A Logistic Regression About Longitudinal Low Birth Weight Study

1. Introduction to the data
NAME: Longitudinal Low Birth Weight Study (CLSLOWBWT.DAT)
SIZE: 488 observations, 8 variables.
SOURCE: Hosmer and Lemeshow (2000) Applied Logistic Regression: Second Edition. These data are copyrighted by John Wiley & Sons Inc. and must be acknowledged and used accordingly.

2.Variable Definitions Study on the Longitudinal Low Birth Weight, impact factor: Smoking Status During Pregnancy, Race, Age of Mother, and Weight of Mother at Last Menstrual Period.
Variable Definitions Definition
Smoking Status During Pregnancy 0=no,1=yes
Race 1=white,2=black,3=others
Age of Mother years
Weight of Mother at Last Menstrual Period Pounds
Response variables:
Weight of Mother at Last Menstrual Period (we let Pounds (=2500 normal) =0), LOW, 1=yes, 0=no
Explanatory variables:
Smoking Status During Pregnancy, SMOKE, 1:Yes 0:No
Race, RACE, 1: White 2: Black 3: Others
Age of Mother, AGE
Weight of Mother at Last Menstrual Period, WT

3.Model

Consider a model with all the main effects. To simply the expression, we use {R1, R2} to denote the indicator variables for the first two (of three) races and use S, AG and WT to denote the explanatory variables of smoke, age and weight.
Then we can build the logistic model as follows.
The parameter indicates the log of the odds ratio between indicator or explanatory variable and response variable, when the other independent variables are controlled.
Model Selection
When we construct a logistic model with so many variables, how can we select a fitted one? There are two important things we should take into consideration: simple and adequate. That means the model should consist of the least of variables but also can fitted enough.

#Model 1
Deviance