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A made-up city records two numbers for eight years…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A made-up city records two numbers for eight years. Its cafes number , , , , , , and . Its cycle lanes measure , , , , , , and km. Find for the two lists. Then find the seven changes from one year to the next for each list, and the correlation between the changes. Give both to three decimal places. Are the cafes and the cycle lanes connected?
Need a reminder? The key ideaShow
A lurking (confounding) variable affects both variables and can create a correlation. A correlation can also come from reverse cause, mixed groups, time or chance. Only a randomised experiment balances lurking variables that nobody knows about.
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. Totals. Both lists rise every year, and .
Step 2. Changes. Cafes: . Cycle lane: km. Their correlation is .
Answer: for the totals and for the changes.
What it means. A year with many new cafes is not a year with much new cycle lane. The high for the totals comes only from both growing over time, with the city. Time is the lurking variable, and there is no sign of a real connection.
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