Suppose measurements of y versus x give three points in the x-y plane withcoordinates (0,6), (1,0), (2,0).(a) Show that there is no straight line that intersects all three points.(b) Find the linear function y = c0 + c1x that best fits this data in the least squares sense, by finding the coefficients c0, c1 using the method of least squares.(c) Show that the solution is the best possible in the sense that it minimizes the length of the residual.

Answered: Suppose measurements of y versus x give…

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

ChapterP: Preliminary Concepts

SectionP.CT: Test

Problem 1CT

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Question

Suppose measurements of y versus x give three points in the x-y plane with
coordinates (0,6), (1,0), (2,0).

(a) Show that there is no straight line that intersects all three points.

(b) Find the linear function y = c₀ + c₁x that best fits this data in the least squares sense, by finding the coefficients c₀, c₁ using the method of least squares.

Expert Solution

Step 1

(a)

Plot the points on the graph. As the points (1,0) and (2,0) are co-linear therefore, it is not possible that one straight line intersects all the 3 points.

Step 2

(b)

For the given points calculate the $\sum_{} X, \sum_{} Y, \sum_{} X^{2} a n d \sum_{} X Y$ .

Points	$X$	$Y$	$X^{2}$	$X Y$
( 0,6 )	0	6	0	0
( 1,0 )	1	0	1	0
( 2,0 )	2	0	4	0
	$\sum_{} X = 3$	$\sum_{} Y = 6$	$\sum X^{2} = 5$	$\sum_{} X Y = 0$

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