Use the given data set to complete parts. (a) through (c) below. (Use α = 0.05.) X y 10 9.14 O A. Ay 8 8.14 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot. Choose the correct graph below. 10- 8- 6 4- 2- 0- 0 4 8 12 16 60000 13 8.73 Q E O B. Ay 10+ 84 9 8.76 6- 4- 2- 0+ 0 0000 88 4 8 12 16 Q Q 11 9.27 14 8.09 *** O C. A 6 6.13 10- 8- 6- 4- 2- 0- 0 4 8 12 16 Q 4 3.09 12 9.12 O D. Ay 10- 8- 6- 4 2- 0- 0 + Fut → . 4 8 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= (Round to three decimal places as needed.) 7 7.26 12 16 Q Q 5 5 4.75 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. E
Use the given data set to complete parts. (a) through (c) below. (Use α = 0.05.) X y 10 9.14 O A. Ay 8 8.14 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot. Choose the correct graph below. 10- 8- 6 4- 2- 0- 0 4 8 12 16 60000 13 8.73 Q E O B. Ay 10+ 84 9 8.76 6- 4- 2- 0+ 0 0000 88 4 8 12 16 Q Q 11 9.27 14 8.09 *** O C. A 6 6.13 10- 8- 6- 4- 2- 0- 0 4 8 12 16 Q 4 3.09 12 9.12 O D. Ay 10- 8- 6- 4 2- 0- 0 + Fut → . 4 8 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= (Round to three decimal places as needed.) 7 7.26 12 16 Q Q 5 5 4.75 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. E
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![### Correlation Analysis: A Step-by-Step Tutorial
#### Data Set
The given data set is as follows (Use α = 0.05):
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
x & 10 & 8 & 13 & 9 & 11 & 14 & 6 & 4 & 12 & 7 & 5 \\
\hline
y & 9.14 & 8.14 & 8.73 & 8.76 & 9.27 & 8.09 & 6.13 & 3.09 & 9.12 & 7.26 & 4.75 \\
\hline
\end{array}
\]
Click [here](#) to view a table of critical values for the correlation coefficient.
#### Step-by-Step Instructions
**a. Construct a Scatterplot**
Choose the correct graph from the options below that represents the data set accurately:
- **Option A:**
- This scatterplot shows a positive linear relationship between x and y.
- **Option B:**
- This scatterplot displays a negative linear relationship between x and y.
- **Option C:**
- This scatterplot indicates a positive but nonlinear relationship between x and y.
- **Option D:**
- This scatterplot suggests a nonlinear relationship between x and y with possible curvature.
**Correct Choice:**
- [ ] A.
- [ ] B.
- [ ] C.
- [ ] D.
**b. Find the Linear Correlation Coefficient, \( r \)**
Calculate the linear correlation coefficient using the given data and determine if there is sufficient evidence to support a claim of linear correlation between the variables. The formula to use is:
\[ r = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{\sqrt{[n\sum{x^2} - (\sum{x})^2][n\sum{y^2} - (\sum{y})^2]}} \]
- Round](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5cc7f00e-28f4-4f9d-9775-3cbc7937b5d3%2Faf85561c-c63b-4673-a3a3-95c6d661a3b1%2F7zuavd_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Correlation Analysis: A Step-by-Step Tutorial
#### Data Set
The given data set is as follows (Use α = 0.05):
\[
\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
x & 10 & 8 & 13 & 9 & 11 & 14 & 6 & 4 & 12 & 7 & 5 \\
\hline
y & 9.14 & 8.14 & 8.73 & 8.76 & 9.27 & 8.09 & 6.13 & 3.09 & 9.12 & 7.26 & 4.75 \\
\hline
\end{array}
\]
Click [here](#) to view a table of critical values for the correlation coefficient.
#### Step-by-Step Instructions
**a. Construct a Scatterplot**
Choose the correct graph from the options below that represents the data set accurately:
- **Option A:**
- This scatterplot shows a positive linear relationship between x and y.
- **Option B:**
- This scatterplot displays a negative linear relationship between x and y.
- **Option C:**
- This scatterplot indicates a positive but nonlinear relationship between x and y.
- **Option D:**
- This scatterplot suggests a nonlinear relationship between x and y with possible curvature.
**Correct Choice:**
- [ ] A.
- [ ] B.
- [ ] C.
- [ ] D.
**b. Find the Linear Correlation Coefficient, \( r \)**
Calculate the linear correlation coefficient using the given data and determine if there is sufficient evidence to support a claim of linear correlation between the variables. The formula to use is:
\[ r = \frac{n(\sum{xy}) - (\sum{x})(\sum{y})}{\sqrt{[n\sum{x^2} - (\sum{x})^2][n\sum{y^2} - (\sum{y})^2]}} \]
- Round
Transcribed Image Text:**Educational Content: Table of Critical Values and Data Visualization**
---
### Table of Critical Values
The table below provides critical values for statistical testing at significance levels of \(\alpha = 0.05\) and \(\alpha = 0.01\). This table is essential in determining whether to reject or fail to reject the null hypothesis in correlation tests.
| \( n \) | \(\alpha = 0.05\) | \(\alpha = 0.01\) |
|:--------:|:----------------:|:-----------------:|
| 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 | 0.623 |
| 17 | 0.482 | 0.606 |
| 18 | 0.468 | 0.590 |
| 19 | 0.456 | 0.575 |
| 20 | 0.444 | 0.561 |
| 21 | 0.433 | 0.549 |
| 22 | 0.423 | 0.537 |
| 23 | 0.413 | 0.526 |
| 24 | 0.404 | 0.515 |
| 25 | 0.396 | 0.505 |
| 26 | 0.388
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