Question

Use the data to create a scatter plot. Estimate the correlation coefficient based on the data.



Data 1 Data 2
0 3
2 6
4 9
6 12
8 15
10 18


(1 point)
Responses

r=0.9
r is equal to 0 point 9

r=−0.9
r is equal to negative 0 point 9

r=1
r is equal to 1

r=−1
r is equal to negative 1

Answer 1

To estimate the correlation coefficient based on the provided data, we can analyze the relationship between Data 1 and Data 2.

The data pairs are as follows:
- (0, 3)
- (2, 6)
- (4, 9)
- (6, 12)
- (8, 15)
- (10, 18)

If we observe the values, we can see that as Data 1 increases, Data 2 also increases proportionally. In fact, Data 2 can be expressed with the equation \( \text{Data 2} = \frac{3}{2} \times \text{Data 1} + 3 \). This indicates a perfect linear relationship.

The correlation coefficient (denoted as \( r \)) reflects the strength and direction of a linear relationship between two variables. Since the points linearly correlate perfectly without any deviation:

- \( r \) is equal to 1 (r = 1).

Thus, the correct response is:

**r=1**
**r is equal to 1**