Back to Matrix Theory and Linear Algebra

Application: Least squares approximations and curve fitting

Finding least squares solutions of inconsistent systems via the normal equations, and fitting lines and parabolas to scattered data points.

Matrix Theory and Linear Algebra, Application: Least squares approximations and curve fitting

Status

FlagsLoading your progress…

4 exercises

Exercise 11.5.1

Find the least squares approximation for the system of equations

3.0

Exercise 11.5.2

Find the least squares approximation for the system of equations

3.0

Exercise 11.5.3

Consider the points $(x_{1},y_{1})=(-1,0)$ , $(x_{2},y_{2})=(0,3)$ , $(x_{3},y_{3})=(1,3)$ , $(x_{4},y_{4})=(2,5)$ , $(x_{5},y_{5})=(3,9)$ . Find the least squares line for these points.

3.0

Exercise 11.5.4

Consider the points $(x_{1},y_{1})=(-1,4)$ , $(x_{2},y_{2})=(0,-2)$ , $(x_{3},y_{3})=(1,4)$ , $(x_{4},y_{4})=(2,2)$ . Find the least squares parabola for these points.

3.0

Adapted from Matrix Theory and Linear Algebra © 2017–2026 Peter Selinger, Lyryx Learning, and Ken Kuttler. Licensed under CC BY 4.0. Source: Matrix Theory and Linear Algebra. Imported at revision d74bc3a.