Answered: The following sample observations were…

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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Exercise 13-2 (LO13-2)

The following sample observations were randomly selected.


x	5	3	6	3	4	4	6	8
y	13	15	7	12	13	11	9	5

Determine the coefficient of correlation and the coefficient of determination. Interpret the association between x and y. (Round your coefficient of determination to 4 decimal places. Round all other answers to 2 decimal places. Negative values should be indicated by a minus sign.)

x	y	x−x¯x-x¯		y−y¯y-y¯	(x−x¯)2x-x¯2		(y−y¯)2y-y¯2	(x−x¯) (y−y¯)x-x¯ y-y¯
5	13					2.38			0.02	5.64	0.30
3	15					4.38			3.52	19.14
6	7		1.13						1.27	13.14	-4.08
3	12		-1.88						3.52	1.89
4	13		-0.88			2.38				5.64	-2.08
4	11		-0.88			0.38				0.14	-0.33
6	9		1.13			-1.63			1.27
8	5		3.13			-5.63			9.77		-17.58
39	85

x¯x¯

y¯y¯

S_x

S_y

The correlation coefficient of indicates a (Click to select) very strong negative moderate inverse strong inverse no very strong positive relationship between x and y. The coefficient of determination is , found by squaring the value of . x accounts for % of the variation in y.

**Exercise 13-2 (LO13-2)**

The following sample observations were randomly selected.

| x | 5 | 3 | 6 | 3 | 4 | 6 | 8 |
|----|---|---|---|---|---|---|---|
| y | 13| 15| 7 | 12| 11| 5 | 9 |

[Click here for the Excel Data File](#)

Determine the coefficient of correlation and the coefficient of determination. Interpret the association between $ x $ and $ y $. (Round your coefficient of determination to 4 decimal places. Round all other answers to 2 decimal places. Negative values should be indicated by a minus sign.)

| x | y | $ x - \bar{x} $ | $ y - \bar{y} $ | $ (x - \bar{x})^2 $ | $ (y - \bar{y})^2 $ | $ (x - \bar{x})(y - \bar{y}) $ |
|-----|-----|-------------------|-------------------|------------------------|------------------------|------------------------------------|
| 5 | 13 | 1.13 | 2.38 | 0.02 | 5.64 | 0.30 |
| 3 | 15 | -0.87 | 4.38 | 0.76 | 19.14 | |
| 6 | 7 | 2.13 | -3.62 | 4.52 | 13.14 | -7.71 |
| 3 | 12 | -0.87 | 1.38 | 0.76 | 1.89 | -1.20 |
| 4 | 11 | 0.13 | 0.38 | 0.02 | 0.14 | 0.05 |
| 6 | 5 | 2.13 | -5.62 | 4.52 | 31.64 | -11.98 |
| 8 |

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