Multiple regression 

Multiple regression is a method used to examine the relationship between one dependent variable Y and 

one or more independent variables Xi.  The regression parameters or coefficients bi in the regression 

equation 

b

=

Y

b

+

X

b

+

X

b

+

X

b

+

. 

. 

.

+

X

0

1

1

2

2

3

3

k

k

are estimated using the method of least squares.  In this method, the sum of squared residuals between 

the regression plane and the observed values of the dependent variable are minimized.  The regression 

equation represents a (hyper)plane in a k+1 dimensional space in which k is the number of independent 

variables X1, X2, X3, ... Xk, plus one dimension for the dependent variable Y. 

The following need to be entered in the Multiple regression dialog box:  

In this dialog box you first identify the dependent variable. For the independent variables you enter the 

names of variables that you expect to influence the dependent variable.  Again, you can click the 

 button 

to obtain a list of variables.  In this list you can select a variable by clicking the variable's name. 

Options 

Method: select the way independent variables are entered into the model.  

  Enter: enter all variables in the model in one single step, without checking 

  Forward: enter significant variables sequentially 

  Backward: first enter all variables into the model and next remove the non significant variables 

sequentially 

  Stepwise: enter significant variables sequentially; after entering a variable in the model, check and 

possibly remove variables that became non significant. 

Enter variable if P< 

A variable is entered into the model if its associated significance level is less than this P value. 

Remove variable if P> 

A variable is removed from the model if its associated significance level is greater than this P value.  

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