Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. 13 15 10 6 12.84 12.21 11.70 6.26 8 9.54 X 14 y 12.66 5- 5 4.21 9 12 10.75 12.74 11 7 8.04 12.35 0 5 10 15 20 25 0 5 10 15 20 25 Identify a characteristic of the data that is ignored by the regression line. OA. There is no trend in the data. OB. There is an influential point that strongly affects the graph of the regression line. OC. The data has a pattern that is not a straight line. OD. There is no characteristic of the data that is ignored by the regression line. C 0 5 10 15 20 25 0 5 10 15 20 25
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. 13 15 10 6 12.84 12.21 11.70 6.26 8 9.54 X 14 y 12.66 5- 5 4.21 9 12 10.75 12.74 11 7 8.04 12.35 0 5 10 15 20 25 0 5 10 15 20 25 Identify a characteristic of the data that is ignored by the regression line. OA. There is no trend in the data. OB. There is an influential point that strongly affects the graph of the regression line. OC. The data has a pattern that is not a straight line. OD. There is no characteristic of the data that is ignored by the regression line. C 0 5 10 15 20 25 0 5 10 15 20 25
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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![**Title: Regression Line Identification and Scatterplot Analysis**
**Task:**
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
**Data Table:**
| x | y |
|----|------|
| 14 | 12.66|
| 5 | 4.21 |
| 11 | 12.35|
| 9 | 10.75|
| 12 | 12.74|
| 7 | 8.04 |
| 13 | 12.84|
| 15 | 12.21|
| 10 | 11.70|
| 6 | 6.26 |
| 8 | 9.54 |
**Equation:**
\[
\hat{y} = \boxed{} + \boxed{} x \quad \text{(Round to two decimal places as needed.)}
\]
**Scatterplot Analysis:**
Create a scatterplot of the data. Choose the correct graph from the options below:
- **Option A:** A spreadout scatterplot with points distributed widely.
- **Option B:** Data points form a curved shape, indicating a possible nonlinear relationship.
- **Option C:** Points roughly form a linear trend, suggesting a relationship suitable for a linear regression line.
- **Option D:** Another nonlinear pattern with an arched layout.
**Explanation:**
The purpose of this exercise is to determine which scatterplot correctly represents the given data and subsequently identify one characteristic of the data that the regression line might overlook, such as curvature or clustering.
When completing this task, ensure to visualize the scatterplot accurately and consider whether a linear model suits the data’s distribution or if any nonlinear trends are present.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F38d7ad60-cd84-472c-8996-4a82bb3a3198%2F6628d72b-a76f-4e05-a3c7-df7c1bed4a3c%2Fk5quhe_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Title: Regression Line Identification and Scatterplot Analysis**
**Task:**
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
**Data Table:**
| x | y |
|----|------|
| 14 | 12.66|
| 5 | 4.21 |
| 11 | 12.35|
| 9 | 10.75|
| 12 | 12.74|
| 7 | 8.04 |
| 13 | 12.84|
| 15 | 12.21|
| 10 | 11.70|
| 6 | 6.26 |
| 8 | 9.54 |
**Equation:**
\[
\hat{y} = \boxed{} + \boxed{} x \quad \text{(Round to two decimal places as needed.)}
\]
**Scatterplot Analysis:**
Create a scatterplot of the data. Choose the correct graph from the options below:
- **Option A:** A spreadout scatterplot with points distributed widely.
- **Option B:** Data points form a curved shape, indicating a possible nonlinear relationship.
- **Option C:** Points roughly form a linear trend, suggesting a relationship suitable for a linear regression line.
- **Option D:** Another nonlinear pattern with an arched layout.
**Explanation:**
The purpose of this exercise is to determine which scatterplot correctly represents the given data and subsequently identify one characteristic of the data that the regression line might overlook, such as curvature or clustering.
When completing this task, ensure to visualize the scatterplot accurately and consider whether a linear model suits the data’s distribution or if any nonlinear trends are present.
Transcribed Image Text:### Finding the Equation of a Regression Line
Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line.
#### Data Table:
- \( x \): 14, 5, 11, 9, 12, 7, 13, 15, 10, 6, 8
- \( y \): 12.66, 4.21, 12.35, 10.75, 12.74, 8.04, 12.84, 12.21, 11.70, 6.26, 9.54
#### Scatterplots:
There are four scatterplots provided:
1. **Scatterplot 1**: Data points are evenly spread without any apparent trend. The x-axis ranges from 0 to 25, and the y-axis ranges from 0 to 5.
2. **Scatterplot 2**: Shows an influential point far from the main cluster of points, affecting the regression line. The axes' scales are the same as in scatterplot 1.
3. **Scatterplot 3**: Data points form a linear pattern, suggesting that most data points align well with a straight trend line. The axis scales remain consistent.
4. **Scatterplot 4**: Points are scattered randomly with no visible relationship or trend between x and y values. Axes scales are unchanged.
#### Question:
Identify a characteristic of the data that is ignored by the regression line:
- **A.** There is no trend in the data.
- **B.** There is an influential point that strongly affects the graph of the regression line.
- **C.** The data has a pattern that is not a straight line.
- **D.** There is no characteristic of the data that is ignored by the regression line.
In this context, the correct choice is likely **B**, as the presence of an influential point can significantly alter the slope and position of the regression line, which may not represent the overall data distribution accurately.
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