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 10 y 7.27 11 10 10 14 12 7.92 6 6.8 13.16 7.36 7.69 8.7 5.97 5.42 6.36 5.98 Create a scatterplot of the data. Choose the correct graph below. O A. O D. Ay 25- 25- Ay 25- Ay 25- 20 20 20 20 15 155 15 10 15 10- 10 10 55 o 0000 55 55 5 8 0- 0 5 0- 10 15 20 25 Ó 5 10 15 20 25 0- O 5 10 15 20 25 0- O 5 10 15 20 25 Find the equation of the regression line. (Round the constant two decimal places as needed. Round the coefficient to three decimal places as needed.)

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Author:Amos Gilat
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Chapter1: Starting With Matlab
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**Exploring Regression and Scatterplots**

**Objective:**
Use the given data to determine 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  | 10  | 9   | 11  | 10  | 14  | 5   | 4   | 12  | 6   | 6   |
|----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----|
| y  | 7.27| 6.8 | 13.16| 7.36| 7.69| 8.7 | 5.97| 5.42| 7.92| 6.36| 5.98 |

**Instructions:**
Create a scatterplot of the data. Choose the correct graph below.

**Scatterplot Options:**

- **A. (Incorrect)**
  - The points do not align with the given data.
  
- **B. (Correct)**
  - The graph accurately represents the data points and shows a possible linear relationship.

- **C. (Incorrect)**
  - The distribution of points does not reflect the given data.

- **D. (Incorrect)**
  - The arrangement of points is not representative of the given dataset.

**Task:**
Find the equation of the regression line in the form \( \hat{y} = b + mx \).

- **Round the constant to two decimal places as needed.**
- **Round the coefficient to three decimal places as needed.**

This exercise aims to improve understanding of data analysis, interpretation of scatterplots, and linear regression.
Transcribed Image Text:**Exploring Regression and Scatterplots** **Objective:** Use the given data to determine 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 | 10 | 9 | 11 | 10 | 14 | 5 | 4 | 12 | 6 | 6 | |----|-----|-----|-----|-----|-----|-----|-----|-----|-----|-----| | y | 7.27| 6.8 | 13.16| 7.36| 7.69| 8.7 | 5.97| 5.42| 7.92| 6.36| 5.98 | **Instructions:** Create a scatterplot of the data. Choose the correct graph below. **Scatterplot Options:** - **A. (Incorrect)** - The points do not align with the given data. - **B. (Correct)** - The graph accurately represents the data points and shows a possible linear relationship. - **C. (Incorrect)** - The distribution of points does not reflect the given data. - **D. (Incorrect)** - The arrangement of points is not representative of the given dataset. **Task:** Find the equation of the regression line in the form \( \hat{y} = b + mx \). - **Round the constant to two decimal places as needed.** - **Round the coefficient to three decimal places as needed.** This exercise aims to improve understanding of data analysis, interpretation of scatterplots, and linear regression.
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