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=−1

r=0.9

r=1

Answer 1

To create a scatter plot based on the provided data:

**Data Points:**
- (0, 3)
- (2, 6)
- (4, 9)
- (6, 12)
- (8, 15)
- (10, 18)

When you plot these points, you will see that as Data 1 increases, Data 2 also increases.

**Estimate of Correlation Coefficient:**
The correlation between the two variables appears to be strong and positive, as the data shows a perfect linear relationship. The formula for the correlation coefficient (r) is given by:

\[
r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}
\]

Calculating quickly:

- \(n = 6\)
- \(\sum x = 0 + 2 + 4 + 6 + 8 + 10 = 30\)
- \(\sum y = 3 + 6 + 9 + 12 + 15 + 18 = 63\)
- \(\sum xy = (0*3) + (2*6) + (4*9) + (6*12) + (8*15) + (10*18) = 0 + 12 + 36 + 72 + 120 + 180 = 420\)
- \(\sum x^2 = 0^2 + 2^2 + 4^2 + 6^2 + 8^2 + 10^2 = 0 + 4 + 16 + 36 + 64 + 100 = 220\)
- \(\sum y^2 = 3^2 + 6^2 + 9^2 + 12^2 + 15^2 + 18^2 = 9 + 36 + 81 + 144 + 225 + 324 = 819\)

Plugging these into the formula gives us a correlation coefficient (r) of 1. This indicates a perfect positive correlation.

Therefore the answer is:

**r = 1**