ISyE6420 FINAL EXAM
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FINAL EXAM
ISyE6420
1. Time to Second Birth. The Medical Birth Registry of Norway was established in 1967 and contains information on all births in Norway since that time.1
The data set (given in a starter odc ile secondbirth0.odc) provides the time between irst and second births for a selection of 16,341 Norwegian women. This time could be possibly inluenced by the age of mother and the fact that the irstborn child died within one year of its birth.
The data set contains the following variables (as columns)
|
mage death time |
age of mother at irst birth (in years) irst child died within one year (0 = no, 1 = yes) time from irst birth to second birth (in days) |
(a) Using WinBUGS establish a regression model with variables mage and death as covariates. What is the 95% CS for the slope β2 corresponding to variable death? Is this variable signiicant?
(b) By analyzing β1 , the coefficient of covariate mage, argue that age of mother is not signiicant factor in inluencing the response time.
(c) Soie is a mother with two children. The children are healthy and growing. Soie was 24 when her irst child was born. What is the predicted time between the births according to your model.
(d) Ingerid lost her irstborn child at its birth when she was 28. She gave a birth to the second child. What is the 95% CS for the predicted time between the births according to your model.
Hint: Be careful: mean times and predicted times are not identical. Since sample size is large, limit your MCMC to 10,000 max after the burn in.
Tasmanian Clouds. The data clouds. csv|dat|xlsx provided by OzDASL were collected in a cloud-seeding experiment in Tasmania between mid-1964 and January 1971. Analysis of these data is discussed in Miller et al. (1979).
Figure 1: T-Rex Cloud Stomping over Tasmania
The rainfalls for target and control areas are given in inches. Variables TE and TW are the east and west target areas, respectively, while CN, CS, and CNW are the corresponding rainfalls in the north, south, and northwest control areas, respectively. S stands for seeded and U for unseeded. Variables C and T are averages of control and target rainfalls. Variable DIFF is the diference T - C.
(a) Provide a comprehensive Bayesian additive two-way ANOVA analysis on the response DIFF to estimate and test the efects of factors Season and Seeded.
(b) Repeat the analysis from (a) after adding the interaction term.
Hint: Consult the Simvastatin example. You will need only three variables form the data: Season, Seeded, and DIFF. Recode the factor levels in Season and Seeded as numbers.
Miller Lumber Company Customer Survey. Kutner et al. (2005)2 analyze a data set from a survey of customers of the Miller Lumber Company. The response is the total number of customers (in a representative 2-week period) coming from a census tract of a metropolitan area within 10 miles from the store.
Figure 2: Miller Lumber Company
The covariates include ive variables concerning the census tracts: number of housing units (in 1,000’s), average income in dollars (in units of $10,000), average housing unit age (in years), distance to nearest competitor (in miles), and distance to store (in miles). Fit and assess a Poisson regression model for the number of customers as predicted by the ive covariates. The data are in odc starter ile lumber0.odc and the variable are customers, hunits, aveinc, aveage, distcomp, and diststore.
(a) Propose a Poisson model with customers as the response variable and hunits, aveinc, aveage, distcomp, and diststore, as covariates. Use noninformative priors on regression coefficients.
(b) If you are to propose a Poisson model with only two covariates which two you will chose? Justify your choice.
(c) Miller Lumber Company is opening a new store in an area for which the covariates are hunits=0.720, aveinc=7, aveage=6, distcomp=4.1, and diststore=8. Find mean response and prediction with 95% for number of customers in a representative 2-week period
2023-12-01