What is the range of covariance? What is the range of correlation?

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Nov 5, 2015

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Since covariance is dependent on the scales of measurement, it can approach positive or negative infinity. Correlation, however, is standardised and thus takes a minimum value of #–1# and a maximum value of #+1.#

Explanation:

#COV_(XY) = (sum(x_i - barx)(y_i - bary))/(N - 1)#

The numerator can approach infinity given a sensitive enough measure of #x# and #y#.

The correlation coefficient, #r = (COV_(XY))/(s_x*s_y)#, and is thus standardised by the scales of measurement for #x# and #y#.

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