Life-Expectancy-Regression

Although there have been lot of studies undertaken in the past on factors affecting life expectancy considering demographic variables, income composition and mortality rates. It was found that affect of immunization and human development index was not taken into account in the past. Also, some of the past research was done considering multiple linear regression based on data set of one year for all the countries. Hence, this gives motivation to resolve both the factors stated previously by formulating a regression model based on mixed effects model and multiple linear regression while considering data from a period of 2000 to 2015 for all the countries. Important immunization like Hepatitis B, Polio and Diphtheria will also be considered. In a nutshell, this study will focus on immunization factors, mortality factors, economic factors, social factors and other health related factors as well. Since the observations this dataset are based on different countries, it will be easier for a country to determine the predicting factor which is contributing to lower value of life expectancy. This will help in suggesting a country which area should be given importance in order to efficiently improve the life expectancy of its population.

Dataset

The dataset used is the Life Expectancy (WHO) (https://www.kaggle.com/kumarajarshi/life-expectancy-who) from Kaggle. This dataset has the following features:

• Country: Name of the country
• Year: Year in numeric form (Ex: 2015)
• Status: Developed or Developing status
• Life expectancy: Life Expectancy in age (which we will predict - Target)
• Adult Mortality: Adult Mortality Rates of both sexes (probability of dying between 15 and 60 years per 1000 population)
• Infant deaths: Number of Infant Deaths per 1000 population
• Alcohol: Alcohol, recorded per capita (15+) consumption (in litres of pure alcohol)
• Percentage Expenditure: Expenditure on health as a percentage of Gross Domestic Product per capita(%)
• Hepatitis B: (HepB) immunization coverage among 1-year-olds (%)
• Measles: number of reported cases per 1000 population
• BMI: Average Body Mass Index of entire population
• under-five deaths: Number of under-five deaths per 1000 population
• Polio: (Pol3) immunization coverage among 1-year-olds (%)
• Total expenditure: General government expenditure on health as a percentage of total government expenditure (%)
• Diphtheria: Diphtheria tetanus toxoid and pertussis (DTP3) immunization coverage among 1-year-olds (%)
• HIV/AIDS: Deaths per 1 000 live births HIV/AIDS (0-4 years)
• GDP: Gross Domestic Product per capita (in USD)
• Population: Population of the country
• thinness 1-19 years: Prevalence of thinness among children and adolescents for Age 10 to 19 (%)
• thinness 5-9 years: Prevalence of thinness among children for Age 5 to 9(%)
• Income composition: Human Development Index in terms of income composition of resources (index ranging from 0 to 1)
• Schooling: Number of years of Schooling(years)

Models used:

1. Linear Regression:

Linear regression a model that assumes a linear relationship between the input variables (x) and the single output variable (y). It is the process of finding a line that best fits the data points available on the plot, so that we can use it to predict output values for inputs that are not present in the data set we have, with the belief that those outputs would fall on the line. A linear regression line has an equation of the form Y = a + bX, where X is the explanatory variable and Y is the dependent variable. The slope of the line is b, and a is the intercept (the value of y when x = 0).

2. Ridge Regression:

Ridge regression is a method of estimating the coefficients of multiple-regression models in scenarios where independent variables are highly correlated. It has been used in many fields including econometrics, chemistry, and engineering. The cost function for ridge regression: Min(||Y – X(theta)||^2 + λ||theta||^2) Lambda is the penalty term. λ given here is denoted by an alpha parameter in the ridge function. So, by changing the values of alpha, we are controlling the penalty term. The higher the values of alpha, the bigger is the penalty and therefore the magnitude of coefficients is reduced.

3. Bayesian Linear Regression:

In statistics, Bayesian linear regression is an approach to linear regression in which the statistical analysis is undertaken within the context of Bayesian inference. Bayesian linear regression allows a useful mechanism to deal with insufficient data, or poor distributed data. It allows you to put a prior on the coefficients and on the noise so that in the absence of data, the priors can take over.

4. SVM:

Support Vector Machine(SVM) is a supervised machine learning algorithm used for both classification and regression. The objective of SVM algorithm is to find a hyperplane in an N-dimensional space that distinctly classifies the data points. The dimension of the hyperplane depends upon the number of features.