9. (a) Consider the data set of (x, y) pairs below.{(1, 2), (1, 4), (2, 4), (2, 6), (3, 6), (3, 8), (4, 8), (4, 10), (5, 10), (5, 12), (6, 12),(6, 14), (7, 14), (7, 16), (8, 16), (8, 18), (9, 18), (9, 20), (10, 20), (10, 22)}The least squares line (i.e., the regression line) for this set is(i) y = x + 1(ii) y = -x+4(iii) y = 2x +1(iv) y = 3x+2Visually compare the plots below for parts (b) and (c).(1)(ii)(ii)(b) If a least squares line was determined for each (x, y) plot, the variances (s²) associated to them wouldbe ordered from smallest to largest (where s, s, and s; are the variances corresponding to, respectively,plot (i), plot (ii), and plot (iii)) as(i) < s < s?(ii) s? < s < si(iii) s? < si < s(iv) si < s < s?(c) Relative to plots (ii) and (ii), the linear relationship between x and y in plot (i) appears to be(i) strong negative(ii) strong positive(iii) weak negative(iv) moderate positive10

Name: 9. (a) Consider the data set of (x, y) pairs below.{(1, 2), (1, 4), (
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Description: 9. (a) Consider the data set of (x, y) pairs below.{(1, 2), (1, 4), (2, 4), (2, 6), (3, 6), (3, 8), (4, 8), (4, 10), (5, 10), (5, 12), (6, 12),(6, 14), (7, 14), (7, 16), (8, 16), (8, 18), (9, 18), (9, 20), (10, 20), (10, 22)}The least squares line (

Answered: 9. (а) Consider the data set of (х, у)…

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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9. (a) Consider the data set of (x, y) pairs below.
{(1, 2), (1, 4), (2, 4), (2, 6), (3, 6), (3, 8), (4, 8), (4, 10), (5, 10), (5, 12), (6, 12),
(6, 14), (7, 14), (7, 16), (8, 16), (8, 18), (9, 18), (9, 20), (10, 20), (10, 22)}
The least squares line (i.e., the regression line) for this set is
(i) y = x + 1
(ii) y = -x+4
(iii) y = 2x +1
(iv) y = 3x+2
Visually compare the plots below for parts (b) and (c).
(1)
(ii)
(ii)
(b) If a least squares line was determined for each (x, y) plot, the variances (s²) associated to them would
be ordered from smallest to largest (where s, s, and s; are the variances corresponding to, respectively,
plot (i), plot (ii), and plot (iii)) as
(i) < s < s?
(ii) s? < s < si
(iii) s? < si < s
(iv) si < s < s?
(c) Relative to plots (ii) and (ii), the linear relationship between x and y in plot (i) appears to be
(i) strong negative
(ii) strong positive
(iii) weak negative
(iv) moderate positive
10

Expert Solution

curve fitting

method of least square: This method is a form of mathematical regression analysis used to determine the line of best fit for a set of data.

The least-squares method is a statistical procedure to find the best fit for a set of data by minimizing the sum of residuals of points from the plotted curve.
The fitted line is used to predict the behavior of dependent variables.

calculation

1. Sum of X=110

Sum of Y+

$\bar{X} = 5.5, \bar{Y} = 12$

X- $\bar{X}$	Y- $\bar{Y}$	${(x - \bar{X})}^{2}$	(X- $\bar{X}$ ) x (Y- $\bar{Y})^{2}$
-4.5	-10	20.25	45
-4.5	-8	20.25	36
-3.5	-8	12.25	28
-3.5	-6	12.25	21
-2.5	-6	6.25	15
-2.5	-4	6.25	10
-1.5	-4	2.25	6
-1.5	-2	2.25	3
-0.5	-2	0.25	1
-.05	0	0.25	0
0.5	0	0.25	0
0.5	2	0.25	1
1.5	2	2.25	3
1.5	4	2.25	6
2.5	4	6.25	10
2.5	6	6.25	15
3.5	6	12.25	21
3.5	8	12.25	28
4.5	8	20.25	36
4.5	10	20.25	45
total		165	330

$r e g r e s s i o n e q u a t i o n : \hat{Y} = b X + a b = \frac{(X - \bar{X}) x (Y - \bar{Y)}}{{(X - \bar{X})}^{2}} = \frac{330}{165} = 2 a = \bar{Y} - b \bar{X} = 12 - (2 * 5.5) = 1 e s t i m a t e d e q u a t i o n i s : \hat{y} = 2 X + 1$

Hence option 3 is correct.

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