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

Which of the following Pearson′s correlation coefficients indicates the strongest correlation? [A] −0.14 [B] −0.87 [C] −0.88 [D] −0.33?

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### Video Transcript

Which of the following Pearson′s correlation coefficients indicates the strongest correlation? Is it (A) negative 0.14, (B) negative 0.87, (C) negative 0.88, or (D) negative 0.33?

We begin by recalling that Pearson′s correlation coefficient describes the measure of linear agreement between two variables. In effect, it tells us how close a set of points sit to a straight line. We know that points with a positive correlation will sit near to a straight line with positive slope or gradient, whereas points with a negative correlation will sit near to a straight line with negative slope, that is, sloping downwards from left to right. Points with a perfect positive linear correlation will sit exactly on a straight line with positive slope or gradient, and the Pearson′s correlation coefficients will be equal to one, whereas points with a perfect negative linear correlation will sit entirely on a straight line with a negative slope, and the correlation coefficient will be equal to negative one.

It is important to note that this does not mean that the gradient or slope of the line will be equal to negative one. Likewise, a correlation coefficient of one does not mean that the slope of the positive correlation line is one. It just means that the points do lie on a straight line with negative gradient and their correlation coefficient is equal to negative one.

We can therefore see that Pearson′s correlation coefficients vary from negative one to one, with a value of negative one indicating the strongest possible negative correlation and a value of positive one indicating the strongest positive correlation. All of the options in this question are negative. So, to find the value that indicates the strongest correlation, we′re looking for the value which is closest to negative one. The correct answer is therefore option (C). Out of the four options, negative 0.88 indicates the strongest correlation.