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Question Video: Determining the Type of Correlation between Two Variables Using the Value of the Correlation Coefficient Mathematics • 9th Grade

Which of the following is the most appropriate interpretation of a product moment correlation coefficient of 0.8? [A] a strong negative linear correlation [B] a moderate negative linear correlation [C] a moderate positive linear correlation [D] a strong positive linear correlation [E] no correlation

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Video Transcript

Which of the following is the most appropriate interpretation of a product-moment correlation coefficient of 0.8? Is it (A) a strong negative linear correlation, (B) a moderate negative linear correlation, (C) a moderate positive linear correlation, (D) a strong positive linear correlation, or (E) no correlation?

We know that Pearson’s product-moment correlation coefficient 𝑟 subscript 𝑥𝑦 or just 𝑟 takes values between negative one and positive one. We also know that if 𝑟 is less than zero and greater than or equal to negative one, then we have inverse or negative correlation and that if 𝑟 is greater than zero and less than or equal to positive one, we have direct or positive correlation. We’re asked which of the given options is the most appropriate interpretation of a product-moment correlation coefficient with a value of 0.8. Since this value is positive, we know that we have direct or positive correlation. This means we can eliminate any of our options that specify negative correlation. So we can eliminate options (A) and (B), since these both specify a negative correlation. We can also eliminate option (E), since no correlation would give us a correlation coefficient of zero. And our correlation coefficient is nonzero; it’s 0.8.

This leaves us with options (C) and (D), a moderate positive linear correlation or a strong positive linear correlation. If we consider the magnitude of the correlation coefficient, the stronger the correlation, the closer the magnitude to one. And the closer the magnitude is to zero, the weaker the correlation. This means then that approximately midway between zero and positive or negative one, we have moderate correlation. Since the given coefficient is 0.8, which is close to positive one, we can therefore say that this represents strong positive correlation. And so the most appropriate interpretation of a product-moment correlation coefficient of 0.8 is option (D), a strong positive linear correlation.

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