To determine the estimated correlation coefficient based on the provided data, we first need to look at the relationship between the two variables displayed in the table:
- The x-values are: 0, 2, 4, 6, 8, 10
- The corresponding y-values are: 3, 6, 9, 12, 15, 18
When you plot these points on a scatter plot, you would get the following pairs:
- (0, 3)
- (2, 6)
- (4, 9)
- (6, 12)
- (8, 15)
- (10, 18)
The points will show a clear linear relationship that increases as the x-values increase. More specifically, as x increases, y also increases at a consistent rate.
Calculating the correlation coefficient (r) helps quantify how well the data points fit a linear trend. In this case, since the relationship is perfectly linear and positive, we can infer that:
- The correlation coefficient (r) would be close to +1.
Considering the provided options, the best estimated correlation coefficient based on the data would be:
1 (indicating a perfect positive linear correlation).
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