The linear correlation coefficient is r= (Round to three decimal places as needed.) Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evider two variables. Choose the correct answer below. A. There is insufficient evidence to support the claim of a nonlinear correlation between the two variable: B. There is insufficient evidence to support the claim of a linear correlation between the two variables. C. There is sufficient evidence to support the claim of a linear correlation between the two variables. O D. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scat A. The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope. B. The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope. C. The scatterplot does not reveal a distinct pattern. D. The scatterplot reveals a distinct pattern that is not a straight-line pattern.

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### Linear Correlation Analysis

#### Data Set
Use the given data set to complete parts (a) through (c) below. (Use α = 0.05.)

| x  | 10 | 8  | 13 | 9  | 11 | 14 | 6  | 4  | 12 | 7  | 5  |
|----|----|----|----|----|----|----|----|----|----|----|----|
| y  | 9.14 | 8.15 | 8.75 | 8.77 | 9.26 | 8.10 | 6.13 | 3.10 | 9.14 | 7.26 | 4.73 |

#### Graphical Representations
Three scatterplots are shown to visualize potential correlations:
1. **Scatterplot 1**: Displays a dataset with a linear pattern that appears to have a positive correlation.
2. **Scatterplot 2**: Displays a dataset with a linear pattern that appears to have a negative correlation.
3. **Scatterplot 3**: Displays a dataset showing a nonlinear pattern.

#### Analysis
**b. Calculate the Linear Correlation Coefficient**

- Find the linear correlation coefficient, \( r \), using the given data and determine if there is sufficient evidence to support a linear correlation between the variables. (Round to three decimal places as needed.)

**Choose the correct interpretation based on the correlation coefficient:**

- A. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables.
- B. There is insufficient evidence to support the claim of a linear correlation between the two variables.
- C. There is sufficient evidence to support the claim of a linear correlation between the two variables.
- D. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables.

**c. Identify Missing Features Without a Scatterplot**

- Determine the characteristic that might be missed if visual analysis is not performed:
  - A. The scatterplot reveals a distinct pattern that is a straight-line pattern with a positive slope.
  - B. The scatterplot reveals a distinct pattern that is a straight-line pattern with a negative slope.
  - C. The scatterplot does not reveal a distinct pattern.
  - D. The scatterplot reveals a distinct pattern that is not a straight-line pattern.

Click to select the answer(s).
Transcribed Image Text:### Linear Correlation Analysis #### Data Set Use the given data set to complete parts (a) through (c) below. (Use α = 0.05.) | x | 10 | 8 | 13 | 9 | 11 | 14 | 6 | 4 | 12 | 7 | 5 | |----|----|----|----|----|----|----|----|----|----|----|----| | y | 9.14 | 8.15 | 8.75 | 8.77 | 9.26 | 8.10 | 6.13 | 3.10 | 9.14 | 7.26 | 4.73 | #### Graphical Representations Three scatterplots are shown to visualize potential correlations: 1. **Scatterplot 1**: Displays a dataset with a linear pattern that appears to have a positive correlation. 2. **Scatterplot 2**: Displays a dataset with a linear pattern that appears to have a negative correlation. 3. **Scatterplot 3**: Displays a dataset showing a nonlinear pattern. #### Analysis **b. Calculate the Linear Correlation Coefficient** - Find the linear correlation coefficient, \( r \), using the given data and determine if there is sufficient evidence to support a linear correlation between the variables. (Round to three decimal places as needed.) **Choose the correct interpretation based on the correlation coefficient:** - A. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables. - B. There is insufficient evidence to support the claim of a linear correlation between the two variables. - C. There is sufficient evidence to support the claim of a linear correlation between the two variables. - D. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. **c. Identify Missing Features Without a Scatterplot** - Determine the characteristic that might be missed if visual analysis is not performed: - A. The scatterplot reveals a distinct pattern that is a straight-line pattern with a positive slope. - B. The scatterplot reveals a distinct pattern that is a straight-line pattern with a negative slope. - C. The scatterplot does not reveal a distinct pattern. - D. The scatterplot reveals a distinct pattern that is not a straight-line pattern. Click to select the answer(s).
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