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Linear Correlation and Regression

Part 3: Causation

When there is a strong correlation between two variables, there may be a cause and effect relationship. It is reasonable, for instance, to suspect that a high score on Test 1 tends to lead to a high score on Test 2. On the other hand, high correlation is often present even when there is not a cause and effect relationship. For instance, the table below shows some statistics for the Duke basketball team during the 1999 NCAA tournament, and the scatter plot shows a strong correlation between total points scored and number of turnovers.

Player Points Turnovers
Brand 102 14
Langdon 91 7
Avery 84 13
Carrawell 62 13
Maggette 51 8
James 22 4
Domzalski 18 4
Burgess 17 2
Simpson 4 3
Bryant 1 2
Calbeck, J 0 1
Calbeck, R 0 1
  1. Does the positive correlation imply that making more turnovers will cause a player to score more points? Does the correlation imply that scoring points causes turnovers? What do you think causes the strong correlation?

    If you would like to read an example in which two variables have a strong correlation, but lack causation, click here.

  2. Explain why you would expect a strong positive correlation between the number of emergency vehicles at the scene of an accident, and the number of injuries in the accident. Does this suggest that dispatching fewer vehicles to the scene of an accident would mean fewer people would be injured? Explain.

  3. Would you expect positive or negative correlation between the number of people at a public swimming pool and the current temperature? Is there a causal relationship? If so, in which direction? Explain. Does it make a difference if we use air or water temperature? Explain.

  4. A State Park Ranger notices that there is a positive correlation between the number of sunbathers and the number of fishermen on the lake from day to day. Is there a causal relationship? If so, in which direction? Explain.

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