Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
For some made-up students, the correlation between the hours of sleep and the number of mistakes in a puzzle is . A researcher makes two new variables: , the sleep in minutes, and , the number of puzzle items done right out of . Find the correlation between and , and the correlation between and .
measures straight-line patterns only. A curve can give near , one outlier can change a lot, and a narrow range of usually lowers . Changing units, or adding a number, leaves alone; multiplying by a negative number changes its sign.
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. and . is in a new unit. A unit change does not change , so the correlation is still .
Step 2. and . adds and multiplies by . The minus sign reverses the direction, so the correlation is .
Answer: and .
Check. It makes sense in words: more sleep goes with fewer mistakes, so more sleep goes with more items right.
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