3. (25 points) Find the line of best fit for the points (0,0), (2, -1), (0,...
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.)
Linear Algebra Question: Least Squares
{(0, b), (1, b2),, , . (k, bk)) İs a set of k points in R2. Show that in the horizontal line 5. Suppose P of best fit f(x) A, A is the average of the numbers b1,. b
{(0, b), (1, b2),, , . (k, bk)) İs a set of k points in R2. Show that in the horizontal line 5. Suppose P of best fit f(x) A, A is the average of the...
(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.
Projections and Least Squares
3. Consider the points P (0,0), (1,8),(2,8),(3,20)) in R2, For each of the given function types f(x) below, . Find values for A, B, C that give the least squares fit to the set of points P . Graph your solution along with P (feel free to graph all functions on the same graph). . Compute sum of squares error ((O) -0)2((1) 8)2 (f(2) -8)2+ (f(3) - 20)2 for the least squares fit you found (a)...
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
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.) 9
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. Normal equations for n points to fit the line y = mx + c: ri 72 yi Problem 1 The data points in the table are given. -2.4 | -5.0 20.81.5 0.3 2.5 1.9 6.4 3.2 11.0 3 Total (a) Fit the best line - to the points (b) Fit the best line y- mr + c to the points (c) Plot the data points and the best fit lines in (a) and (b). Which of the lines is...
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.
Make predictions using a line of best fit Question The table shows data collected on the relationship between the average number of minutes spent exercising per day and math test scores. The line of best fit for the data is 9 = 0.44x + 65.2. Assume the line of best fit is significant and there is a strong linear relationship between the variables. Minutes Test Score 25 30 35 40 (a) According to the line of best fit, what would...