Given are five observations for two variables, and y a. Which of the following scatter diagrams accurately represents the data? 1. 05 05 7 1,5 2 2,5 3 3,5 4 4,5 $ $.$. X 2. 45$.$.$.X 5 2 7 7 4 5 11 16
Given are five observations for two variables, and y a. Which of the following scatter diagrams accurately represents the data? 1. 05 05 7 1,5 2 2,5 3 3,5 4 4,5 $ $.$. X 2. 45$.$.$.X 5 2 7 7 4 5 11 16
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
Transcribed Image Text:### Scatter Diagrams for Data Representation
#### Given Data
The given table presents five observations for two variables, \( x \) and \( y \):
| \( x \) | 1 | 2 | 3 | 4 | 5 |
|---------|---|---|---|---|---|
| \( y \) | 4 | 7 | 7 | 11 | 16 |
#### Scatter Diagram Comparison
Two scatter diagrams are provided. Your task is to determine which of the following scatter diagrams accurately represents the given data.
##### Scatter Diagram 1:
- **Axis Labels:**
- x-axis: \( x \)
- y-axis: \( y \)
- The axes are labeled with values from 0.5 to 5.5 for \( x \) and from 0 to 16 for \( y \).
- **Data Points:**
- The points plotted are:
- (1,4)
- (2,7)
- (3,7)
- (4,11)
- (5,16)
##### Scatter Diagram 2:
- **Axis Labels:**
- x-axis: \( x \)
- y-axis: \( y \)
- The axes are labeled with values from 0.5 to 5.5 for \( x \) and from 0 to 16 for \( y \).
- **Data Points:**
- The points plotted are:
- (1,4)
- (2,7)
- (3,7)
- (4,11)
- (5,16)
Both diagrams display the same data points. Therefore, both diagrams accurately represent the given data.
#### Conclusion
Upon close examination, both scatter diagrams 1 and 2 accurately represent the observed data points. Hence, either of these diagrams can be used to visualize the relationship between variables \( x \) and \( y \).
### Exercise:
- Plot the given data points on a scatter diagram.
- Compare your plot with the provided diagrams to ensure accuracy.
- Understand how changes in data affect the scatter plot and identify any trends or patterns visible from the graph.
![### Scatter Plots and Regression Analysis
This educational content focuses on regression analysis, including the development of estimated regression equations using scatter diagrams and linear equations.
#### Scatter Diagrams
1. **Scatter Diagram #1**
- The scatter plot consists of a set of data points that are clustered in an upward trend.
- The x-axis (horizontal) ranges from 0 to 5.5, and the y-axis (vertical) ranges from -4 to 16.
- A blue regression line is fitted through the data points, indicating a positive linear relationship between the x and y variables.
2. **Scatter Diagram #2**
- The scatter plot also consists of a set of data points, but these points are clustered in a downward trend.
- The x-axis (horizontal) ranges from 0 to 5.5, and the y-axis (vertical) ranges from -4 to 16.
- A blue regression line is fitted through the data points, indicating a negative linear relationship between the x and y variables.
#### Developing the Estimated Regression Equation
To develop the estimated regression equation, we compute the values of \( b_0 \) and \( b_1 \) using the following equations:
- Equation 14.6 and Equation 14.7 (the specific equations are not provided in the content).
The resulting estimated regression equation is given by:
\[ \hat{y} = 2.8 + 0.2x \]
where \( \hat{y} \) is the predicted value of y, and x is the independent variable.
#### Predicting Values Using the Estimated Regression Equation
To predict the value of y when \( x = 4 \), we substitute x into the regression equation:
\[ \hat{y} = 2.8 + 0.2(4) \]
After calculating, we find:
\[ \hat{y} = 11.4 \]
Thus, the predicted value of y when \( x = 4 \) is 11.4.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb4d7f062-e810-4648-a5a3-ae31eaebc212%2F2eddefde-828a-4b93-9245-062a3e6ec3f8%2F7e97ys9_processed.png&w=3840&q=75)
Transcribed Image Text:### Scatter Plots and Regression Analysis
This educational content focuses on regression analysis, including the development of estimated regression equations using scatter diagrams and linear equations.
#### Scatter Diagrams
1. **Scatter Diagram #1**
- The scatter plot consists of a set of data points that are clustered in an upward trend.
- The x-axis (horizontal) ranges from 0 to 5.5, and the y-axis (vertical) ranges from -4 to 16.
- A blue regression line is fitted through the data points, indicating a positive linear relationship between the x and y variables.
2. **Scatter Diagram #2**
- The scatter plot also consists of a set of data points, but these points are clustered in a downward trend.
- The x-axis (horizontal) ranges from 0 to 5.5, and the y-axis (vertical) ranges from -4 to 16.
- A blue regression line is fitted through the data points, indicating a negative linear relationship between the x and y variables.
#### Developing the Estimated Regression Equation
To develop the estimated regression equation, we compute the values of \( b_0 \) and \( b_1 \) using the following equations:
- Equation 14.6 and Equation 14.7 (the specific equations are not provided in the content).
The resulting estimated regression equation is given by:
\[ \hat{y} = 2.8 + 0.2x \]
where \( \hat{y} \) is the predicted value of y, and x is the independent variable.
#### Predicting Values Using the Estimated Regression Equation
To predict the value of y when \( x = 4 \), we substitute x into the regression equation:
\[ \hat{y} = 2.8 + 0.2(4) \]
After calculating, we find:
\[ \hat{y} = 11.4 \]
Thus, the predicted value of y when \( x = 4 \) is 11.4.
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