Describe the range of values for the correlation coefficient.

MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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### Understanding the Range of Values for the Correlation Coefficient

To test your understanding of the correlation coefficient, answer the following question.

**Question:**
Describe the range of values for the correlation coefficient.

**Choose the correct answer below:**

- **A.** The range of values for the correlation coefficient is 0 to 1, inclusive.
- **B.** The range of values for the correlation coefficient is -1 to 1, not inclusive.
- **C.** The range of values for the correlation coefficient is 0 to 1, not inclusive.
- **D.** The range of values for the correlation coefficient is -1 to 1, inclusive. *(Correct Answer)*

Select the correct option by clicking on it, and then click "Check Answer."

### Explanation:
The correlation coefficient, typically represented by \( r \), quantifies the linear relationship between two variables. Its value can range from -1 to 1, inclusive. This means:

- \( r = 1 \) indicates a perfect positive linear relationship.
- \( r = -1 \) indicates a perfect negative linear relationship.
- \( r = 0 \) indicates no linear relationship.
- Values between these extremes indicate varying degrees of linear relationships.

### Interaction:
Once you make your selection, you can verify your answer by clicking the "Check Answer" button. If you need to start over, use the "Clear All" button.

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**Note:** The image also includes a visual of a computer keyboard, which is not relevant to the educational content described. There are no graphs or diagrams included in the image that require further explanation.
Transcribed Image Text:### Understanding the Range of Values for the Correlation Coefficient To test your understanding of the correlation coefficient, answer the following question. **Question:** Describe the range of values for the correlation coefficient. **Choose the correct answer below:** - **A.** The range of values for the correlation coefficient is 0 to 1, inclusive. - **B.** The range of values for the correlation coefficient is -1 to 1, not inclusive. - **C.** The range of values for the correlation coefficient is 0 to 1, not inclusive. - **D.** The range of values for the correlation coefficient is -1 to 1, inclusive. *(Correct Answer)* Select the correct option by clicking on it, and then click "Check Answer." ### Explanation: The correlation coefficient, typically represented by \( r \), quantifies the linear relationship between two variables. Its value can range from -1 to 1, inclusive. This means: - \( r = 1 \) indicates a perfect positive linear relationship. - \( r = -1 \) indicates a perfect negative linear relationship. - \( r = 0 \) indicates no linear relationship. - Values between these extremes indicate varying degrees of linear relationships. ### Interaction: Once you make your selection, you can verify your answer by clicking the "Check Answer" button. If you need to start over, use the "Clear All" button. --- **Note:** The image also includes a visual of a computer keyboard, which is not relevant to the educational content described. There are no graphs or diagrams included in the image that require further explanation.
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