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In a made-up survey of working adults, the correlation between the hours spent travelling to work…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
In a made-up survey of working adults, the correlation between the hours spent travelling to work each week and the hours spent on a hobby is . What percentage of the variation in the hobby hours does the least-squares line account for? What percentage is left in the residuals?
Need a reminder? The key ideaShow
is the share of the variation in that the line accounts for; with the sign of the slope. A residual plot with a pattern (a curve, a fan) shows that a straight line is not the right model.
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.
Step 1. , so the line accounts for of the variation in the hobby hours.
Step 2. is left in the residuals.
Answer: and .
Watch out. A negative still gives a positive . And does not mean that the line explains . Other things, such as family duties, also take hobby time.
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