Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 10 8 13 12.73 7.45 6.77 Click here to view a table of critical values for the correlation coefficient. X y a. Construct a scatterplot. Choose the correct graph below. OA Ay 16- 12- 8- 4 ● ** 14 8 12 16 Q 5 OB. Ay 16- 12- 8- 4- 0- 0 9 7.12 8 12 16 11 7.81 BECED 14 8.85 Dia A 16- 12- 8- 4. **** 18 6 6.08 ****** 12 16 Q C 4 5.38 12 8.14 A 16- 12- 8 4 10- 7 6.43 ********* 8 12 16 ROO 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=1 (Round to three decimal places as needed) 5 5.7
Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 10 8 13 12.73 7.45 6.77 Click here to view a table of critical values for the correlation coefficient. X y a. Construct a scatterplot. Choose the correct graph below. OA Ay 16- 12- 8- 4 ● ** 14 8 12 16 Q 5 OB. Ay 16- 12- 8- 4- 0- 0 9 7.12 8 12 16 11 7.81 BECED 14 8.85 Dia A 16- 12- 8- 4. **** 18 6 6.08 ****** 12 16 Q C 4 5.38 12 8.14 A 16- 12- 8 4 10- 7 6.43 ********* 8 12 16 ROO 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=1 (Round to three decimal places as needed) 5 5.7
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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Question
Please answer part b
![### Statistical Analysis and Correlation
**Use the given data set to complete parts (a) through (c) below. (Use \( \alpha = 0.05 \))**
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
x & 10 & 8 & 13 & 9 & 11 & 14 & 6 & 4 & 12 & 7 & 5 \\
\hline
y & 7.45 & 6.77 & 12.73 & 7.12 & 7.81 & 8.85 & 6.08 & 5.38 & 8.14 & 6.43 & 5.72 \\
\hline
\end{array}
\]
*Click here to view a table of critical values for the correlation coefficient.*
#### a. Construct a Scatterplot. Choose the correct graph below.
Select the scatterplot that corresponds to the given data points.
- **Option A:**
- This scatterplot shows a non-linear pattern with varying increases and decreases in y-values as x-values increase.
- **Option B:**
- This scatterplot shows a clear upward trend, with y-values increasing as x-values increase.
- **Option C:**
- This scatterplot shows a downward trend, with y-values decreasing as x-values increase.
- **Option D:**
- This scatterplot (marked as correct) shows a general upward trend, indicating a positive association between the variables x and y.
#### b. Find the Linear Correlation Coefficient
*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.*
\[
\text{The linear correlation coefficient is } r = \underline{\phantom{000}} \quad \text{(Round to three decimal places as needed.)}
\]
---
By analyzing scatterplot D, it is clear that there is a general positive trend, which hints at a positive linear correlation between the variables x and y. This positive trend suggests that as x increases, y tends to increase as well, albeit with some variability.
Note that mathematical computation is required to find the exact value of \( r \), using the statistical formula for the linear correlation coefficient. This value will then be](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff4d48073-abff-4916-a28c-5f35ecf23479%2F47d72204-d7fe-4c80-970b-560b9d95ceee%2Fd9k3ien_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Statistical Analysis and Correlation
**Use the given data set to complete parts (a) through (c) below. (Use \( \alpha = 0.05 \))**
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline
x & 10 & 8 & 13 & 9 & 11 & 14 & 6 & 4 & 12 & 7 & 5 \\
\hline
y & 7.45 & 6.77 & 12.73 & 7.12 & 7.81 & 8.85 & 6.08 & 5.38 & 8.14 & 6.43 & 5.72 \\
\hline
\end{array}
\]
*Click here to view a table of critical values for the correlation coefficient.*
#### a. Construct a Scatterplot. Choose the correct graph below.
Select the scatterplot that corresponds to the given data points.
- **Option A:**
- This scatterplot shows a non-linear pattern with varying increases and decreases in y-values as x-values increase.
- **Option B:**
- This scatterplot shows a clear upward trend, with y-values increasing as x-values increase.
- **Option C:**
- This scatterplot shows a downward trend, with y-values decreasing as x-values increase.
- **Option D:**
- This scatterplot (marked as correct) shows a general upward trend, indicating a positive association between the variables x and y.
#### b. Find the Linear Correlation Coefficient
*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.*
\[
\text{The linear correlation coefficient is } r = \underline{\phantom{000}} \quad \text{(Round to three decimal places as needed.)}
\]
---
By analyzing scatterplot D, it is clear that there is a general positive trend, which hints at a positive linear correlation between the variables x and y. This positive trend suggests that as x increases, y tends to increase as well, albeit with some variability.
Note that mathematical computation is required to find the exact value of \( r \), using the statistical formula for the linear correlation coefficient. This value will then be
Transcribed Image Text:### Table of Critical Values for the Correlation Coefficient
This table provides the critical values for the Pearson correlation coefficient at significance levels of \(\alpha = 0.05\) and \(\alpha = 0.01\). It is a valuable reference for hypothesis testing when evaluating the strength and significance of the relationship between two variables.
| \( n \) | \(\alpha = 0.05\) | \(\alpha = 0.01\) |
|--------|------------------|------------------|
| 4 | 0.950 | 0.990 |
| 5 | 0.878 | 0.959 |
| 6 | 0.811 | 0.917 |
| 7 | 0.754 | 0.875 |
| 8 | 0.707 | 0.834 |
| 9 | 0.666 | 0.798 |
| 10 | 0.632 | 0.765 |
| 11 | 0.602 | 0.735 |
| 12 | 0.576 | 0.708 |
| 13 | 0.553 | 0.684 |
| 14 | 0.532 | 0.661 |
| 15 | 0.514 | 0.641 |
| 16 | 0.497 | 0.625 |
| 17 | 0.482 | 0.606 |
| 18 | 0.468 | 0.590 |
| 19 | 0.456 | 0.575 |
| 20 | 0.444 | 0.561 |
| 25 | 0.396 | 0.505 |
| 30 | 0.361 | 0.465 |
| 35 | 0.335 | 0.430 |
| 40 | 0.312 | 0.402 |
| 45 | 0.294 | 0.378 |
| 50 | 0.279 | 0.361 |
| 60
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