2. (Six parts; 22 marks in total) Persistent patent ductus arteriosus (PDA) is a medical condition that affects many very low-birth weight infants. Infants with PDA have an increased risk of serious ailment such as severe heart failure. The Apgar score is used to assess the health of an infant one minute after birth. The one-minute Apgar score measures how well the newborn tolerated the birthing process. A score of seven to 10 is normal and indicates the newborn is in good condition. Any score less than seven indicates that the baby needs assistance such as helping the infant breathe. Airway pressure is a measure of respiratory status, usually measured seven days after birth. Some researchers determined that early ibuprofen administration might prevent PDA in preterm neonates. A sample of 130 such infants was randomly divided into 4 groups. 32 were treated with one dose of ibuprofen, 33 with two doses, 33 with three doses, and 32 with a saline solution. The following is the description of variables under study. Variable Gender Dose Weight Age Score Pressure Description of Variables Male OR Female, Dose of ibuprofen (an integer from 0 to 3), Birth weight (in pounds), Gestational age (in weeks), One-minute Apgar score, Air-way pressure (in cm H2O) seven days after birth. Define variables Gender and Dose using the following indicator variables: male 1 for a Male and male = 0 for a Female, D1 = 1 if Dose of ibuprofen is 1 and D1 = 0 otherwise, D2 = 1 if Dose of ibuprofen is 2 and D2 = 0 otherwise, D3 = 1 if Dose of ibuprofen is 3 and D3 = 0 otherwise. Note: No output is needed for questions (a) to (c). Consider the following regression model with pressure as the response: {pressure | weight, GENDER, DOSE} = B + Bweight + male + D1 + D2 + D3 + B(weight male) + B(weight D1) + +B10 (weight maleD1) + B (weight This model will be referred to as the 'original' model. (weight D2) + B(weight D3) male D2) + B (weight x male xD3) Stat 252 - Homework # 4 Questions - Winer 2024 a) (5 marks: 1 for the general effect, 0.5 for each individual one) Referring to the original model, in terms of the regression coefficients, what is the effect of weight on mean pressure, after accounting for gender and dose? Define this effect in general, and then summarize it for each combination of gender and dose of ibuprofen. Summarize your results in a chart like the one below. Dose of ibuprofen 0 Gender Male Male 1 Effect of weight on mean pressure Male 2 Male 3 Female 0 Female 1 Female 2 Female 3 b) (2 marks) Modify the original model to specify that the effect of weight on the mean of pressure is the same for males and females with the same dose of ibuprofen; otherwise, the effect of weight on the mean of pressure is possibly different for males and females without having the same dose of ibuprofen. Just state the constraint(s) needed. You do not have to rewrite the model.