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Question Video: Selecting the Correlation Coefficient Value That Indicates the Strongest Correlation Mathematics • 9th Grade

Which of the following Pearson’s correlation coefficients indicates the strongest correlation? [A] 0.31 [B] 0.43 [C] 0.69 [D] 0.71

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Video Transcript

Which of the following Pearson’s correlation coefficients indicates the strongest correlation? Is it (A) 0.31, (B) 0.43, (C) 0.69, or (D) 0.71?

We begin by recalling that we can use Pearson’s correlation coefficient to determine the strength of linear correlation between two sets of data. The coefficient known as 𝑟 can take values greater than or equal to negative one and less than or equal to one and tells us how strongly two variables are correlated. We know that points with a positive correlation will sit near to a straight line with positive slope, or gradient.

Points with perfect positive correlation will sit exactly on a straight line with positive slope. In this case, the value of Pearson’s correlation coefficient 𝑟 is one. It is important to note that this does not mean that the slope of the straight line is equal to one. It just means that all of the points lie on a line with positive slope.

In this question, we are given four options and asked to find the value that indicates the strongest correlation. As all four values are positive, this will be the value that is closest to one. We can therefore conclude that the correct answer is option (D) 0.71, as this is closer to one than 0.31, 0.43, and 0.69.

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