Suppose that a scientist has reason to believe that two quantities x and y are related and b. linearly, that is, y = mx + b, at least approximately, for some values of The scientist performs an experiment and collects data in the form of points (x₁, y₁), (x2, y2), (Xn, yn), and then plots these points. The points do not lie exactly on a straight line, so the scientist wants to find constants m and b so that the line y = mx + b fits the points as well as possible, as shown in the figure. Let di y₁ − (mx¡ + b) be the vertical deviation of the point (x₁, y₁) from the line. The method of least squares determines m and b so as to minimize f(m, b) = [₁ d, the sum of the squares of these deviations. Show that, according to this method, the line of - best fit is obtained when =WI Xi m+nb = n Σx²m+ Exib i=1 = n Σyi i=1 Exiyi- i=1 = Thus, the line is found by solving these two equations in the unknowns m and b.

Suppose that a scientist has reason to believe that two quantities x and y are related and b. linearly, that is, y = mx + b, at least approximately, for some values of The scientist performs an experiment and collects data in the form of points (x₁, y₁), (x2, y2), (Xn, yn), and then plots these points. The points do not lie exactly on a straight line, so the scientist wants to find constants m and b so that the line y = mx + b fits the points as well as possible, as shown in the figure. Let di y₁ − (mx¡ + b) be the vertical deviation of the point (x₁, y₁) from the line. The method of least squares determines m and b so as to minimize f(m, b) = [₁ d, the sum of the squares of these deviations. Show that, according to this method, the line of - best fit is obtained when =WI Xi m+nb = n Σx²m+ Exib i=1 = n Σyi i=1 Exiyi- i=1 = Thus, the line is found by solving these two equations in the unknowns m and b.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Similar questions

can you complete the follow up question i posted
Could you perhaps draw this?
Can you also complete parts D,E, and F, please?
Can you please answer question 8 and 9 please and show Work
are you sure?