MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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please show all work and please organize answers to questions in order so it’s not difficult to understand
**Scatter Diagram and Correlation Analysis** Below is a scatter diagram for variables \( x \) and \( y \). The sample correlation coefficient for the data is \( r = -0.823 \). **Scatter Diagram Description:** The scatter diagram consists of several plotted points that represent paired values of \( x \) and \( y \). The \( x \)-axis ranges from 0 to 35, while the \( y \)-axis ranges from 0 to 100. The points appear to follow a downward trend, suggesting a possible negative relationship between the two variables. **Questions for Analysis:** 1. **Is there a linear correlation between \( x \) and \( y \)?** - Use the "Critical Values for Correlation Coefficient" table provided to justify your answer. 2. **If there is linear correlation, is it positive or negative?** Based on the given information, since \( r = -0.823 \), it indicates a strong negative linear correlation between \( x \) and \( y \).
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Transcribed Image Text:**Scatter Diagram and Correlation Analysis** Below is a scatter diagram for variables \( x \) and \( y \). The sample correlation coefficient for the data is \( r = -0.823 \). **Scatter Diagram Description:** The scatter diagram consists of several plotted points that represent paired values of \( x \) and \( y \). The \( x \)-axis ranges from 0 to 35, while the \( y \)-axis ranges from 0 to 100. The points appear to follow a downward trend, suggesting a possible negative relationship between the two variables. **Questions for Analysis:** 1. **Is there a linear correlation between \( x \) and \( y \)?** - Use the "Critical Values for Correlation Coefficient" table provided to justify your answer. 2. **If there is linear correlation, is it positive or negative?** Based on the given information, since \( r = -0.823 \), it indicates a strong negative linear correlation between \( x \) and \( y \).
### Critical Values for Correlation Coefficient The table below provides the critical values for the correlation coefficient. These values are essential for determining the statistical significance of a correlation in hypothesis testing. The column labeled "n" represents the sample size, while the adjacent numbers indicate the critical correlation coefficients for that particular sample size. | n | Coefficient | n | Coefficient | n | Coefficient | n | Coefficient | |----|-------------|----|-------------|----|-------------|----|-------------| | 3 | 0.997 | 10 | 0.632 | 17 | 0.482 | 24 | 0.404 | | 4 | 0.950 | 11 | 0.602 | 18 | 0.468 | 25 | 0.396 | | 5 | 0.878 | 12 | 0.576 | 19 | 0.456 | 26 | 0.388 | | 6 | 0.811 | 13 | 0.553 | 20 | 0.444 | 27 | 0.381 | | 7 | 0.754 | 14 | 0.532 | 21 | 0.433 | 28 | 0.374 | | 8 | 0.707 | 15 | 0.514 | 22 | 0.423 | 29 | 0.367 | | 9 | 0.666 | 16 | 0.497 | 23 | 0.413 | 30 | 0.361 | #### Explanation: - **Sample Size (n):** This is the number of paired observations. - **Critical Value of Correlation Coefficient:** The smallest value for the correlation coefficient that can be considered statistically significant at a given significance level, typically 0.05. This table is utilized in statistical analysis to determine if the observed correlation in a sample is significantly different from zero at a certain significance level.
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Transcribed Image Text:### Critical Values for Correlation Coefficient The table below provides the critical values for the correlation coefficient. These values are essential for determining the statistical significance of a correlation in hypothesis testing. The column labeled "n" represents the sample size, while the adjacent numbers indicate the critical correlation coefficients for that particular sample size. | n | Coefficient | n | Coefficient | n | Coefficient | n | Coefficient | |----|-------------|----|-------------|----|-------------|----|-------------| | 3 | 0.997 | 10 | 0.632 | 17 | 0.482 | 24 | 0.404 | | 4 | 0.950 | 11 | 0.602 | 18 | 0.468 | 25 | 0.396 | | 5 | 0.878 | 12 | 0.576 | 19 | 0.456 | 26 | 0.388 | | 6 | 0.811 | 13 | 0.553 | 20 | 0.444 | 27 | 0.381 | | 7 | 0.754 | 14 | 0.532 | 21 | 0.433 | 28 | 0.374 | | 8 | 0.707 | 15 | 0.514 | 22 | 0.423 | 29 | 0.367 | | 9 | 0.666 | 16 | 0.497 | 23 | 0.413 | 30 | 0.361 | #### Explanation: - **Sample Size (n):** This is the number of paired observations. - **Critical Value of Correlation Coefficient:** The smallest value for the correlation coefficient that can be considered statistically significant at a given significance level, typically 0.05. This table is utilized in statistical analysis to determine if the observed correlation in a sample is significantly different from zero at a certain significance level.
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Step 1

Given:

Sample size n = 7

The correlation coefficient r = -0.823

Formula Used:

If the amount of coefficient of correlation is greater than critical value, Then there is a linear relationship.

 

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