Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below.
Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below.
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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Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below.

Transcribed Image Text:**Data Analysis Exercise: Correlation and Scatterplots**
---
**Dataset:**
| x | y |
|----|------|
| 10 | 9.13 |
| 8 | 8.14 |
| 13 | 8.75 |
| 9 | 8.76 |
| 11 | 9.26 |
| 14 | 6.13 |
| 6 | 3.09 |
| 4 | 3.09 |
| 12 | 9.13 |
| 7 | 7.26 |
| 5 | 4.74 |
**Instructions:**
1. **Scatterplot Construction:**
- Choose the correct scatterplot that represents the given dataset from the options below.
- **Scatterplot Options:**
- **A:** A scatterplot with a negative trend.
- **B:** A scatterplot with no clear trend.
- **C:** A scatterplot that exhibits a positive linear trend.
- **D:** A scatterplot showing a curved (non-linear) pattern.
2. **Correlation Coefficient Calculation:**
- Calculate the linear correlation coefficient \( r \) for the dataset.
- **Result:**
- The linear correlation coefficient is \( r = 0.818 \).
- Round to three decimal places as needed.
3. **Evidence for Correlation:**
- Using the calculated correlation coefficient, determine if there is sufficient evidence to support the claim of a linear correlation between the variables.
- **Options:**
- **A:** Insufficient evidence for a linear correlation.
- **B:** Sufficient evidence for a linear correlation.
- **C:** Sufficient evidence for a nonlinear correlation.
- **D:** Insufficient evidence for a nonlinear correlation.
---
**Graph Analysis:**
- **Graph C** is the correct choice as it displays a positive linear trend, consistent with the calculated correlation coefficient of \( 0.818 \).
- Given the value of the correlation coefficient, **Option B** is correct, indicating sufficient evidence to support the claim of a linear correlation between the variables.
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