# Why is pure sample covariance a bad metric to understand the degree of correlation between two variables?

Covariance helps you understand how variables are linearly related.

Would it be possible to have two pairs of variables in a deterministic relationship (i.e. linearly correlated variables) that have different values for the covariance?

My guess would be that if you had one pair with low sample variances and the other pair with high sample variances, you could have the same relationship but a different covariance. Am I on the right path?

• Because it is not invariant under scaling. – André Nicolas Feb 26 '15 at 19:13
• So you mean the covariance accounts for the differences in variance, but a measure like the correlation doesn't? – Schnokeyboy Feb 26 '15 at 19:15
• I mean that if heights are measured in inches, the covariance is very different from the covariance if heights are measured in feet. Correlation coefficient is by contrast invariant under scaling. – André Nicolas Feb 26 '15 at 19:22
• Great, thanks for your help! – Schnokeyboy Feb 26 '15 at 19:24