Correlation does not equal Causation!

You were given the data at the right comparing the weight of cars in pounds with their highway gas mileage.  You found a linear regression equation and determined that your model was a good fit.

So, you now state for the whole world to hear that heavier cars get less gas mileage.  Right???

Not necessarily.  Your statement may be correct for this particular set of data, but it may not be a universal truth.

It may also be true that the weight of the car has nothing to do with the gas mileage.  Perhaps some other factor is affecting the gas mileage.

Just because a correlation exists does not guarantee that the change in one of your variables is causing the change in the other variable.

 Car Weight in Pounds Gas Mileage MPG (highway) 3489 28 3955 25 3345 27 3085 29 4915 18 4159 21 4289 20 3992 26

 Consider this situation:

During the months of March and April, the weekly weight increases of a puppy in New York were collected.  For the same time frame, the retail price increases of snowshoes in Alaska were collected.  The data was examined and was found to have a very strong linear correlation.

So, this must mean that the weight increase of a puppy in New York is causing snowshoe prices in Alaska to increase.  Of course this is not true!

The moral of this example is:  "be careful what you infer from your statistical analyses."  Be sure your relationship makes sense.  Also keep in mind that other factors may be involved in a cause-effect relationship.

 Weekly Data Collection The weight of a growing puppy in New York The retail price of snowshoes in Alaska 8 pounds \$32.45 8.5 \$32.95 9 \$33.45 9.6 \$34.00 10.1 \$34.50 10.7 \$35.10 11.5 \$35.63