a) Suppose you are given the following (x, y) data pairs. x 2 3 6 y 4 3 9 Find the least-squares equation for these data (rounded to four digits after the decimal). ŷ = + x (b) Now suppose you are given these (x, y) data pairs. x 4 3 9 y 2 3 6 Find the least-squares equation for these data (rounded to four digits after the decimal). ŷ = + x (c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair? YesNo (d) Solve your answer from part (a) for x (rounded to four digits after the decimal). x = + y Do you get the least-squares equation of part (b) with the symbols x and y exchanged? YesNo (e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (x, y). If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs (y, x), (with x and y exchanged)? Explain using parts (a) through (d). Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.In general, switching x and y values produces a different least-squares equation. In general, switching x and y values produces the same least-squares equation

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Question

(a) Suppose you are given the following (x, y) data pairs.

x	2	3	6
y	4	3	9

Find the least-squares equation for these data (rounded to four digits after the decimal).
ŷ = + x

(b) Now suppose you are given these (x, y) data pairs.

x	4	3	9
y	2	3	6

Find the least-squares equation for these data (rounded to four digits after the decimal).
ŷ = + x

(c) In the data for parts (a) and (b), did we simply exchange the x and y values of each data pair?

YesNo

(d) Solve your answer from part (a) for x (rounded to four digits after the decimal).
x = + y

Do you get the least-squares equation of part (b) with the symbols x and y exchanged?

YesNo

(e) In general, suppose we have the least-squares equation y = a + bx for a set of data pairs (x, y). If we solve this equation for x, will we necessarily get the least-squares equation for the set of data pairs (y, x), (with x and y exchanged)? Explain using parts (a) through (d).

Switching x and y values sometimes produces the same least-squares equation and sometimes it is different.In general, switching x and y values produces a different least-squares equation. In general, switching x and y values produces the same least-squares equation.

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