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.

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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.
**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.
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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