Introductory Biostatistics

as compared to the results from Example 8.7:

SSR¼ 1810 :93 with 3 df

The significance of the additional contribution of the five new factors, consid-
ered together, is judged using theFstatistic:

F¼

ð 1944 : 70 
 1810 : 93 Þ= 5

19 : 19

¼ 0 :80 atð 5 ; 12 Þdf

In other words, all five quadratic and product terms considered together do
not contribute significantly to the prediction/explanation of the second mea-
surement of the systolic pressure of the hepatic artery; the model with three
original factors is adequate.

Stepwise Regression In many applications, our major interest is to identify
important risk factors. In other words, we wish to identify from many available
factors a small subset of factors that relate significantly to the outcome (e.g.,
the disease under investigation). In that identification process, of course, we
wish to avoid a large type I (false positive) error. In a regression analysis, a type
I error corresponds to including a predictor that has no real relationship to
the outcome; such an inclusion can greatly confuse the interpretation of the
regression results. In a standard multiple regression analysis, this goal can be
achieved by using a strategy that adds into or removes from a regression model
one factor at a time according to a certain order of relative importance.
Therefore, the two important steps are as follows:

1. Specify a criterion or criteria for selecting a model.


2. Specify a strategy for applying the criterion or criteria chosen.

Strategies This is concerned with specifying the strategy for selecting vari-
ables. Traditionally, such a strategy is concerned with whether and which par-
ticular variable should be added to a model or whether any variable should be
deleted from a model at a particular stage of the process. As computers became
more accessible and more powerfull, these practices became more popular.

Forward selection procedure

1. Fit a simple linear regression model to each factor, one at a time.


2. Select the most important factor according to certain predetermined
   criterion.


3. Test for the significance of the factor selected in step 2 and determine,
   according to a certain predetermined criterion, whether or not to add
   this factor to the model.

MULTIPLE REGRESSION ANALYSIS 303