The paired data below consist of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands): Cost 9 4 2 3 Number 85 |68 53 55 Find the value of the linear correlation coefficient r. 0.9703 0.235 0.246 0.708

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
icon
Concept explainers
Question
### Correlation Between Advertising Costs and Product Sales

Understanding the relationship between advertising expenses and the number of products sold is crucial for making informed business decisions. Below, we analyze paired data to determine this relationship and find the linear correlation coefficient \( r \).

#### Paired Data
The table below consists of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands):

| Cost (in thousands of dollars) | Number of Products Sold (in thousands) |
|-------------------------------|----------------------------------------|
| 9                             | 85                                     |
| 4                             | 68                                     |
| 2                             | 53                                     |
| 3                             | 55                                     |

#### Task
Find the value of the linear correlation coefficient \( r \).

#### Options
- \( r = 0.9703 \)
- \( r = 0.235 \)
- \( r = 0.246 \)
- \( r = 0.708 \)

The linear correlation coefficient, \( r \), measures the strength and direction of the relationship between two variables. It ranges from \( -1 \) to \( 1 \), where values closer to \( 1 \) or \( -1 \) indicate a stronger linear relationship.

#### Solution
To find the correlation coefficient, we typically use statistical software or a calculator to input the data pairs. Once the values are input, the software computes \( r \).

After performing the calculations, select the correct value of \( r \) from the given options.

### Conclusion
Understanding the linear correlation coefficient helps businesses gauge how effectively their advertising spend translates into sales. Higher positive values indicate a strong positive correlation, meaning increased advertising spending tends to result in more product sales. 

For more detailed explanation and examples of correlation coefficient calculations, please refer to our statistical analysis course.
Transcribed Image Text:### Correlation Between Advertising Costs and Product Sales Understanding the relationship between advertising expenses and the number of products sold is crucial for making informed business decisions. Below, we analyze paired data to determine this relationship and find the linear correlation coefficient \( r \). #### Paired Data The table below consists of the costs of advertising (in thousands of dollars) and the number of products sold (in thousands): | Cost (in thousands of dollars) | Number of Products Sold (in thousands) | |-------------------------------|----------------------------------------| | 9 | 85 | | 4 | 68 | | 2 | 53 | | 3 | 55 | #### Task Find the value of the linear correlation coefficient \( r \). #### Options - \( r = 0.9703 \) - \( r = 0.235 \) - \( r = 0.246 \) - \( r = 0.708 \) The linear correlation coefficient, \( r \), measures the strength and direction of the relationship between two variables. It ranges from \( -1 \) to \( 1 \), where values closer to \( 1 \) or \( -1 \) indicate a stronger linear relationship. #### Solution To find the correlation coefficient, we typically use statistical software or a calculator to input the data pairs. Once the values are input, the software computes \( r \). After performing the calculations, select the correct value of \( r \) from the given options. ### Conclusion Understanding the linear correlation coefficient helps businesses gauge how effectively their advertising spend translates into sales. Higher positive values indicate a strong positive correlation, meaning increased advertising spending tends to result in more product sales. For more detailed explanation and examples of correlation coefficient calculations, please refer to our statistical analysis course.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Knowledge Booster
Correlation, Regression, and Association
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.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
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 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…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
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
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman