### Correlation Strength in Paired Data Sets**Problem Statement:**If one set of paired data $ x $ and $ y $ has an $ r = 0.58 $ and a different set of paired data $ c $ and $ d $ has an $ r = -0.83 $, then which set of paired data has the stronger correlation? (Assume both sets have the same sample size.)**Options:**a) $ x $ and $ y $ b) $ c $ and $ d $ c) there is no significant difference d) not enough information e) none of these**Solution Explanation:**The correlation coefficient $ r $ measures the strength and direction of the linear relationship between two variables. Correlation coefficients range from $ -1 $ to $ 1 $.- A correlation of $ 1 $ implies a perfect positive linear relationship.- A correlation of $ -1 $ implies a perfect negative linear relationship.- A correlation of $ 0 $ implies no linear relationship.In this problem: - $ r = 0.58 $ for the $ x $ and $ y $ data pair indicates a moderate positive correlation.- $ r = -0.83 $ for the $ c $ and $ d $ data pair indicates a strong negative correlation.To determine which correlation is stronger, we compare the absolute values of the correlation coefficients. - The absolute value of $ 0.58 $ is $ 0.58 $.- The absolute value of $ -0.83 $ is $ 0.83 $.Since $ 0.83 $ is greater than $ 0.58 $, the correlation between $ c $ and $ d $ is stronger than the correlation between $ x $ and $ y $.Therefore, the correct answer is:b) $ c $ and $ d $

Correlation between two variables measure the strength and direction between two variables. It…

5. If one set of paired data x and y has an r=0.58 and a different set of paired data c and d has an r =- 0.83, then which set of paired data has the stronger correlation? (assume both sets have the same sample size.) a) x and y b) c and d c) there is no significant difference d) not enough information e) none of these

5. If one set of paired data x and y has an r=0.58 and a different set of paired data c and d has an r =- 0.83, then which set of paired data has the stronger correlation? (assume both sets have the same sample size.) a) x and y b) c and d c) there is no significant difference d) not enough information e) none of these

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

### Correlation Strength in Paired Data Sets

**Problem Statement:**

If one set of paired data $ x $ and $ y $ has an $ r = 0.58 $ and a different set of paired data $ c $ and $ d $ has an $ r = -0.83 $, then which set of paired data has the stronger correlation? (Assume both sets have the same sample size.)

**Options:**
a) $ x $ and $ y $
b) $ c $ and $ d $
c) there is no significant difference
d) not enough information
e) none of these

**Solution Explanation:**

The correlation coefficient $ r $ measures the strength and direction of the linear relationship between two variables. Correlation coefficients range from $ -1 $ to $ 1 $.

- A correlation of $ 1 $ implies a perfect positive linear relationship.
- A correlation of $ -1 $ implies a perfect negative linear relationship.
- A correlation of $ 0 $ implies no linear relationship.

In this problem:

- $ r = 0.58 $ for the $ x $ and $ y $ data pair indicates a moderate positive correlation.
- $ r = -0.83 $ for the $ c $ and $ d $ data pair indicates a strong negative correlation.

To determine which correlation is stronger, we compare the absolute values of the correlation coefficients.

- The absolute value of $ 0.58 $ is $ 0.58 $.
- The absolute value of $ -0.83 $ is $ 0.83 $.

Since $ 0.83 $ is greater than $ 0.58 $, the correlation between $ c $ and $ d $ is stronger than the correlation between $ x $ and $ y $.

Therefore, the correct answer is:
b) $ c $ and $ d $

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