9. (а) Consider the data set of (х, у) рairs 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)}
9. (а) Consider the data set of (х, у) рairs 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)}
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Topic Video
Question

Transcribed Image Text: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+
X- | Y- | (X-) x (Y- | |
-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 |
Hence option 3 is correct.
Step by step
Solved in 4 steps

Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Recommended textbooks for you

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc

Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning

Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning

Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON

The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman

Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman