**Example Problem on Linear Correlation****Problem Statement:**Use the given data set to complete parts (a) through (c) below. (Use \(\alpha = 0.05\) )\[\begin{array}{c|cccccccccc}x & 10 & 8 & 13 & 9 & 11 & 14 & 6 & 4 & 12 & 7 & 5 \\\hliney & 9.14 & 8.14 & 8.74 & 8.77 & 9.27 & 8.11 & 6.13 & 3.11 & 9.12 & 7.25 & 4.75 \\\end{array}\]To calculate the linear correlation coefficient \( r \), click here to view a table of critical values for the correlation coefficient.**Part (a):**Calculate the linear correlation coefficient \( r \):\[ r = \_\_\_\_\_ \](Round to three decimal places as needed.)**Part (b):**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:- 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 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 linear correlation between the two variables.**Part (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:- A. The scatterplot reveals a distinct pattern that is a straight-line pattern with a negative slope.- B. The scatterplot reveals a distinct pattern that is a straight-line pattern with a positive slope.- C. The scatterplot reveals a distinct pattern that is not a straight-line pattern.- D. The scatterplot does not reveal a distinct pattern.--- ## Data Analysis and Correlation ### Given Data SetThe following table presents the values for variables \( x \) and \( y \):| \( x \) | 10 | 8 | 13 | 9 | 11 | 14 | 6 | 4 | 12 | 7 | 5 ||------|----|---|----|---|----|----|---|---|----|---|---|| \( y \) | 9.14 | 8.14 | 8.74 | 8.77 | 9.27 | 8.11 | 6.13 | 3.11 | 9.12 | 7.25 | 4.75 |### Instructions: 1. **Scatterplot Construction**: - Construct a scatterplot using the provided data set to visually assess the relationship between variables \( x \) and \( y \). - Choose the correct scatterplot from the options provided (A, B, C, D).2. **Scatterplot Options**: - **Option A**: Graph with a positive linear trend. - **Option B**: Shows a curved trend, indicating a potential non-linear relationship. - **Option C**: Graph with a negative linear trend. - **Option D**: Another graph with a positive linear trend but with a different pattern.3. **Correlation Analysis**: - Calculate the linear correlation coefficient, \( r \), to evaluate the linear relationship between \( x \) and \( y \). - Round your answer to three decimal places as necessary. - Based on the calculated correlation coefficient, determine if there is sufficient evidence to support a claim of a linear correlation between the two variables. - Choose the correct statement from the provided options.#### Scatterplot Construction:**Choose the correct graph:**- **A.** ![Graph A](#)- **B.** ![Graph B](#)- **C.** ![Graph C](#)- **D.** ![Graph D](#)#### Linear Correlation Coefficient:1. **Find the Linear Correlation Coefficient \( r \)**: - The linear correlation coefficient is \( r = \_\_\_\_\_\_\_\_\_\_\_\_\_\_ \). - \( r \) should be calculated and rounded to three decimal places as needed

The data given is: x y 10 9.14 8 8.14 13 8.74 9 8.77 11 9.27 14 8.11 6 6.13 4…

Use the given data set to complete parts (a) through (c) below. (Use a= 0.05.) X 10 8 13 9. 11 14 4 7. 7.25 y 9.14 8.14 8.74 12 8.77 9.27 8.11 6.13 3.11 9.12 4.75 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot Choose the correct graph below. O A. OB. OD. Ay 10- Ay 1어 Ay 10- 10- 8- 8- 8- 6- 6- 6- ....... .. 12 6- 4- 4- 4- 4- 2- 2- 2- 2- ....... 0- 12 16 12 16 12 16 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 rD (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.

Use the given data set to complete parts (a) through (c) below. (Use a= 0.05.) X 10 8 13 9. 11 14 4 7. 7.25 y 9.14 8.14 8.74 12 8.77 9.27 8.11 6.13 3.11 9.12 4.75 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot Choose the correct graph below. O A. OB. OD. Ay 10- Ay 1어 Ay 10- 10- 8- 8- 8- 6- 6- 6- ....... .. 12 6- 4- 4- 4- 4- 2- 2- 2- 2- ....... 0- 12 16 12 16 12 16 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 rD (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.

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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