**Best Subsets Regression** is a method used to
help determine which predictor (independent) variables should be included in a multiple
regression model. This method
involves examining all of the models created from all possible combination of
predictor variables. Best Subsets Regression uses R^{2} to check for the
best model. It would not be fun or
fast to compute this method without the use of a statistical software
program.

First, all models that have only one predictor
variable included are checked and the two models with the highest R^{2}
are selected. Then all models that have only two predictor variables
included are checked and the two models with the highest R^{2} are
chosen, again. This process
continues until all combinations of all predictors variables have been taken
into account.

**Specific
Example:** Assume that during a three-hour period spent outside, a person
recorded the temperature, the time spent mowing the lawn,
weather there was sun or not (0 or 1) and their water
consumption. The experiment was
conducted on 7 randomly selected days during the summer. By using our
imaginations we can come up with some other possible predictors that might give
us a more accurate model, such as temp^2 and mowing time * temperature.
Now, we have 5 possible predictors to include in our model. With only 7
data points, it would not be wise to include all five. In fact, including
some of these predictors may even decrease the accuracy of the model. So
we are left with how to decide which predictors to included and which to
not.

Next, learn the Procedure for calculating Best Subsets Regression.

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