Stat 539 Spring 2006: Homework 2 Due Tuesday February 7 The following data were collected from 48 women who were at least 40 years old when they gave birth to their first child. The data concern the gestation period of that pregnancy, and related variables on the child and mother. The columns are, from left to right: 1) ID 2) The child's gestation period, in weeks 3) Sex of the child (0=Male, 1=Female) 4) Birth Weight of child, in grams 5) Number of cigarettes smoked per day (on average) by the mother 6) Height of mother in cm 7) Weight of mother in kilograms at first prenatal visit 8) Weight of mother in kilograms at final prenatal visit 1 36 0 3300 0 160.0 67.3 82.7 2 38 0 3300 60 167.6 52.7 76.0 3 38 0 4100 20 167.6 64.2 79.6 4 38 1 2900 10 163.9 72.7 95.8 5 39 0 2820 0 161.3 50.0 63.3 6 39 0 3040 0 158.8 49.1 61.5 7 39 0 4120 0 160.0 57.7 73.5 8 39 0 4200 0 174.0 68.0 86.8 9 39 1 3100 0 171.5 67.3 85.6 10 39 1 3330 0 160.0 74.0 90.5 11 39 1 3410 0 165.1 55.9 70.7 12 39 1 3420 0 162.6 52.3 66.0 13 40 0 2450 20 167.6 61.4 72.5 14 40 0 2885 0 167.7 60.0 78.6 15 40 0 3235 0 170.2 50.0 65.5 16 40 0 3320 0 165.1 63.6 80.2 17 40 0 3600 0 165.1 53.2 68.7 18 40 0 3720 0 165.0 57.7 74.4 19 40 0 3720 0 172.7 61.4 80.0 20 40 0 3820 0 175.3 60.8 78.1 21 40 0 3840 0 167.0 60.5 83.9 22 40 0 3880 0 156.2 57.3 73.7 23 40 0 3960 0 157.5 52.7 68.2 24 40 0 4465 0 157.5 51.4 66.4 25 40 1 2980 0 160.0 47.7 55.2 26 40 1 3040 0 162.0 49.0 60.3 27 40 1 3060 20 157.5 61.0 75.0 28 40 1 3100 0 170.2 55.5 64.6 29 40 1 3120 0 160.3 56.8 75.4 30 40 1 3205 0 172.7 58.2 75.5 31 40 1 3220 0 170.0 64.6 86.0 32 40 1 4100 40 167.0 67.0 85.0 33 41 0 3100 0 168.9 61.4 69.2 34 41 0 3720 0 170.2 57.7 67.7 35 41 0 3720 20 170.2 57.7 80.5 36 41 0 3900 0 167.0 68.0 85.4 37 41 0 3990 0 165.1 52.3 71.2 38 41 0 4050 0 167.6 61.0 78.5 39 41 0 4080 0 162.6 59.1 83.1 40 41 0 4100 0 165.1 60.5 86.5 41 41 0 4460 20 165.1 56.8 88.0 42 41 0 5220 0 157.5 56.8 68.2 43 41 1 3300 40 162.6 74.1 89.7 44 41 1 3400 0 172.7 71.4 87.8 45 41 1 4000 0 165.1 90.0 100.8 46 41 1 4030 0 166.0 63.0 95.3 47 43 1 3220 0 166.4 60.9 72.0 48 43 1 4270 0 162.6 54.5 70.3 YOU SHOULD BE ABLE TO CUT THE DATA OUT OF THE HOMEWORK ASSIGNMENT, PUT IT INTO A FILE, AND THEN DIRECTLY IMPORT IT INTO STATA. 1) Plot the birth weight (BW) against the length of gestation (LG). Describe the relationship. Looking at the plot, should the sample correlation between BW and LG be positive, negative, or nearly zero? 2) Compute the Pearson and Spearman correlations between BW and LG. Comment. Test the hypothesis that the population correlation between BW and LG is zero. Comment on the tests. 3) Provide an equation for the least squares line for predicting BW from LG. Test the hypothesis that the slope of the population regression line is zero. [We can think of this as a test that LG is important for explaining the observed variation in BW]. Superimpose the LS line on the data plot and comment on whether the simple linear regression model appears to adequately summarize the relationship between BW and LG. 4) What percentage (or proportion) of the variability in BW is explained by the linear relationship between BW and LG? 5) Make appropriate residual plots to check for inadequacies with the model. Comment on the plots. 6) Superimpose on the data plot a 95% confidence band for the population mean BW, as a function of LG. Give an estimate, with a 95% CI, for the mean BW of all children with gestation lengths of 39 weeks. 7) Superimpose on the data plot a 95% confidence band for the predicted BW of a single child, as a function of their gestation length. Give an estimate, with a 95% CI, for the BW of a single child with a gestation length of 40 weeks. Provide a short summary of your analysis.