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) c) (3 marks) Referring to the original model, write the null and alternative hypothesis, in terms of the coefficients, to test whether the effect of weight is the same for all doses of ibuprofen for females. What is the distribution of the test statistic under the null hypothesis? d) (3 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 gender on mean pressure, after accounting for weight and dose? Define this effect in general, and then summarize it for each dose of ibuprofen. Summarize your results in a chart like the one below. Dose of ibuprofen 0 Effect of gender on mean pressure 1 2 3 Stat 252 - Homework # 4 Questions - Winer 2024 e) (2 marks) Rewrite the original model indicating that gender has no effect on mean pressure. 4