# Tag Archives: least squares

## Linear Algebra and Its Applications, Exercise 3.4.25

Exercise 3.4.25. Given over the interval what is the closest line to the parabola formed by ? Answer: This amounts to finding a least-squares solution to the equation , where the entries 1, , and are understood as functions of … Continue reading

## Linear Algebra and Its Applications, Exercise 3.4.17

Exercise 3.4.17. Given the matrix from the previous exercise and the vector , solve by least squares using the factorization . Answer: From the previous exercise we have To find the least squares solution to where , we take advantage … Continue reading

## Linear Algebra and Its Applications, Exercise 3.4.15

Exercise 3.4.15. Given the matrix find the orthonormal vectors and that span the column space of . Next find the vector that completes the orthonormal set, and describe the subspace of of which is an element. Finally, for find the … Continue reading

## Linear Algebra and Its Applications, Exercise 3.4.1

Exercise 3.4.1. a) Given the following four data points: write down the four equations for fitting to the data. b) Find the line fit by least squares and calculate the error . c) Given the value of what is in … Continue reading

## Linear Algebra and Its Applications, Exercise 3.3.26

Exercise 3.3.26. A middle-aged man is stretched on a rack with various forces. Given the measurements of length (in feet) at forces (in tons), and assuming that Hooke’s Law applies, use least squares to find the man’s length when no … Continue reading

## Linear Algebra and Its Applications, Exercise 3.3.25

Exercise 3.3.25. Given the measurements at  from the previous exercise, what would be the coefficient matrix , the unknown vector , and the data vector if we wish to fit the data using a parabola of the form ? Answer: We would … Continue reading

## Linear Algebra and Its Applications, Exercise 3.3.24

Exercise 3.3.24. Given the measurements at use least squares to find the line of best fit. Answer: This corresponds to a system of the form as follows: To find the least squares solution we multiply both sides by to create a system … Continue reading

## Linear Algebra and Its Applications, Exercise 3.3.23

Exercise 3.3.23. Given measurements show that the best least squares fit to the horizontal line is given by Answer: This corresponds to the system where is an by 1 matrix with all entries equal to 1 and . To find the … Continue reading