1. Birthweight (gms) BPDNProp. 0-95049680.721 951-135018800.225 1351-17509750.120 Total762230.341 BPD (Bronchopulmonary Dysplasia) by birth weight Proportion of BPD decreases with birthweight.

2. Q: Can we give a more precise functional form to the relationship between the probability of having BPD and birthweight? Ans: Yes, if exact birthweights rather than birthweight categories are recorded. By fitting a logistic regression model to the dichotomous response BPD.

3. BPD No BPD Dichotomous Outcomes

4. In linear regression, continuous Y: Topic 18: Logistic regression

5. Dichotomous Outcomes

6. Logistic regression

8. Plot of logistic

9. Maximum likelihood estimation of the parameters

10. Likelihood Ratio Test

11. Logistic regression of BPD on birthweight Logit estimates Number of obs = 223 W = 62.42 (df=1) p value = 0.0000 Log likelihood = -111.86031 ----------------------------------------------------------------------------------------- BPD | Coef. Std. Err. z P>|z| [95% Conf. Interval] ---------+------------------------------------------------------------------------------- birthwt | -.0042291.0006409 -6.599 0.000 -.0054852 -.0029731 _cons | 4.034291.6957847 5.798 0.000 2.670578 5.398004 ------------------------------------------------------------------------------------------

12. Logistic regression of BPD on birthweight Logit estimates Number of obs = 223 W = 62.42 (df=1) p value = 0.0000 Log likelihood = -111.86031 ------------------------------------------------------------------------------ BPD | Odds Ratio Std. Err. z P>|z| [95% Conf. Interval] ---------+-------------------------------------------------------------------- birthwt |.9957798.0006381 -6.599 0.000.9945298.9970313 ------------------------------------------------------------------------------

14. Birthweight (gms) Obsrvd BPD Fitted BPD N 0-950(750)0.7210.70868 951- 1350(1150) 0.2250.31180 1351- 1750(1550) 0.1200.07875 Total223 Observed versus fitted