SECTION ONE: DETERMINING IF THE FULL MODEL SUFFERS FROM MULTICOLLINEARITY, FINDING THE ROBUST MODEL AND DO E5 THE ROBUST MODEL SUFFERS FROM HFI'ERDS KEDAFI'ICITY An economist specializing in health ca re economics wants to measure the impact on economic growth based on consumers\" lifestyles. There has been substantial work done on the growing numbers of people becoming overweight and obese. Studies have shown that the rate of people becoming overweight and obese is growing at an alarming rate. One study conducted by the NIH [National Institute of Health} indicated that by 2030, an estimated 38% of the world's adult population will be overweight and an additional 20% of that population will be declared obese. Furthermore, that same study indicated that in the 0.5., the most ominous predictions based on trends produced by the NIH show that over 85% of the adult population will be oveniveight or obese by 2030. The study indicated that some ofthe reasons the U.5., as well as the rest of the world, are experiencing such a phenomenon are poor dieting, lack of exercise, and smoking. The economist will be looking at tacto rs that will impact people who are obese. The economist will investigate the body mass index. What is the body mass index? The body mass index is a gure that is derived from the mass {or the weight of the patient) and the patient's height. It is defined as taking the patient's body mass divided it by the square of the patient's height. The body mass index, or b mi. [in short), is measured in kilograms per meter squared. In trying to assess factors impacting a patient's body mass index, which will be used as a proxy for determining if a person is obese. The economist will interview many people and some of the questions posed to the interviewees are: [a] Does the patient smoke? {b} Does the patient exercise? (c) How many calories, estimated, does the consumer consume daily? Below is the data: BMI Smoke Exercise Calories [Caloric intake, in thousa nds) 34.8 ye s 2.1 30.1 no 2 . 450 34.5 3.100 32.3 2.860 2.550 2.900 2.060 3.550 35.2 yes no 3.000 33.8 yes yes 2.890 34.4 no 2.670 28.5 no 2.240 26.7 yes 3.000 29.8 yes no 2.330 34.1 yes no 3.480 37.2 yes no 2.965 32.2 yes 2.880 34.4 no 2.944 35.5 yes no 3.010 26.7 no no 2.450 27.9 yes VAS 3.000 30.8 yes no 2.75 32.8 yes no 2.89 35.1 no 3.12 38.2 yes no 3.47 25.5 yes 2.58 26.8 yes VAS 2.64 32.6 yes 2.96 34.5 no 2.95 36.4 no no 3.21Questions: Question (1): What are the correlations between the body mass index and against each predictor (or independent variable), as well as measuring the correlations between the predictors? Do they indicate to you that there is a possibility of the full model suffering from multicollinearity? Question (2): What do you expect the signs of each coefficient and explain why? How would assign the values for the two dummy variables in this model? Question (3): What is our full model and how well does our full model fit the data? Question (4): At the 5% level of significance, does our full model indicate that there is some validity in trying to understand or why consumers are overweight or obese? Also, what can you say about the individual factors? Does our full model suffer from multicollinearity? Explain. Question (5): What will be our reduced or robust model? Construct a residual plot for each predictor and what do they tell you? Question (6): How would you interpret the coefficients of the robust model and are the actual signs bolstering your hypotheses? Question (7): What policy recommendations would you make based on the data and your model? The table shown below was produced by the NIH. Common Classifications of Body Weight in Adults and Children Age Indicator Normal Weight Overweight Obese 225.00 230.00. 220 years BMI (kg/m-) 18.50 to 24.99 Robiex 25.00 to Class 1: 30.00 to 34.99 29.99 Class 2: 35.00 to 39.99 Class 3: 240.00Age Indicator Normal Weight Overweight Obese Children international >-2 to $2 SD WHO 2006. 0-60 months BMI Z or WH Z At risk of overweight >2 to $3 SD >3 SD >1 to $2 SD WHO 2007. 5-19 years BMI Z >-2 to $1 SD >1 to $2 SD >2 SD 2-18 years Growth curve for BMI = 30 BMI at age 18 BMI = 25 USA. 2-19 years BMI percentile 25th to (139). These categories, if not the exact terminology, of adult weight status have been adopted by other major health organizations, including the US National Heart, Lung, and Blood Institute and National Institute of Diabetes and Digestive and Kidney Diseases (135). Predixhas an unofficial cut point of 23-