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The scatter plot of a data set is found to show a strong linear relationship between the variables x and y. The values used to determine this are given in the table below. x y 1.3 2.2 4.2 5.1 3.5 4.1 5.7 5.9 2.9 3.7 What is the correlation coefficient of this data set? A. 0.982 B. 0.862 C. 1.167 D. 0.991

User Kltft
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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.

User Samgakhyeong
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