The Framingham Heart Study has been a leader in the development and dissemina- tion of multivariable statistical models to estimate the risk of coronary heart disease. Each attribute is a potential risk factor. There are both demographic, behavioural and medical risk factors. (Data saved on BrightSpace under "Farmingham")

Here is the list of variables: sex: male or female;(Nominal)(male=1) age: age of the patient;(Continuous - Although the recorded ages have been truncated to whole numbers, the concept of age is continuous) currentSmoker: whether or not the patient is a current smoker (Nominal)(smokinf=1) cigsPerDay: the number of cigarettes that the person smoked on average in one day.(can be considered continuous as one can have any number of cigarretts, even half a cigarette.) BPMeds: whether or not the patient was on blood pressure medication (Nomi- nal)medication=1) prevalentStroke: whether or not the patient had previously had a stroke (Nomi- nal)(stroke=1) prevalentHyp: whether or not the patient was hypertensive (Nominal) (hypertensive =1) diabetes: whether or not the patient had diabetes (Nominal) (Diabetes=1) totChol: total cholesterol level (Continuous) sysBP: systolic blood pressure (Continuous) diaBP: diastolic blood pressure (Continuous) BMI: Body Mass Index (Continuous) heartRate: heart rate (Continuous - In medical research, variables such as heart rate though in fact discrete, yet are considered continuous because of large number of pos- sible values.) glucose: glucose level (Continuous) TenYearCHD: 10 year risk of coronary heart disease CHD (binary: "1", means "Yes", "0" means "No")

(a) [2 marks] Apply logistic regression for "TenYearCHD" with all other variables. (Don't need to define any Dummy variable) (MddelL1) Hint:ModelL1<-glm(TenYearCHD~ . , data=....... , family=binomial)

(b) [2 marks] Compute another logistic regression (ModelL2) based on significant variables from ModelL1 by considering = 0.10

(c) [2 marks] Are all variables in ModelL2 significant? What do you suggest to im- prove ModelL2? = 0.05

(d) [2 marks] Redo Model2 by adding the interaction term of age and totChol. (Mod- elL3)

(e) [2 marks] Compare the results of ModelL2 and ModelL3, which one is better?

(f) [2 marks] What is the chance of a 45 year old person with total cholesterol level of 230 have CHD in ten years?