Which of the following correlation coefficients indicates the strongest correlation? The options are negative 0.14, negative 0.87, negative 0.88, or negative 0.33.
Correlation coefficients describe the measure of linear agreement between two variables. They tell us how close the points sit to a straight line. Points with a positive correlation will sit near to a straight line with positive gradient whereas points with a negative correlation will sit near to a straight line with negative gradient, that is, sloping downwards from left to right.
Points with a perfect positive linear correlation will sit exactly on a straight line, with positive gradient. And the correlation coefficient will be equal to one whereas points with a perfect negative linear correlation will sit entirely on a straight line with a negative gradient. And their correlation coefficient will be equal to negative one.
This doesn’t mean that the gradient of the straight line will be equal to negative 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. So correlation coefficients vary from negative one to one, with a value of negative one indicating perfect, that’s the strongest possible negative correlation, and a value of positive one indicating perfect. That’s the strongest possible positive correlation.
All of the values that we’ve been given are negative. So we’re just looking for the value which is closest to negative one.
From our list, the value which is closest to negative one is negative 0.88. So of the four correlation coefficients, this indicates the strongest correlation.