A. OB. OC. OD. 20- Ay 20- By hand, compute the correlation coefficient. e correlation coefficient is r= (Round to three decimal places as needed.) Determine whether there is a linear relation between x and y. v and the absolute value of the correlation coefficient, V linear relation exists between x and y cause the correlation coefficient is und to three decimal places as needed.) is V than the critical value for this data set,
A. OB. OC. OD. 20- Ay 20- By hand, compute the correlation coefficient. e correlation coefficient is r= (Round to three decimal places as needed.) Determine whether there is a linear relation between x and y. v and the absolute value of the correlation coefficient, V linear relation exists between x and y cause the correlation coefficient is und to three decimal places as needed.) is V than the critical value for this data set,
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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Concept explainers
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Question
Transcribed Image Text:### Data Input Section
- **Table of Values:**
- \( x \): 2, 4, 6, 8, 7
- \( y \): 4, 8, 12, 14, 18
- **Buttons:**
- "Print"
- "Done"
### Critical Values for Correlation Coefficient
This section provides a table of critical values for the correlation coefficient, useful for determining statistical significance in correlation studies.
- **Table:**
- Each row lists the sample size (\( n \)) and corresponding critical value.
- The critical values decrease as the sample size increases, showing the inverse relationship between sample size and the minimum required correlation for significance.
| \( n \) | Critical Value |
|---------|----------------|
| 3 | 0.997 |
| 4 | 0.950 |
| 5 | 0.878 |
| 6 | 0.811 |
| 7 | 0.754 |
| 8 | 0.707 |
| 9 | 0.666 |
| 10 | 0.632 |
| 11 | 0.602 |
| 12 | 0.576 |
| 13 | 0.553 |
| 14 | 0.532 |
| 15 | 0.514 |
| 16 | 0.497 |
| 17 | 0.482 |
| 18 | 0.468 |
| 19 | 0.456 |
| 20 | 0.444 |
| 21 | 0.433 |
| 22 | 0.423 |
| 23 | 0.413 |
| 24 | 0.404 |
| 25 | 0.396 |
| 26 | 0.388 |
| 27 | 0.381 |
| 28 | 0.374 |
| 29 | 0.367 |
| 30 | 0.361 |
This table is critical for researchers and students to determine if the observed correlation in their datasets is statistically significant based on their sample size.
![The image displays a statistical exercise involving scatter plots and the calculation of a correlation coefficient. It is divided into three parts: (a), (b), and (c).
### (a) Draw a scatter diagram of the data. Choose the correct graph below.
Four scatter plots are provided, labeled A, B, C, and D. Each plot is on a grid where the X-axis ranges from 0 to 10, and the Y-axis ranges from 0 to 20. Each plot contains five data points, but the arrangement differs:
- **A**: The points are clustered closely together, suggesting a strong positive correlation.
- **B**: The points are descending from the top left to the bottom right, indicating a negative correlation.
- **C**: The points appear randomly dispersed, suggesting little to no correlation.
- **D**: The points are ascending from the bottom left to the top right, indicating a positive correlation but more spread out than in A.
The task is to select the scatter plot that correctly represents the data.
### (b) By hand, compute the correlation coefficient.
A prompt is provided to calculate the correlation coefficient \( r \):
- "The correlation coefficient is \( r = \) [Box]. (Round to three decimal places as needed.)"
There is a box to input the computed value.
### (c) Determine whether there is a linear relation between x and y.
This section instructs on evaluating the implications of the correlation coefficient:
- "Because the correlation coefficient is [Box] and the absolute value of the correlation coefficient, [Box], is [Dropdown: less than/greater than] the critical value for this data set, [Box], [Dropdown: a/no] linear relation exists between x and y."
Users fill in these boxes based on their calculations and comparisons.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fba8c7a8d-a032-4c0f-852a-7ede8b8dbe8f%2F06c76b65-6528-4345-a18f-1e63d881d5fb%2F5spn4ub_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image displays a statistical exercise involving scatter plots and the calculation of a correlation coefficient. It is divided into three parts: (a), (b), and (c).
### (a) Draw a scatter diagram of the data. Choose the correct graph below.
Four scatter plots are provided, labeled A, B, C, and D. Each plot is on a grid where the X-axis ranges from 0 to 10, and the Y-axis ranges from 0 to 20. Each plot contains five data points, but the arrangement differs:
- **A**: The points are clustered closely together, suggesting a strong positive correlation.
- **B**: The points are descending from the top left to the bottom right, indicating a negative correlation.
- **C**: The points appear randomly dispersed, suggesting little to no correlation.
- **D**: The points are ascending from the bottom left to the top right, indicating a positive correlation but more spread out than in A.
The task is to select the scatter plot that correctly represents the data.
### (b) By hand, compute the correlation coefficient.
A prompt is provided to calculate the correlation coefficient \( r \):
- "The correlation coefficient is \( r = \) [Box]. (Round to three decimal places as needed.)"
There is a box to input the computed value.
### (c) Determine whether there is a linear relation between x and y.
This section instructs on evaluating the implications of the correlation coefficient:
- "Because the correlation coefficient is [Box] and the absolute value of the correlation coefficient, [Box], is [Dropdown: less than/greater than] the critical value for this data set, [Box], [Dropdown: a/no] linear relation exists between x and y."
Users fill in these boxes based on their calculations and comparisons.
Expert Solution
Step 1
Given information
Given is bivariate data regarding two variables X and Y and it is required to draw scatter plot of both first, then find the correlation coefficient between two random variables and whether there is linear relation between them or not.
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