But the direction of the correlations is different: a negative correlation corresponds to a decreasing relationship, while and a positive correlation corresponds to an increasing relationship. The strength of the nonzero correlations are the same: 0.90. The scatterplots below show correlations that are r = +0.90, r = 0.00, and r = -0.90, respectively. Note: The direction and strength of a correlation are two distinct properties. The strength can be assessed by these general guidelines (which may vary by discipline): +1 : perfectly positive linear relationship.-1 : perfectly negative linear relationship.The sign of the correlation coefficient indicates the direction of the relationship, while the magnitude of the correlation (how close it is to -1 or +1) indicates the strength of the relationship. ![]() Where cov( x, y) is the sample covariance of x and y var( x) is the sample variance of x and var( y) is the sample variance of y.Ĭorrelation can take on any value in the range. The sample correlation coefficient between two variables x and y is denoted r or r xy, and can be computed as: $$ r_ $$
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