Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 8 14 10 7.46 13 9 7.11 6 6.08 12 8.14 5 5.74 11 4 6.78 12.74 7,81 8.85 5.38 6.43 Click here to view a table of critical values for the correlation coefficient. 12- 12- 12- 12- 8- 8- 8- 8- 4- 4- 4- .... 4- 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 r=. (Round to three decimal places as needed.)
Use the given data set to complete parts (a) through (c) below. (Use a = 0.05.) 8 14 10 7.46 13 9 7.11 6 6.08 12 8.14 5 5.74 11 4 6.78 12.74 7,81 8.85 5.38 6.43 Click here to view a table of critical values for the correlation coefficient. 12- 12- 12- 12- 8- 8- 8- 8- 4- 4- 4- .... 4- 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 r=. (Round to three decimal places as needed.)
MATLAB: An Introduction with Applications
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Author:Amos Gilat
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Chapter1: Starting With Matlab
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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.
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#### Graphs:
Four different scatter plots are provided to help visualize the data and identify possible relationships. Each of these graphs displays the data plotting `y` against `x`.
1. **First Graph**: It shows a scatter plot where the pattern of the points forms a downward parabolic curve, suggesting a quadratic relationship rather than a linear one.
2. **Second Graph**: This scatter plot displays a slightly upward trend, indicating a potential positive linear relationship between `x` and `y`.
3. **Third Graph**: Here, the scatter plot points form a straight downward trend, which signifies a negative linear correlation between the variables `x` and `y`.
4. **Fourth Graph**: This plot indicates an evident upward curve, suggesting a stronger, perhaps exponential, relationship between `x` and `y`.
#### Task:
b. **Find the Linear Correlation Coefficient, r:**
The objective is to calculate the linear correlation coefficient `r`, and then determine if there is enough evidence to support the hypothesis of a linear correlation between the two variables.
**Procedure:**
1. Use statistical formulas or software to calculate the linear correlation coefficient `r` to three decimal places.
2. Compare the calculated `r` with the critical value obtained from the table of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd247ad53-60ba-4f40-9f9c-b4b6807e7e4d%2F9b7a39df-5139-403b-9071-9232cece9794%2Fai5h9dq_processed.png&w=3840&q=75)
Transcribed Image Text:### Correlation and Data Analysis: A Practical Exercise
#### Data Set for Analysis:
Use the given data set to complete parts (a) through (c) below. (Use α = 0.05.)
| x | 10 | 8 | 13 | 9 | 11 | 14 | 6 | 4 | 12 | 7 | 5 |
|-----|------|------|------|------|------|------|------|-----|------|-----|------|
| y | 7.46 | 6.78 | 12.74| 7.11 | 7.81 | 8.85 | 6.08 | 5.38| 8.14 | 6.43| 5.74 |
[Click here to view a table of critical values for the correlation coefficient.](#)
#### Graphs:
Four different scatter plots are provided to help visualize the data and identify possible relationships. Each of these graphs displays the data plotting `y` against `x`.
1. **First Graph**: It shows a scatter plot where the pattern of the points forms a downward parabolic curve, suggesting a quadratic relationship rather than a linear one.
2. **Second Graph**: This scatter plot displays a slightly upward trend, indicating a potential positive linear relationship between `x` and `y`.
3. **Third Graph**: Here, the scatter plot points form a straight downward trend, which signifies a negative linear correlation between the variables `x` and `y`.
4. **Fourth Graph**: This plot indicates an evident upward curve, suggesting a stronger, perhaps exponential, relationship between `x` and `y`.
#### Task:
b. **Find the Linear Correlation Coefficient, r:**
The objective is to calculate the linear correlation coefficient `r`, and then determine if there is enough evidence to support the hypothesis of a linear correlation between the two variables.
**Procedure:**
1. Use statistical formulas or software to calculate the linear correlation coefficient `r` to three decimal places.
2. Compare the calculated `r` with the critical value obtained from the table of
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