To analyze the given data and estimate the correlation coefficient based on it, we first need to see the relationship between the two sets of numbers in the table. The pairs (x, y) from the table are:
- (0, 3)
- (2, 6)
- (4, 9)
- (6, 12)
- (8, 15)
- (10, 18)
Next, let's observe the pattern in the data:
- As the x-values increase (0, 2, 4, 6, 8, 10), the y-values also increase (3, 6, 9, 12, 15, 18).
- The values of y appear to increase consistently as x increases.
This suggests a strong positive linear correlation because as one variable increases, the other variable consistently increases as well.
To estimate the correlation coefficient (r), we look at the possible answers given:
- −0.9
- 1
- −1
- 0.9
Given the data shows a clear positive trend with no deviations, we can conclude that the correlation coefficient is very close to +1, as the relationship is strong and indeed linear.
Therefore, the best estimate from the provided choices is 1.
The reasoning for this is that a correlation coefficient of +1 indicates a perfect positive correlation, and while the exact r might not be precisely 1 (based solely on the data points), it is very close given the perfectly linear relationship observed in the data.