Suppose that we are interested in identifying factors that influence the probability that a low birth weight infant will experience a germinal matrix hemorrhage - a hemorrhage in the brain. Germinal matrix hemorrhage is a dichotomous random variable that takes the value 1 if this event occurs and 0 if it does not. Use the sample of 100 low birth weight infants born in Boston, Massachusetts, to estimate the probability of a hemorrhage. The data is attached with this question. (Don't forget to check your assumptions!)

1. Perform a hypothesis test for testing that head circumference is a significant predictor.

2. Interpret the odds ratio (and CI) for head circumference.

3. Now perform a logistic regression with both variables and test that gender (1 for male, 0 for female) affects hemorrhage. What do you conclude about the effect of gender?

4. Interpret the odds ratio (and CI) for gender. Explain how the confidence interval confirms the results from #3.

gmh	Headcirc	sex
0	32	1
0	29	1
0	31	0
0	35	0
0	27	0
1	27	1
0	30	1
0	25	0
0	27	0
0	33	0
0	29	0
1	28	0
0	25	0
0	26	0
0	26	1
0	27	1
0	34	0
0	28	0
0	34	0
0	35	0
0	26	1
0	34	0
0	25	1
0	25	1
0	28	0
0	33	1
1	20	0
0	34	1
0	27	0
0	31	0
0	27	1
0	26	0
0	27	0
0	29	1
0	32	0
0	34	0
0	26	1
0	26	0
1	25	1
1	27	0
0	27	1
0	29	1
0	26	1
1	21	0
0	28	0
1	24	0
0	26	1
0	33	1
0	31	0
0	26	0
0	27	0
0	31	1
0	30	1
0	35	1
0	35	0
0	33	1
0	32	0
0	25	0
1	22	0
0	30	0
0	33	1
0	26	0
1	24	1
0	27	1
0	30	0
1	21	0
0	26	0
0	35	0
1	24	0
0	28	0
0	27	1
0	27	1
0	33	0
0	31	0
0	26	1
0	26	1
0	34	1
0	33	0
0	29	0
1	28	0
1	25	0
0	31	0
0	35	0
0	26	0
0	35	1
0	31	1
0	34	1
0	33	1
0	26	1
0	31	1
0	26	1
1	25	1
0	31	0
0	27	1
0	25	1
1	24	0
0	26	1
0	27	1
0	31	0
0	26	0