2 6. 13 20 Yi 7 18 9 26 23 a. Which of the following scatter diagrams accurately represents the data? A. В. 24+ 24- 20- 20- 16- 16 ㅇ 12- 12- 8- 4- -0 00 0 이 이 O o o
2 6. 13 20 Yi 7 18 9 26 23 a. Which of the following scatter diagrams accurately represents the data? A. В. 24+ 24- 20- 20- 16- 16 ㅇ 12- 12- 8- 4- -0 00 0 이 이 O o o
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Question
Transcribed Image Text:**Scatter Plot Analysis**
Given the dataset:
- \( x_i \): 2, 6, 9, 13, 20
- \( y_i \): 7, 18, 9, 26, 23
**Task:**
Determine which scatter diagram best represents the data.
### Data Points:
1. (2, 7)
2. (6, 18)
3. (9, 9)
4. (13, 26)
5. (20, 23)
### Scatter Diagrams:
#### Diagram A:
- Has points plotted far apart on the x-axis, ranging up to 28.
- Point placement does not consistently match the data set pattern.
#### Diagram B:
- Matches data points:
- (2, 7) near (2, 8)
- (6, 18) correctly placed
- (9, 9) correctly placed
- (13, 26) correctly placed
- (20, 23) correctly placed
- Correctly represents given data.
#### Diagram C:
- Displays points grouped on the lower end of the x-axis.
- Incorrectly represents the data points as the placement is inconsistent.
#### Diagram D:
- Shows a different arrangement than expected.
- The point correlation does not align with the given data set.
**Conclusion:** Diagram B accurately represents the data. It maintains the correct order and positioning of the data points in relation to the x and y values given in the dataset.
![The image contains two scatter plots labeled C and D, both of which feature graphs with data points plotted on Cartesian coordinates.
### Scatter Plot C:
- **Axes**: The x-axis ranges approximately from -4 to 28, and the y-axis ranges from -4 to 28 as well.
- **Data Points**: There are six data points scattered across the plot at various x and y values, such as (4, 8), (8, 20), (12, 16), (20, 24), and others.
### Scatter Plot D:
- **Axes**: Similar to Plot C, the x-axis ranges approximately from -4 to 28, and the y-axis ranges from -4 to 28.
- **Data Points**: This plot also contains six data points positioned at different x and y values, like (4, 12), (12, 8), (24, 16), and others.
### Instructions Below the Plots:
- **b.** Develop the estimated regression equation for these data (rounded to one decimal place).
- \( b_1 = \) [Input Box]
- \( b_0 = \) [Input Box]
- \( \hat{y} = \) [Input Box] + [Input Box] \( x \)
- **c.** Use the estimated regression equation to predict the value of \( y \) when \( x = 6 \) (rounded to one decimal place).
- \( \hat{y} = \) [Input Box]
There is also a dropdown menu labeled “Select your answer” and a hint section indicated at the bottom of the image.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6387f1fe-f7de-460c-a439-51c8967659dd%2Fb999a4d3-4b7b-4793-aa80-831ed30797b6%2Fzuh61gl_processed.jpeg&w=3840&q=75)
Transcribed Image Text:The image contains two scatter plots labeled C and D, both of which feature graphs with data points plotted on Cartesian coordinates.
### Scatter Plot C:
- **Axes**: The x-axis ranges approximately from -4 to 28, and the y-axis ranges from -4 to 28 as well.
- **Data Points**: There are six data points scattered across the plot at various x and y values, such as (4, 8), (8, 20), (12, 16), (20, 24), and others.
### Scatter Plot D:
- **Axes**: Similar to Plot C, the x-axis ranges approximately from -4 to 28, and the y-axis ranges from -4 to 28.
- **Data Points**: This plot also contains six data points positioned at different x and y values, like (4, 12), (12, 8), (24, 16), and others.
### Instructions Below the Plots:
- **b.** Develop the estimated regression equation for these data (rounded to one decimal place).
- \( b_1 = \) [Input Box]
- \( b_0 = \) [Input Box]
- \( \hat{y} = \) [Input Box] + [Input Box] \( x \)
- **c.** Use the estimated regression equation to predict the value of \( y \) when \( x = 6 \) (rounded to one decimal place).
- \( \hat{y} = \) [Input Box]
There is also a dropdown menu labeled “Select your answer” and a hint section indicated at the bottom of the image.
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