In: Statistics and Probability
Explain why ρ is preferable to Cov(X,Y) in measuring the strength of relationship between X and Y
ρ or the correlation coefficient is preferable because it allows comparing the magnitude and the direction of the strength of the relationship between X and Y very easily. ρ can take values between -1 and 1. Since we have a fixed scale between which ρ lies, it is easier to discern the magnitude of the linear relationship between the two variables. For example, if ρ = -1, it means that the variables are perfect negatively correlated. It increasing from -1 to 0 shows that the degree of the negative association between the two variables is becoming weaker. 0 means the absence of a linear relationship. As ρ increases from 0 to 1, the degree of the positive association between the variables increase.
since Cov(X,Y) can take any value, comparing the magnitude or strength of the relationship between X and Y is not possible. Hence ρ is preferrable.
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