MULTIPLE REGRESSION

The REGRESSION command can use more than one independent variable in the same equation ("multiple regression"). To use multiple independent variables, just name them all on the VARIABLES subcommand. All the variables except the one you name on the DEPENDENT subcommand are used in the equation.

With multiple independent variables, you can specify how they should be entered into the equation using the METHOD subcommand. The following methods are available.

• ENTER: Enter a group of variables all at once . This is the method we have been using throughout the chapter. You can specify the names of specific variables after the keyword ENTER.

• REMOVE: Remove a group of variables all at once . These must be variables that entered the equation on a previous METHOD subcommand. You must specify the names of specific variables after the keyword REMOVE.

• FORWARD: Enter the variables one at a time.

• BACKWARD: Remove the variables one at a time . If some variables are already in the equation from a previous METHOD subcommand, they are removed one at a time. Otherwise, all variables are entered and then removed one at a time.

• STEPWISE: Enter and remove variables one at a time , until the F statistics do not indicate that any variables in the equation should be removed or that any variables that are on the VARIABLES subcommand but not in the equation need to be entered.

You can specify several METHOD subcommands after a single DEPENDENT subcommand. The methods are applied one after the other.

How can you test hypotheses about the population regression line, based on the values you obtain in a sample? Here are the important principles:

• To draw conclusions about the population regression line, you must assume that for each value of the independent variable, the distribution of values of the dependent variable is normal, with the same variance. The means of these distributions must all fall on a straight line.

• The test of the null hypothesis that the slope is zero is a test of whether a linear relationship exists between the two variables.

• The confidence interval for the population slope provides you with a range of values that, with a designated likelihood , includes the population value.

• When a single independent variable is present, the analysis of variance table for the regression is equivalent to the test that the slope is zero.