The following dataset is from a study of the effects of second hand smoking in Baltimore, MD, and Washington, DC. For the 25 children involved in this study the outcome variable is the presence of respiratory symptoms when they were 8, 9, 10, and 11 years old. The predictor variables include age, city, and a measure of second hand smoking in the home (coded 0, 1, and 2, corresponding to the amount of exposure to second hand smoking). The SAS data step follows:
data one;
input id city$ @@;
do i=1 to 4;
input age shsmoke resp @@;
output;
end;
datalines;
1 Baltimore 8 0 1 9 0 1 10 0 1 11 0 0
2 Baltimore 8 2 1 9 2 1 10 2 1 11 1 0
3 Baltimore 8 2 1 9 2 0 10 1 0 11 0 0
4 Washington 8 0 0 9 1 1 10 1 1 11 0 0
5 Baltimore 8 0 0 9 1 0 10 1 0 11 1 0
6 Washington 8 0 1 9 0 0 10 0 0 11 0 1
7 Baltimore 8 1 1 9 1 1 10 0 1 11 0 0
8 Washington 8 1 0 9 1 0 10 1 0 11 2 0
9 Washington 8 2 1 9 2 0 10 1 1 11 1 0
10 Baltimore 8 0 0 9 0 0 10 0 0 11 1 0
11 Baltimore 8 1 1 9 0 0 10 0 0 11 0 1
12 Washington 8 0 0 9 0 0 10 0 0 11 0 0
13 Baltimore 8 2 1 9 2 1 10 1 0 11 0 1
14 Washington 8 0 1 9 0 1 10 0 0 11 0 0
15 Baltimore 8 2 0 9 0 0 10 0 0 11 2 1
16 Washington 8 1 0 9 1 0 10 0 0 11 1 0
17 Washington 8 0 0 9 0 1 10 0 1 11 1 1
18 Baltimore 8 1 1 9 2 1 10 0 0 11 1 0
19 Baltimore 8 2 1 9 1 0 10 0 1 11 0 0
20 Washington 8 0 0 9 0 1 10 0 1 11 0 0
21 Baltimore 8 1 0 9 1 0 10 1 0 11 2 1
22 Washington 8 0 1 9 0 1 10 0 0 11 0 0
23 Baltimore 8 1 1 9 1 0 10 0 1 11 0 0
24 Washington 8 1 0 9 1 1 10 1 1 11 2 1
25 Washington 8 0 1 9 0 0 10 0 0 11 0 0;
Use a statistical model to evaluate the associations between the three predictor variables and the presence of respiratory symptoms. Interpret the estimated odds ratios and the corresponding 95% confidence intervals for these associations.