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.
