Car 1


3 comma 7753,775

2121

Car 2


3 comma 9443,944

1818

Car 3


3 сотта 5903,590

2121

Car 4


3 comma 1753,175

2222

Car 5


2 comma 5802,580

2727

Car 6


3 comma 7303,730

1818

Car 7


2 comma 6052,605

2626

Car 8


3 comma 7723,772

1717

Car 9

3 comma 3103,310

2020

Car 10

2,991

2525

Car 11

2752

2626

Car 12

3305

19

Compute the linear correlation coefficient with Car 12 included.

The linear correlation coefficient with Car 12 included is r=

(Round to three decimal places as needed.)

To compute the linear correlation coefficient \( r \), we need to clarify the data for the cars. It appears that the data may represent two variables for each car, but the format is inconsistent. Let's break down the information more clearly, separating the two variables for each car. I'll interpret the data based on typical patterns and then calculate \( r \).

### Interpreted Data

1. **Car 1**: \( (37753.775, 2121) \)
2. **Car 2**: \( (39443.944, 1818) \)
3. **Car 3**: \( (35903.590, 2121) \)
4. **Car 4**: \( (31753.175, 2222) \)
5. **Car 5**: \( (25802.580, 2727) \)
6. **Car 6**: \( (37303.730, 1818) \)
7. **Car 7**: \( (26052.605, 2626) \)
8. **Car 8**: \( (37723.772, 1717) \)
9. **Car 9**: \( (33103.310, 2020) \)
10. **Car 10**: \( (2991, 2525) \)
11. **Car 11**: \( (2752, 2626) \)
12. **Car 12**: \( (3305, 19) \)

### Values to Use
- Let \( x \) be the first value (interpreted from each car's data).
- Let \( y \) be the second value.

Now we have the following pairs:

| Car   | \( x \)        | \( y \)  |
|-------|----------------|----------|
| Car 1 | 37753.775      | 2121     |
| Car 2 | 39443.944      | 1818     |
| Car 3 | 35903.590      | 2121     |
| Car 4 | 31753.175      | 2222     |
| Car 5 | 25802.580      | 2727     |
| Car 6 | 37303.730      | 1818     |
| Car 7 | 26052.605      | 2626     |
| Car 8 | 37723.772      | 1717     |
| Car 9 | 33103.310      | 2020     |
| Car 10| 2991           | 2525     |
| Car 11| 2752           | 2626     |
| Car 12| 3305           | 19       |

### Steps to Compute \( r \)

1. **Calculate the means of \( x \) and \( y \)**.
2. **Calculate the covariance of \( x \) and \( y \)**.
3. **Calculate the standard deviations of \( x \) and \( y \)**.
4. **Use the formula for the correlation coefficient**:

\[
r = \frac{cov(X, Y)}{std(X) \cdot std(Y)}
\]

I'll calculate these now.The linear correlation coefficient \( r \) with Car 12 included is approximately **0.124** (rounded to three decimal places).

Would you like to explore more about correlation coefficients or any other related topics? Here are some questions you might consider:

1. How is the correlation coefficient interpreted in context?
2. What are the limitations of using correlation coefficients?
3. How does one perform regression analysis after calculating the correlation?
4. What factors can affect the correlation between two variables?
5. How can we visualize the correlation between these variables?

Tip: Always visualize your data with scatter plots to better understand relationships before relying solely on correlation coefficients.

Compute the linear correlation coefficient with Car 12 included.

Explore how to compute the linear correlation coefficient r with data from 12 cars, including Car 12. This example illustrates the use of statistical formulas and concepts, aimed at students in Grades 10-12.

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