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. X 11 7 12 14 7 13 10 13.32 6.78 7.89 8.93 7 5 y 7.59 6.64 4 13 5.44 8.05 5.83 6.3 5.94 OA. B. O C. O D. Q 25- Q 25- Q 25- 25 205 20 20 205 15: Q 15: Q 153 153 10 10 G 105 10 Do you 5 Tanken 0%0.0 G 5 5 5 0 0- 0 0 5 10 15 20 25 0- 0 5 10 15 20 25 0 5 10 15 20 25 0 5 10 15 20 25 Find the equation of the regression line. ŷ=0+0x (Round the y-intercept two decimal places as needed. Round the slope to three decimal places as needed.) Ay Av Aу Aу

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
icon
Related questions
Question
### Understanding Linear Regression and Data Patterns

**Objective:**
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  | 11  | 7   | 13  | 10  | 12  | 14  | 7   | 4   | 13  | 7   | 5   |
|----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| y  | 7.59 | 6.64 | 13.32 | 6.78 | 7.89 | 8.93 | 5.83 | 5.44 | 8.05 | 6.3 | 5.94 |

#### Scatterplot Analysis:
There are four scatterplots labeled A through D:

- **Scatterplot A:** Features data points that appear to cluster and vary consistently along both axes.
- **Scatterplot B:** Shows a non-linear pattern, indicating that the relationship between \( x \) and \( y \) may not be adequately modeled by a straight line.
- **Scatterplot C:** Contains a potential outlier that may strongly affect the regression line.
- **Scatterplot D:** Similar to Scatterplot A, this plot shows a distribution of data that can be interpreted linearly but is less consistent than Scatterplot B.

#### Steps to Find the Regression Line:
1. **Equation Format:** 
   \[
   \hat{y} = \boxed{\text{(Intercept)}} + \boxed{\text{(Slope)}} x
   \]

2. **Round-off Instructions:**
   - Round off the \( y \)-intercept to two decimal places.
   - Round off the slope to three decimal places.

3. **Answer Choices for Characteristics Ignored by the Regression Line:**
   - **A.** There is no characteristic of the data that is ignored by the regression line.
   - **B.** The data has a pattern that is not a straight line.
   - **C.** There is an influential point that strongly affects the graph of the regression line.
   - **D.** The data has a pattern that is not consistent.

#### Identification:
Based on analysis, **Option B** is selected, indicating that the data has a pattern that is
Transcribed Image Text:### Understanding Linear Regression and Data Patterns **Objective:** 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 | 11 | 7 | 13 | 10 | 12 | 14 | 7 | 4 | 13 | 7 | 5 | |----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| | y | 7.59 | 6.64 | 13.32 | 6.78 | 7.89 | 8.93 | 5.83 | 5.44 | 8.05 | 6.3 | 5.94 | #### Scatterplot Analysis: There are four scatterplots labeled A through D: - **Scatterplot A:** Features data points that appear to cluster and vary consistently along both axes. - **Scatterplot B:** Shows a non-linear pattern, indicating that the relationship between \( x \) and \( y \) may not be adequately modeled by a straight line. - **Scatterplot C:** Contains a potential outlier that may strongly affect the regression line. - **Scatterplot D:** Similar to Scatterplot A, this plot shows a distribution of data that can be interpreted linearly but is less consistent than Scatterplot B. #### Steps to Find the Regression Line: 1. **Equation Format:** \[ \hat{y} = \boxed{\text{(Intercept)}} + \boxed{\text{(Slope)}} x \] 2. **Round-off Instructions:** - Round off the \( y \)-intercept to two decimal places. - Round off the slope to three decimal places. 3. **Answer Choices for Characteristics Ignored by the Regression Line:** - **A.** There is no characteristic of the data that is ignored by the regression line. - **B.** The data has a pattern that is not a straight line. - **C.** There is an influential point that strongly affects the graph of the regression line. - **D.** The data has a pattern that is not consistent. #### Identification: Based on analysis, **Option B** is selected, indicating that the data has a pattern that is
Expert Solution
steps

Step by step

Solved in 5 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman