K represent the weights of various cars and their gas mileages. Complete parts (a) through (d). on coefficient in Coefficient - X Miles per Car Weight (pounds) Gallon 3175 22 A 3590 18 3000 22 3565 20 2580 27 tical values table. BUDE В C The explanatory variable is the weight and the response variable is the miles per gallon O The explanatory variable is the miles per gallon and the response variable is the weight (b) Draw a scatter diagram of the data. Choose the correct scatter plot. OA B. 4000 E O C. 2500+ 15 30-4 4 15+ 2500 mpg . 4000 Weight (lbs) Q Q Q Q 30-4 (Round to three decimal places as needed.) 15+ 2500 O D. Weight (lbs) 4000 D 2500- 15 4000 mpg Q Q G (c) Compute the linear correlation coefficient between the weight of a car and its miles per gallon.

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### Exploring the Relationship between Car Weight and Gas Mileage

An engineer aimed to uncover how the weight of a car impacts its gas mileage. The data provided here represents the weights of various cars and their corresponding gas mileages. Follow through the analysis by completing parts (a) through (d).

#### Data Table:
| Car | Weight (pounds) | Miles per Gallon |
|-----|-----------------|------------------|
| A   | 3175            | 22               |
| B   | 3590            | 18               |
| C   | 3000            | 22               |
| D   | 3565            | 20               |
| E   | 2580            | 27               |

#### Tasks:
1. **Determine Variables:**
   - Identify the explanatory variable and the response variable from the given data.
     - The explanatory variable is the weight and the response variable is the miles per gallon.

2. **Draw a Scatter Diagram:**
   - Based on the data, choose the correct scatter plot from the given options.

#### Scatter Plot Options:
   - **Option A:** Incorrect
   - **Option B:** Correct (Scatter plot showing a visual representation with car weights on the x-axis and miles per gallon on the y-axis)
   - **Option C:** Incorrect
   - **Option D:** Incorrect

3. **Compute the Linear Correlation Coefficient:**
   - Calculate the linear correlation coefficient (r) between the weight of the car and its miles per gallon, rounding to three decimal places as needed.

#### Critical Values for Correlation Coefficient:
To determine the significance of the linear correlation coefficient, refer to the critical values for different sample sizes (n).

| n  | r     |
|----|-------|
| 3  | 0.997 |
| 4  | 0.950 |
| 5  | 0.878 |
| 6  | 0.811 |
| 7  | 0.754 |
| 8  | 0.707 |
| 9  | 0.666 |
| 10 | 0.632 |
| 11 | 0.602 |
| 12 | 0.576 |
| 13 | 0.553 |
| 14 | 0.532 |
| 15 | 0.514 |
| 16 | 0.497 |
| 17 |
Transcribed Image Text:### Exploring the Relationship between Car Weight and Gas Mileage An engineer aimed to uncover how the weight of a car impacts its gas mileage. The data provided here represents the weights of various cars and their corresponding gas mileages. Follow through the analysis by completing parts (a) through (d). #### Data Table: | Car | Weight (pounds) | Miles per Gallon | |-----|-----------------|------------------| | A | 3175 | 22 | | B | 3590 | 18 | | C | 3000 | 22 | | D | 3565 | 20 | | E | 2580 | 27 | #### Tasks: 1. **Determine Variables:** - Identify the explanatory variable and the response variable from the given data. - The explanatory variable is the weight and the response variable is the miles per gallon. 2. **Draw a Scatter Diagram:** - Based on the data, choose the correct scatter plot from the given options. #### Scatter Plot Options: - **Option A:** Incorrect - **Option B:** Correct (Scatter plot showing a visual representation with car weights on the x-axis and miles per gallon on the y-axis) - **Option C:** Incorrect - **Option D:** Incorrect 3. **Compute the Linear Correlation Coefficient:** - Calculate the linear correlation coefficient (r) between the weight of the car and its miles per gallon, rounding to three decimal places as needed. #### Critical Values for Correlation Coefficient: To determine the significance of the linear correlation coefficient, refer to the critical values for different sample sizes (n). | n | r | |----|-------| | 3 | 0.997 | | 4 | 0.950 | | 5 | 0.878 | | 6 | 0.811 | | 7 | 0.754 | | 8 | 0.707 | | 9 | 0.666 | | 10 | 0.632 | | 11 | 0.602 | | 12 | 0.576 | | 13 | 0.553 | | 14 | 0.532 | | 15 | 0.514 | | 16 | 0.497 | | 17 |
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