the column space of A = 1 10 1 2
q We would like to fit a line y = cx + d to the following data х у -1 -3 0 -1 0 2 3 using the method of least squares. (a) Write down the (overdetermined) linear system this problem gives rise to in the form Ax = b, where x = (..) (b) Find the best-fit line by computing the least-squares solution of the system Ax = b.
(a) Sketch the line that appears to be the best fit for the given points. (b) Find the least squares regression line. y(x)= (c) Calculate the sum of squared error. 11. [-13.22 Points] DETAILS LARLINALG8 2.6.017. Consider the following. 5 (1,5) 4 (2, 4) 3 2 (2, 2) (3, 1) - Х - 1 2 3 4 -14 (a) Sketch the line that appears to be the best fit for the given points.
2. For the data plotted below, draw (visually) a best-fit line. Then write down an equation for the best-fit line you have drawn. Finally, extrapolate (i.e. pred value when the independent variable is at 3.5. It is not necessary to calculate the least-squares best-fit line! lict) the dependent variable 3.5 2.5 1.5 0.5 0 0.5 1 1.522.5 3 3.5 3.5 T 2.5 1.5 0.5 1.5 2.5
Find the line y = a + bx which best fits the data points (x, y): (0, 1), (1, 1), (1, 2) in the least squares sense. must use matrix
Let y = a + bx be the best-fit straight line for the data pairs (1, 1), (1, 2), (2, 0). Find b.
least squares to fit a straight line Pre-lab A-3 Least Squares Fit to a Straight Line Read lab A-3: Least squares fit to a straight line. A set of data is given in the following table and plotted on the right: x(s) y (m) Lab 3 exercise 27 Use the graph on the right to calculate the slope and the intercept of the line. 1 2 3 4 5 Slope Intercept Use equations (6) in the lab manual to calculate...