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FOREIGN TRADE UNIVERSITY FACULTY OF INTERNATIONAL ECONOMICS - - ECONOMETRICS REPORT Class: KTEE218.1 GROUP 11 Name Đàm Thanh Bình Thái Mỹ Hạnh Phạm Khắc Dương Nguyễn Thị Hằng Đoàn Thanh Tùng Students’ ID 1814450016 1814450038 1814450025 1814450106 1814450072 Lecturer: MSc Quynh Thuy Nguyen Hanoi, 26th September 2019 FOREIGN TRADE UNIVERSITY FACULTY OF INTERNATIONAL ECONOMICS - - ECONOMETRICS REPORT Class: KTEE218.1 GROUP 11 Name Đàm Thanh Bình Thái Mỹ Hạnh Phạm Khắc Dương Nguyễn Thị Hằng Đoàn Thanh Tùng Students’ ID 1814450016 1814450038 1814450025 1814450106 1814450072 Lecturer: MSc Quynh Thuy Nguyen Hanoi, 26th September 2019 TABLE OF CONTENTS ABSTRACT INTRODUCTION Research objective Rationale of study Object and scope of study .7 Structure of scope SECTION I: OVERVIEW OF THE TOPIC General definitions and economic theories 1.1 General definitions .8 1.2 Economic theories related to the research Literature view 12 2.1 Related published researches 12 2.2 Research hypotheses 12 2.3 BMR 13 2.4 Calorie Expenditure of Exercise 13 2.5 Calories expenditure of Common Foods 14 SECTION II: MODEL SPECIFICATION 16 Methodology .16 1.1 Method you use to derive the model .16 Theoretical model specification 17 2.1 Specification of the model 17 2.3 Describe the data 21 SECTION III: ESTIMATED MODEL and statistical inferences.24 Estimated model: 24 1.1Estimation result: 24 1.3 Explain the meanings of estimated coefficients .25 1.4 The coefficient of determination 26 Hypothesis Testing .26 2.1 Testing the significance of an individual regression coefficient 26 2.2 The confidence interval approach 27 2.3 The T-distribution approach 27 The P-value approach 28 Testing the overall significance 28 4.1 The F-test of significance approach 28 4.2 The P-value approach 29 Conclusion: 30 ABSTRACT In the last a few decades, BMI index has been becoming one of the growing concerns all over the world, especially to the health conscious as well as health public researchers BMI is a measurement of a person's leanness or corpulence based on their height and weight, and is intended to quantify tissue mass It is widely used as a general indicator of whether a person has a healthy body weight for their height Specifically, the value obtained from the calculation of BMI is used to categorize whether a person is underweight, normal weight, overweight, or obese depending on what range the value falls between This is the World Health Organization's (WHO) recommended body weight based on BMI values for adults It is used for both men and women, age 18 or older This provides the answer to our question why BMI is one of the most reliable index reflecting the recent health situation BMI plays a crucial role in analyzing the status of well-being, measuring the risk of hazardous diseases resulting from overweight like obesity, cardiovascular diseases, high blood pressure or from underweight like malnutrition, vitamin deficiencies, etc However, in reality, to achieve an ideal BMI index, we have to pay more attention to a number of factors directly affecting it, namely nutritious intake in each portion, daily eating habit, average workout hours, sex, age, etc So in this study we will gain deeper insight into the primary factors affecting BMI index and shed light on the optimal approaches to reach standardized BMI, improve the general public well-being We would like to give our appreciation to your useful lectures of this course and instruction to fulfill this report Throughout process of making this report, our team did try our best to gather data, conduct researches and utilize available materials to analyze the result However, mistakes are inevitable Therefore, please let us know if there are some ones that must be fixed to achieve more accurate result INTRODUCTION Research objective The main purposes of this study is to provide thorough understanding of BMI index, and analyze fundamental elements contributing to fluctuation of BMI ranging from nutritious regime, eating habit to workout routine To be more specific, it also supplies data about every single substance in daily diets, frequency and the typical amount of calorie burned in exercising, the number and rational distribution of daily meals This study also enables people to foresee the positive or negative trend of BMI in the future, gives recommendations for them to propose long-term plan for the sustainable development of public health Rationale of study There are a few motivations prompting us to this research: - The lifestyle in the modern societies pose various threats to our health, particularly for youngster The consumption of junk food has been considerably increasing year by year Besides, the rate of children as well as adults becoming obese is so alarming, which has been linked to a lack of physical exercises On the contrary, in the most remote areas, many families have to struggle to feed themselves so malnutrition is a very common tendency The underweight and overweight is associated with a plenty of dangerous diseases for health: - Being overweight increases the risk of a number of serious diseases and health conditions Below is a list of said risks, according to the Centers for Disease Control and Prevention (CDC): High blood pressure Higher levels of LDL cholesterol, which is widely considered "bad cholesterol," lower levels of HDL cholesterol, considered to be good cholesterol in moderation, and high levels of triglycerides Type II diabetes Coronary heart disease Stroke Gallbladder disease Osteoarthritis, a type of joint disease caused by breakdown of joint cartilage Sleep apnea and breathing problems Certain cancers (endometrial, breast, colon, kidney, gallbladder, liver) Low quality of life Mental illnesses such as clinical depression, anxiety, and others Body pains and difficulty with certain physical functions Generally, an increased risk of mortality compared to those with a healthy BMI - Being underweight has its own associated risks, listed below: Malnutrition, vitamin deficiencies, anemia (lowered ability to carry blood vessels) Osteoporosis, a disease that causes bone weakness, increasing the risk of breaking a bone A decrease in immune function Growth and development issues, particularly in children and teenagers Possible reproductive issues for women due to hormonal imbalances that can disrupt the menstrual cycle Underweight women also have a higher chance of miscarriage in the first trimester Potential complications as a result of surgery Generally, an increased risk of mortality compared to those with a healthy BMI Therefore, more attention should be placed on and more investigation should be conducted on a regular basis to get deep understanding of primary elements having influences on BMI index From those data and results of this paper, a specific plan can be set up to regulate the amount of nutrition intake, time for exercise and outdoors activities, which can help control weight, height and lead a healthier lifestyle Object and scope of study In this study, we will concentrate on young people at ages ranging from 18 to 22 both female and male These are the most adequate and ideal ages to get variables directly affecting BMI as well as the most accurate consequences A range of research methodologies was used to investigate current practice and to capture data about the scope and fundamental contributors in BMI index Using a software Stata used for statistical analysis; descriptive statistics and summary methods to analyze the information from the survey Structure of scope The report has been structured to reflect the different research goals for the project This report is organized as follows: Sections I will overview definitions Section II will explore methodology of study: Factors that affect BMI index and analyze dependent and independent variables in the OLS model Section III will explain result we get from the Stata and test initial hypotheses Finally, give some recommendations and effective way to positively alter daily diets and workout routine, improving the state of well-being and reaching an ideal BMI SECTION I: OVERVIEW OF THE TOPIC General definitions and economic theories 1.1 General definitions 1.1.1 Definition and formula of BMI a Definition of BMI - The BMI formula uses your weight (in kg or pounds) and your height (in meters or inches) to form a simple calculation that provides a measure of your body fat The formula for BMI was devised in the 1830s by Belgian mathematician Adolphe Quetelet and is universally expressed in kg/m2 - Body mass index is a measure of body fat and is commonly used within the health industry to determine whether your weight is healthy BMI applies to both adult men and women and is the calculation of body weight in relation to height This article delves into the BMI formula and demonstrates how you can use it to calculate your own BMI b Formula of BMI The first formula we've listed is the metric BMI formula, using kilograms and meters The second one is the imperial BMI formula, which uses units of pounds and inches Metric BMI Formula: BMI = Imperial BMI Formula: BMI = 703 1.1.2 BMI categorization The BMI statistical categories below are based on BMI scores and apply to adults of age 20 years and upwards The World Health Organisation (WHO) regards a healthy adult BMI to be between 18.5 and 25 BMI BMI Category Less than 15 Very severely underweight Between 15 and 16 Severely underweight Between 16 and 18.5 Underweight Between 18.5 and 25 Normal (healthy weight) Between 25 and 30 Overweight Between 30 and 35 Moderately obese Between 35 and 40 Severely obese Over 40 Very severely obese Table 1.1.3 Current problems around BMI It is a common argument that the results the BMI formula provides are too general and not consider the gender, build, age or ethnicity of a person For example, professional athletes are often considered overweight or obese when using BMI measurements due to their muscle content, which weighs more than fat Similarly, as people age their bone density decreases So, although they may seem to have a weight within the normal BMI range, their measurement actually needs to be scaled-down to reflect this In a study published in the Journal of Economics in 2008, John Cawley, professor at Cornell University, was able to demonstrate that, relative to percent body fat, BMI appears to misclassify substantial fractions of individuals as obese or non-obese 1.2 Economic theories related to the research a The three-variable model Population regression function: E (YX2i, X3i) = β1 + β2X2i + β3X3i Stochastic form Yi = β1 + β2X2i + β3X3i + ui Where: Y: dependent variable X2, X3: independent variables β 1: intercept term β 2, β 3: partial regression coefficients ui: disturbance The meaning of partial regression coefficients - β measures the change in the conditional mean value of Y, E(YX2i, X3i), per unit change in X2, holding the value of X3 constant β2= - If we increase X2 by one unit and keep other variables constant, the expected value of Y increase by β2 units - Similarly, β3 measures the change in the mean value of Y, E(Y), per unit change in X3, holding the value of X2 constant β3= b Coefficient of determination R2 and the adjusted R2 The multiple coefficient of determination R2 The extent to which all the independent variables jointly (i.e., the model) explain the variation in the dependent variable R2 = = - = Problems with R2 - Analyze: With the assistance of Stata 14 software and the following step to analyze data + Step 1: Data Validation The purpose of data validation is to find out, as far as possible, whether the data collection was done as per the pre-set standards and without any bias It is a four-step process, which includes… Fraud, to infer whether each respondent was actually interviewed or not Screening, to make sure that respondents were chosen as per the research criteria Procedure, to check whether the data collection procedure was duly followed Completeness, to ensure that the interviewer asked the respondent all the questions, rather than just a few required ones To this, we would need to pick a random sample of completed surveys and validate the collected data For example, we sort out people into many ranges of age, many kinds of activities to specify to suitable burned calories After that we can reach out to them through email or phone and check their responses to a certain set of questions + Step 2: Data Editing Typically, large data sets include errors To make sure that there are no such errors, we conduct basic data checks, check for outliers, and edit the raw research data to identify and clear out any data points that may hamper the accuracy of the results + Step 3: Data Coding This is one of the most important steps in data preparation It refers to grouping and assigning values to responses from the survey.For example, some of the acronyms we use to assign values such as: Height-hght, Weight- wght, Theoretical model specification 2.1 Specification of the model According to previous published researches, our group has established a function to analyze the relationships between related variables and the BMI index as well as the effects of those variables toward the dependent variable: BMI = f(Ag, Gdr, Eht, Avgcalo, Rarcnca) Where: BMI: Body Mass Index Ag: Age Gdr: Gender Eht: Eating habit Avgcalo: Average calories burned per day Rarcnca: Rate of absorbed calories over necessary calories Thus, according to the economic theories, in order to analyze the factors influencing the BMI index, our group has discussed and decided to choose the regression analysis models 2.1.1 POPULATION REGRESSION MODEL (PRM) Where: β0: the intercept term of the model β1: the regression coefficient of “age” β2: the regression coefficient of “gender” β3: the regression coefficient of “eating habit” β4: the regression coefficient of “average calories burned per day” : the regression coefficient of “rate of absorbed calories over necessary calories” : the disturbance term of the model, represents other factors that affect UEM but not mentioned in the model + Explain the variables, proxies to measure and their units Name Y Acronym Method Body Mass BMI Index Unit weight (kg) / height2 (m) kg/m X1 Age Ag Do survey Year X2 Gender Gdr Do survey With Female - and Male - free X3 Eating habit Eht Do survey and summary base on the free amount of water per day, level of healthy eating time, numerous of means per day Interval of Eht is [1,4], the higher Eht is, the healthier eating habit they have X4 Average Avgcalo calories burned per day Do survey about kind of activities, amount of time for it and frequency per day Then use Table to calculate Calo X5 Rate of Rarcnca absorbed calories over necessary calories absorbed calories/ necessary calories Calo Height hght Do survey m Weight wgth Do survey kg absorbed calories arc Basal BMR Metabolic Rate Do survey and calculate by Table calo Use the following equations to find calo your BMR by hand Men: (0.1 × weight) + (6.25 × height*100) - (5 × age) +5 Women: (0.1 × weight) + (6.25 × height*100) - (5 × age) -161 Necessary Nca calories An average woman needs to eat about calo 2000 calories per day to maintain, and 1500 calories to lose one pound of weight per week An average man needs 2500 calories to maintain, and 2000 to lose one pound of weight per week Table Dependent variables : Y = BMI Independent variables : X1 = Ag which stands for: Age X2 = Gdr which stands for: Gender X3 = Eht which stands for: Eating habit X4 = Avgcalo which stands for: Average calories burned per day X5 = Rarcnca calories which stands for: Rate of absorbed calories over necessary According to our aforementioned research, many factors can affect your BMI and lead to overweight or obesity Some of these factors may make it hard for you to lose weight or avoid regaining weight that you’ve lost - Age: Many people gain weight as they age Adults who have a normal BMI often start to gain weight in young adulthood and continue to gain weight until they are ages 60 to 65 In addition, children who have obesity are more likely to have obesity as adults - Gender: A person’s gender may also affect where the body stores fat Women tend to build up fat in their hips and buttocks Men usually build up fat in their abdomen or belly Extra fat, particularly if it is around the abdomen, may put people at risk of health problems even if they have a normal weight - Eating and physical activity habits: Your eating and physical activity habits may raise your chances of becoming overweight and having obesity if you · eat and drink a lot of foods and beverages that are high in calories, sugar, and fat · drink a lot of beverages that are high in added sugars · spend a lot of time sitting or lying down and have limited physical activity 2.1.2 Sample Regression Model (SRM) Sample Regression Function: Where: : the estimator of β1 : the estimator of β2 : the estimator of β3 : the estimator of β4 : the estimator of β5 : the estimator of − the residuals term 2.3 Describe the data + Specify the sources of data + Descriptive statistics and interpretation for each variable Using STATA 14 for model description with des command, we have collected this result: We continue use “sum” command for data description “sum” has shown us number of observation (Obs), mean, standard deviation (std dev.), and also maximum value (Max), minimum value (Min) of variables + Correlation matrix between variables Using “corr” command to test the correlation of variables Explaining variables relationship: - Correlative coefficient between BMI and Ag is 0.1827 => positive relationship - Correlative coefficient between BMI and Gdr is 0.4213 => positive relationship - Correlative coefficient between BMI and Eht is 0.2142 => positive relationship - Correlative coefficient between BMI and Avgcalo is 0.3499 => positive relationship - Correlative coefficient between BMI and Rarcnca is -0.0972 => negative relationship - According to the figures from the table, there are no coefficient greater than 0.8 => Therefore, the multicollinearity didn’t occur in our model SECTION III: ESTIMATED MODEL AND STATISTICAL INFERENCES Estimated model: 1.1Estimation result: - Run regression model diagnosis: Using “reg” command to run regression model in STATA, we have: Y = BMI X1 = Ag, X2 = Gdr, X3 = Eht, X4 = Avgcalo, X5 = Rarcnca + 1.2 Sample regression model (SRM) SAMPLE REGRESSION FUNCTION (SRF) The model studies about dependence between level of BMI and Age (Ag), Height (Hght), Gender (Gdr), Eating habit (Eht), Average calories burned per day (Avgcalo), rate of absorbed calories over necessary calories (Rarcnca) According to this result, = 0.3488639, 0.0033525, = 7.416015, = -3.089573 Therefore, we have SRM is: = 2.442524, = 0.7689835, = 1.3 Explain the meanings of estimated coefficients Regression Coefficient Value Meanings 0.3488639 > Ceteris paribus, when Age increase by unit, BMI increase by 0.3488639 unit The increase in BMI goes hand in hand with the increase of age That means normally the older you are, the higher BMI is 2.442524 > Ceteris paribus, when Gdr increase by unit, BMI increase by 2.442524 unit The BMI varies from sex to sex In general, BMI of men is higher than that of women In fact, as the result of the survey we conducted, this element has minor effect on our dependent variable 0.7689835 > Ceteris paribus, when Eht increase by unit, BMI increase by 0.7689835 unit.The habit of eating clean exerts strong influences on BMI Should you digest more food rich in high-quality protein, vital nutrition and mineral and distribute daily meals appropriately, your BMI can definitely reach the standardized level 0.0033525 > Ceteris paribus, when avegcalo increase by unit, BMI increase by 0.0033525 unit The amount of calorie burned every single day via exercising, fitness regime determines largely the variation of BMI Although β4 is small, it’s interval is about [1500,3000] As a result, by using the linear regression function learned from this course, we can draw a conclusion that this factor has the most powerful effect on BMI 7.416015 > Ceteris paribus, when rarcnca increase by unit, BMI increase by 7.416015 unit Table 1.4 The coefficient of determination When run “reg” command we also have this table: Look at this table, R2 = 0.3474 => Independent variables can explain 34.74% of dependent variable’s fluctuation Hypothesis Testing 2.1 Testing the significance of an individual regression coefficient State the Hypotheses: 2.2 The confidence interval approach According to the results from Stata using the Ordinary Least Squares regression analysis method, we obtained the confidence interval for the regression coefficients of each variable at a significance level of 5% as below: For the variable Eht, the value of belongs to the confidence interval [−0.0570135, 1.594981], which means we don’t have enough evidence to reject H0 Therefore, the regression coefficient of Eht isn’t statistically significant at a significance level of 5% For the remain variables, which are Ag, Gdr, Avgcalo, Rarcnca and constant, the value of doesn’t belong to the confidence interval of each variable Therefore, the regression coefficients of these variables are statistically significant at a significance level of 5% 2.3 The T-distribution approach Specify the critical T-value tc = = = 1,984 n = 150: the number of observations or sample size k = 6: the number of variables α = 0.05: the significant level, for two-tailed test, = 0.025 According to the test statistic = of each variable at the significance level of 5%, we have: - For the Ag: || = 2.66 > 1.984, we can reject H0; therefore, the regression coefficient of Ag is statistically significant at a significance level of 5% - For the Gdr: |ts| = 5.73 > 1.984, we can reject H0; therefore, the regression coefficient of Gdr is statistically significant at a significance level of 5% - For the Eht: |ts| = 1.84 < 1.984, we don’t have evidence to reject H0; therefore, the regression coefficient of Eht isn’t statistically significant at a significance level of 5% - For the Avgcalo : |ts| = 3.67 > 1.984, we can reject H0; therefore, the regression coefficient of Avgcalo is statistically significant at a significance level of 5% - For the Rarcnca: |ts| = 3.83 > 1.984, we can reject H0; therefore, the regression coefficient of Rarcnca is statistically significant at a significance level of 5% - For the variable constant: |ts| = 0.79 < 1.984, we don’t have evidence to reject H0; therefore, the regression coefficient of constant isn’t statistically significant at a significance level of 5% The P-value approach The P-value (probability value)is the lowest significance level at which the Null Hypothesis H0 can be reject We have: Level of α significant of model (α) equals to 5% This hypothesis is two-tail test => Therefore the factor is statistically significant if it has P-value smaller than 5% or 0.05 - For the variable Ag, its P-value is approximately equal to 0.002, which is smaller than 0.05 - For the variables Eht, its P-value is approximately equal to 0.068, which is more than 0.05 - For the variables constant, its P-value are approximately equal to 0.432, which is more than 0.05 - For the variable Gdr, Avgcalo, Rarcnca, their P-value is approximately equal to 0.000, which are smaller than 0.05 In conclusion, by approaching three methods to test the significance of individual regression coefficients, we can conclude that the regression coefficients of Ag, Gdr, Avgcalo, Rarcnca are statistically significant Testing the overall significance State the Hypotheses: 4.1 The F-test of significance approach The F-test of overall significance indicates whether your linear regression model provides a better fit to the data than a model that contains no explanatory variables Specify the critical F-value Fc== = 2.3 n: the number of observations or sample size, n = 150 k: the number of variables, k = Calculate the test statistic = = = 15.33 >2.3 => From the result of , we can reject null hypotheses Therefore, the overall model is statistically significant at the level of significance of 5% 4.2 The P-value approach According to the result obtained from the OLS regression analysis by Stata, we have the P-value that P (Fs > Fc) = 0.000 < 0.05 As a result, we can reject H0 and conclude that the overall model is statistically significance at a significance level of 5% In conclusion, by approaching two methods to test the significance of the whole model, we can conclude that the overall model is statistically fitted at a significance level of 5% CONCLUSION: By analyzing data, running the model and conducting tests, overcoming the phenomena of the model, we can summarize the following key issues: Sample Regression Model: = -3.09 – 0.35.Ag + 2.44.Gdr – 0.77.Eth + 0.0034.Avgcalo + 7.42.Rarcnca Or Thus, the above steps helped to answer the question raised in the Research Hypothesis: Are the factors such as Age, Gender, Eating habit, Average calories burned per day and Rate of absorbed calories over necessary calories influenced more or less on the BMI of 18-22 years old people? And how does it affect? The variable “Avgcalo” has the strongest relationship and the variable “Gdr” has the weakest relationship with the dependent variable “BMI” This shows that people who burn more calories through activities like playing sports, doing workout or hand-working seem to have a better BMI than people with less working out Possibly, they are so busy with the office work with hour and hour of sitting in front of the screen and not have time for doing outside exercise In contrast, people’s gender or genetic factors has low effect on their BMI As a student studying in Foreign Trade University, we should know how important the BMI is in our body development We not only need to have smart brains but we also need a good BMI means a healthy and balance bodies After this research, we have some recommendations for you, me, our families, friends and relatives to have good BMI: - We all know that exercise is an essential part in our daily lives, but we may not know why or what exercise can for us There is no doubt that having a regular exercising routine brings us a healthy and balanced lifestyle It’s important to remember that we have evolved from nomadic ancestors who spent all their time moving around in search of food and shelter, travelling large distances on a daily basis Our bodies are designed and have evolved to be regularly active There are many benefits of regular exercise and maintaining fitness and these include: + First of all, exercise increases your energy levels Exercise improves both the strength and the efficiency of your cardiovascular system to get the oxygen and nutrients to your muscles When your cardiovascular system works better everything seems easier and you have more energy for the fun stuff in life + Secondly, regular exercise improves muscle strength Staying active keeps muscles strong and joints, tendons and ligaments flexible, allowing you to move more easily and avoid injury Strong muscles and ligaments reduce your risk of joint and lower back pain by keeping joints in proper alignment They also improve coordination and balance + Thirdly, exercise can help you to maintain a healthy weight The more you exercise, the more calories you burn In addition, the more muscle you develop, the higher your metabolic rate becomes, so you burn more calories even when you’re not exercising The result? You may lose weight and look better physically which will boost your self-esteem + Last but not least, Exercise improves a good brain function Exercise increases blood flow and oxygen levels in the brain It also encourages the release of the brain chemicals (hormones) that are responsible for the production of cells in the hippocampus, the part of the brain that controls memory and learning This, in turn, boosts concentration levels and cognitive ability, and helps reduce the risk of cognitive degenerative diseases such as Alzheimer’s Therefore, each of us should build our own consistent and feasible exercise routine to control an ideal BMI Due to the length of the essay and the limited time it takes, our team only came up with a few solutions as above Over all, we hopes to present more detailed solutions for improving BMI and introduce more knowledge about the understanding of having a good exercising routine significantly reflect our health in a remarkable way - The end - ... reaching an ideal BMI SECTION I: OVERVIEW OF THE TOPIC General definitions and economic theories 1.1 General definitions 1.1.1 Definition and formula of BMI a Definition of BMI - The BMI formula uses... and women and is the calculation of body weight in relation to height This article delves into the BMI formula and demonstrates how you can use it to calculate your own BMI b Formula of BMI The. .. is the metric BMI formula, using kilograms and meters The second one is the imperial BMI formula, which uses units of pounds and inches Metric BMI Formula: BMI = Imperial BMI Formula: BMI
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