The manager of a salmon cannery suspects that the demand for her product is closely related to the disposable income of her target region. To test out this hypothesis she collected the following data for five different target regions, where x represents the annual disposable income for a region in millions of dollars and y represents sales volume in thousands of cases. y I 4. 10 1 20 3 3. 40 4. 50 30 1 10 30 40 50 (a) Draw the scatter graph of this set of data. (h) Compute the correlation coefficient r. (c) Find and graph the least square line. 20
The manager of a salmon cannery suspects that the demand for her product is closely related to the disposable income of her target region. To test out this hypothesis she collected the following data for five different target regions, where x represents the annual disposable income for a region in millions of dollars and y represents sales volume in thousands of cases. y I 4. 10 1 20 3 3. 40 4. 50 30 1 10 30 40 50 (a) Draw the scatter graph of this set of data. (h) Compute the correlation coefficient r. (c) Find and graph the least square line. 20
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![**9. Analysis of Sales Volume and Disposable Income**
The manager of a salmon cannery suspects that the demand for her product is closely related to the disposable income of her target region. To test this hypothesis, she collected the following data for five different target regions:
- \( x \): Represents the annual disposable income for a region in millions of dollars
- \( y \): Represents sales volume in thousands of cases
The data is represented in the table below:
| \( x \) (Millions of dollars) | \( y \) (Thousands of cases) |
|:-----------------------------:|:---------------------------:|
| 10 | 1 |
| 20 | 3 |
| 40 | 4 |
| 50 | 5 |
| 30 | 2 |
Tasks:
(a) **Draw the Scatter Graph**: Plot the given set of data on a graph with \( x \) on the horizontal axis and \( y \) on the vertical axis.
(b) **Compute the Correlation Coefficient (\( r \))**: Calculate the correlation coefficient to determine the strength and direction of the relationship between disposable income and sales volume.
(c) **Find and Graph the Least Squares Line**: Determine the line of best fit for the data and graph it.
(d) **Predict Sales Volume**: If a region has disposable annual income of $25,000,000, predict the sales volume.
**Graph Explanation**: The scatter plot grid provided allows for visual representation of the data points and aids in plotting the line of best fit. Each axis is labeled with the corresponding variable and increment.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a60a588-11d8-4f2d-b1cd-23407590806e%2F763aaee0-1c10-4e60-b7e2-28cfdf7985f4%2Fq4mzin_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**9. Analysis of Sales Volume and Disposable Income**
The manager of a salmon cannery suspects that the demand for her product is closely related to the disposable income of her target region. To test this hypothesis, she collected the following data for five different target regions:
- \( x \): Represents the annual disposable income for a region in millions of dollars
- \( y \): Represents sales volume in thousands of cases
The data is represented in the table below:
| \( x \) (Millions of dollars) | \( y \) (Thousands of cases) |
|:-----------------------------:|:---------------------------:|
| 10 | 1 |
| 20 | 3 |
| 40 | 4 |
| 50 | 5 |
| 30 | 2 |
Tasks:
(a) **Draw the Scatter Graph**: Plot the given set of data on a graph with \( x \) on the horizontal axis and \( y \) on the vertical axis.
(b) **Compute the Correlation Coefficient (\( r \))**: Calculate the correlation coefficient to determine the strength and direction of the relationship between disposable income and sales volume.
(c) **Find and Graph the Least Squares Line**: Determine the line of best fit for the data and graph it.
(d) **Predict Sales Volume**: If a region has disposable annual income of $25,000,000, predict the sales volume.
**Graph Explanation**: The scatter plot grid provided allows for visual representation of the data points and aids in plotting the line of best fit. Each axis is labeled with the corresponding variable and increment.
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