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