Final answer:
The correlation coefficient (r) gauges the relationship between two variables. It ranges from -1 to +1, with values near +1 indicating a strong positive linear relationship. Given the options and the strong linear relationship mentioned, plausible values are 0.982 or 0.991, which are near +1.
Step-by-step explanation:
The correlation coefficient, symbolized as r, is a statistical measure that calculates the strength of the relationship between the relative movements of two variables. In this scenario, we have pairs of x and y values provided, and we are tasked with determining the correlation coefficient of this dataset.
To find the r value, we use the formula for the Pearson correlation coefficient, which involves the mean and standard deviation of both x and y, as well as the product of their deviations from their respective means.
Based on the given options, the correlation coefficient would be expected to be a value between -1 and +1, where a value of +1 indicates a perfect positive linear relationship. While the exact manual calculation can be complex, it typically involves statistical software or a calculator with statistical functions.
As none of the provided options exceed the range of -1 to +1, we can eliminate option C as it is outside this range. Since we are informed that the data set has a strong linear relationship, we are looking for a number that is close to 1.
The value of 0.982 (Option A) or 0.991 (Option D) could represent such a strong positive correlation. Without calculating the exact number, we cannot determine which one is correct; however, both A and D are plausible given the range for r and the strong linear relationship described.