### Educational Content for Correlation Coefficient Analysis#### Problem DescriptionUsing the given data set, complete parts (a) through (c) below (α = 0.05).#### Data Set:| \(x\) |10| 8 | 13 | 9 | 11 | 14 | 6 | 4 | 12 | 7 | 5 ||-----|---|---|----|---|----|----|---|---|----|---|---|| \(y\) |7.46| 6.77 | 7.74 | 7.11 | 7.81 | 8.84 | 6.09 | 5.39 | 8.14 | 6.43 | 5.72 |### Step b: Find the Linear Correlation Coefficient#### Linear Correlation Coefficient Calculation:The linear correlation coefficient \( r \) is computed and found to be: \[ r = 0.816 \]*The result is rounded to three decimal places.*### Interpretation:Based on the linear correlation coefficient \( r \) obtained, we analyze whether there is sufficient evidence to support the claim of a linear correlation between the two variables.### Graphical Representations:- **Graph A**: Plots \( x \) against \( y \) (appears nonlinear).- **Graph B**: Plots \( x \) against \( y \) (appears linear). \\ **This graph is marked as the correct one based on the analysis.**- **Graph C**: Plots \( x \) against \( y \) (appears negatively correlated and nonlinear).- **Graph D**: Plots \( x \) against \( y \) (appears parabolic).### Conclusion Based on Linear Correlation Coefficient: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.#### Options for Conclusion:A. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables.B. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables.C. There is insufficient evidence to support the claim of a linear correlation between the two variables.D. There is sufficient evidence to support the claim of a linear correlation between the two variables.#### Correct Answer:D. There is sufficient evidence

The following data for the X and Y variables are provided to find the sample correlation…

Click here to view a table of critical values for the correlation coefficient. B. Oc. OD. 16 16 16 16- 12- 12 12- 12- 8- 8- *.. 4- 12 16 12 16 12 16 12 b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is r= 0.816. (Round to three decimal places as needed.) 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. O A. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables. O B. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. OC. There is insufficient 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 linear correlation between the two variables.

Click here to view a table of critical values for the correlation coefficient. B. Oc. OD. 16 16 16 16- 12- 12 12- 12- 8- 8- *.. 4- 12 16 12 16 12 16 12 b. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is r= 0.816. (Round to three decimal places as needed.) 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. O A. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables. O B. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. OC. There is insufficient 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 linear correlation between the two variables.

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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Which of the following is TRUE about the correlation coefficient? Choose the correct answer below. O A. We should only find correlation between two variables if they are quantitative, the association is straight enough, and there are no outliers. O B. We should always calculate the correlation between two variables. O C. Correlation proves causation.
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Use the given data set to complete parts (a). (Use α=0.05.) a. Find the linear correlation coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. The linear correlation coefficient is r= (Round to three decimal places as needed.)
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