K Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 8 13 9 8.15 8.73 8.77 X y 10 9.14 11 9,26 Click here to view a table of critical values for the correlation coefficient. 14 8.11 6 6.12 4 3.09 OA. The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope. OB. The scatterplot reveals a distinct pattern that is not a straight-line pattern. O c. The scatterplot does not reveal a distinct pattern. OD. The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope. 12 9.12 7 7.27 5 4.74 OC. There is sufficient evidence to support the claim of a linear correlation between the two variables. O D. There is insufficient 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 scatterplot. Choose the correct answer below. P
K Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 8 13 9 8.15 8.73 8.77 X y 10 9.14 11 9,26 Click here to view a table of critical values for the correlation coefficient. 14 8.11 6 6.12 4 3.09 OA. The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope. OB. The scatterplot reveals a distinct pattern that is not a straight-line pattern. O c. The scatterplot does not reveal a distinct pattern. OD. The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope. 12 9.12 7 7.27 5 4.74 OC. There is sufficient evidence to support the claim of a linear correlation between the two variables. O D. There is insufficient 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 scatterplot. Choose the correct answer below. P
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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Transcribed Image Text:**Data and Correlation Analysis**
Given Data Set: Complete the analysis for parts (a) through (c) using the given data (α = 0.05).
| x | y |
|----|------|
| 10 | 9.14 |
| 8 | 8.15 |
| 13 | 8.73 |
| 9 | 8.77 |
| 11 | 9.26 |
| 14 | 8.11 |
| 6 | 6.12 |
| 4 | 3.09 |
| 12 | 9.12 |
| 7 | 7.27 |
| 5 | 4.74 |
Click to view a table of critical values for the correlation coefficient.
**Questions:**
(a) Analyze the correlation evidence:
- **C.** There is sufficient evidence to support the claim of a linear correlation between the two variables.
- **D.** There is insufficient evidence to support the claim of a nonlinear correlation between the two variables.
(b) Identify the missing feature if a scatterplot is not constructed:
- **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 not a straight-line pattern.
- **C.** The scatterplot does not reveal a distinct pattern.
- **D.** The scatterplot reveals a distinct pattern that is a straight-line pattern with a negative slope.
Use this analysis to understand the relationship between variables and the importance of visual data representation through scatterplots.
Transcribed Image Text:**Data Set Analysis for Linear Correlation**
The table below displays values for two variables, \( x \) and \( y \), which will be used to complete parts (a) through (c). The level of significance (\( \alpha \)) for this analysis is 0.05.
| \( x \) | 10 | 8 | 13 | 9 | 11 | 14 | 6 | 4 | 12 | 7 | 5 |
|---------|----|---|----|---|----|----|---|---|----|---|---|
| \( y \) | 9.14 | 8.15 | 8.73 | 8.77 | 9.26 | 8.11 | 6.12 | 3.09 | 9.12 | 7.27 | 4.74 |
**Instructions for Calculating Linear Correlation Coefficient**
- The linear correlation coefficient is denoted as \( r \).
- Round your answer to three decimal places.
**Next Steps:**
Using the linear correlation coefficient determined from the data, assess whether there is enough evidence to support the hypothesis of a linear relationship between the two variables. Select the appropriate option below:
- **A.** There is sufficient 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 insufficient evidence to support the claim of a nonlinear correlation between the two variables.
To make this determination, refer to a table of critical values for the correlation coefficient.
---
This guidance outlines the process for testing the linear correlation between two variables using statistical analysis. It emphasizes the importance of calculating and interpreting the correlation coefficient accurately to draw valid conclusions.
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