ow are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using a =0.01. Is i seals from photographs and the weights of the seals? cient evidence to conclude that there is a linear correlation between overhead widths head Width ht 7.0 7.4 9.7 9.2 8.9 8.3 O 109 178 241 196 204 188
ow are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using a =0.01. Is i seals from photographs and the weights of the seals? cient evidence to conclude that there is a linear correlation between overhead widths head Width ht 7.0 7.4 9.7 9.2 8.9 8.3 O 109 178 241 196 204 188
MATLAB: An Introduction with Applications
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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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![### Analysis of Correlation Between Overhead Widths and Weights of Seals
#### Data Provided:
The following table lists the overhead widths (in cm) of seals measured from photographs, and their corresponding weights (in kg).
| Overhead Width (cm) | 7.0 | 7.4 | 9.7 | 9.2 | 8.9 | 8.3 |
|----------------------|-----|-----|-----|-----|-----|-----|
| Weight (kg) | 109 | 178 | 241 | 196 | 204 | 188 |
#### Goals:
1. **Construct a Scatterplot:**
- Plot the overhead widths on the x-axis and the weights on the y-axis.
2. **Calculate the Linear Correlation Coefficient (r):**
- Determine the value of the linear correlation coefficient (r) to assess the strength and direction of the relationship between overhead width and weight.
3. **Find Critical Values for r:**
- At a significance level (\(\alpha\)) of 0.01, determine the critical values for r.
4. **Interpret the Evidence:**
- Assess whether there is sufficient evidence to conclude a linear correlation between the two variables.
#### Instructions for Interpretation:
1. **Scatterplot Construction:**
- Create a graph with overhead width on the horizontal axis and weight on the vertical axis.
- Plot each pair of values as a point on the graph to visualize the relationship.
2. **Calculating the Linear Correlation Coefficient (r):**
- Use the formula for Pearson's correlation coefficient:
\[
r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}
\]
- Where \( x_i \) and \( y_i \) represent individual sample points of overhead width and weight, respectively. \( \bar{x} \) and \( \bar{y} \) are the means of overhead widths and weights, respectively.
3. **Finding Critical Values:**
- Using statistical tables for correlation coefficients, find the critical values corresponding to a significance level of 0.01 for the given degrees of freedom (n-2, where n is the number of sample pairs).
4. **Conclusion:](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa5534fc6-b142-4cfc-8ed1-53ce39208227%2Fbd3264e2-8939-460b-995e-0b639e4c24c6%2Fom0pga_processed.png&w=3840&q=75)
Transcribed Image Text:### Analysis of Correlation Between Overhead Widths and Weights of Seals
#### Data Provided:
The following table lists the overhead widths (in cm) of seals measured from photographs, and their corresponding weights (in kg).
| Overhead Width (cm) | 7.0 | 7.4 | 9.7 | 9.2 | 8.9 | 8.3 |
|----------------------|-----|-----|-----|-----|-----|-----|
| Weight (kg) | 109 | 178 | 241 | 196 | 204 | 188 |
#### Goals:
1. **Construct a Scatterplot:**
- Plot the overhead widths on the x-axis and the weights on the y-axis.
2. **Calculate the Linear Correlation Coefficient (r):**
- Determine the value of the linear correlation coefficient (r) to assess the strength and direction of the relationship between overhead width and weight.
3. **Find Critical Values for r:**
- At a significance level (\(\alpha\)) of 0.01, determine the critical values for r.
4. **Interpret the Evidence:**
- Assess whether there is sufficient evidence to conclude a linear correlation between the two variables.
#### Instructions for Interpretation:
1. **Scatterplot Construction:**
- Create a graph with overhead width on the horizontal axis and weight on the vertical axis.
- Plot each pair of values as a point on the graph to visualize the relationship.
2. **Calculating the Linear Correlation Coefficient (r):**
- Use the formula for Pearson's correlation coefficient:
\[
r = \frac{\sum (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum (x_i - \bar{x})^2 \sum (y_i - \bar{y})^2}}
\]
- Where \( x_i \) and \( y_i \) represent individual sample points of overhead width and weight, respectively. \( \bar{x} \) and \( \bar{y} \) are the means of overhead widths and weights, respectively.
3. **Finding Critical Values:**
- Using statistical tables for correlation coefficients, find the critical values corresponding to a significance level of 0.01 for the given degrees of freedom (n-2, where n is the number of sample pairs).
4. **Conclusion:
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