To analyze the given data and estimate the correlation coefficient, let's first consider the data points:
Data 1: 0, 2, 4, 6, 8, 10
Data 2: 3, 6, 9, 12, 15, 18
By plotting these data points on a scatter plot, we can observe a strong linear relationship between Data 1 and Data 2. The values in Data 2 consistently increase as the values in Data 1 increase, suggesting a positive correlation.
To estimate the correlation coefficient (r), we compute it based on the linear relationship. Given that the relationship appears to be linear, we would expect a correlation coefficient close to +1.
Considering the options:
- \( r = 0.9 \): This option indicates a strong positive correlation.
- \( r = -1 \): Indicates a perfect negative correlation, which does not apply to this dataset.
- \( r = 1 \): Indicates a perfect positive correlation, which may be close but not exactly accurate due to an assumption of slight measurement error or variation.
- \( r = -0.9 \): Indicates a strong negative correlation, which does not apply.
Given that the data points appear to form a perfectly linear relationship, the closest estimate for the correlation coefficient is \( r = 1 \). However, in practical situations with slight variations due to measurement errors, the value may often be reported as close to \( r = 0.9 \).
Best estimate based on the options provided:
- r = 1 (if assuming perfect linearity)
- r = 0.9 (if considering practical variations).
Since it is exactly stated as \( r = 1 \):
The estimated correlation coefficient is \( r = 1 \).