A negative correlation between screen time and sleep

Question

For a group of students, evening screen time $X$ and hours of sleep $Y$ have covariance $-6$ . Screen time has standard deviation $3$ and sleep has standard deviation $5$ .

What is the correlation between screen time and sleep?

Accepted Answer

Rescale the covariance by both standard deviations to get a unit-free correlation: ho = \frac{\mathrm{Cov}(X, Y)}{\mathrm{SD}(X)\,\mathrm{SD}(Y)}. The covariance is already given, and so are the two standard deviations, so just divide: ho = \frac{-6}{3 	imes 5} = \frac{-6}{15} = -0.4. The sign of the correlation always matches the sign of the covariance, because standard deviations are never negative. Here the negative value says more screen time goes with less sleep, a moderate inverse link. Takeaway. Dividing by the two standard deviations never changes the sign, since they are positiv…

A negative correlation between screen time and sleep

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