HardStatistics & Data ScienceHigh School (9–10)High School (11–12)UndergraduateGeneralStatistics Basics › Correlation and Regression Statistics Basics › Study Design and ExperimentsNumericalConceptual

A made-up online survey of 2000 adults finds a correlation of r = 0.3 between hours of sleep and a…

Contributed by StemPy Lab

Try it on paper first. A hint, the key idea and the worked solution are here when you need them.

A made-up online survey of $2000$ adults finds a correlation of $r = 0.3$ between hours of sleep and a happiness score. A news site writes: "Sleep is the key to happiness: more sleep makes you happier." What percentage of the variation in happiness can a straight line on sleep account for? Give three reasons why the headline goes too far.

Need a reminder? The key ideaShow

Growth by an equal factor each step is a straight line on a log scale: $\log_{10} y = a + bx$ , with a factor of $10^{b}$ per unit of $x$ and a doubling time of $\dfrac{\log_{10} 2}{b}$ . A square root straightens a quantity that grows like a square.

The worked solution

Have you tried it?

Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.

← All Problems

← In a made-up physics club, a ball is dropped and its fall is timed…A made-up street has 5 households. They keep 0, 1, 1, 3 and 5 pets… →

More onStatistics Basics › Correlation and Regression Statistics Basics › Study Design and Experiments

Discussion (0)

Loading…