For the assignment I will examine whether or not a linear regression model is suitable for estimating the relationship between Human development index (HDI) and its components. Linear Regression is a statistical technique that correlates the change in a variable to other variable/s, the representation of the relationship is called the linear regression model.
Variables are measurements of occurrences of a recurring event taken at regular intervals or measurements of different instances of similar events that can take on different possible values. A dependent variable is a variable whose value depends on the value of other variables in a model. Hence, an independent variable is a variable whose value is not dependent on other variables in a model. The dependent variable here is HDI and this will be regressed against the independent variables which include Life expectancy at birth, Mean years of schooling, expected years of schooling and Gross National Income per capita Hence we can model this into Yi = b0 + b1 xi + b2 xi + b3 xi + b4 xi + where Y is HDI, β0 is a constant, β1 β2 β3 β4 are the coefficients and denotes for random/error term.
R2 is how much your response variable (y) is explained by your explanatory variable (x). The value of R2 ranges between 0 and 1, and the value will determine how much of the independent variable impacts on the dependent variable. The R2 value will show how reliable the regression represents the actual data in forecasting population values of Human Development. R2=1-(∑e2/∑y2) where ∑y2 is Total sum of squares (TSS) and ∑y2 is Residual sum of squares (RSS)
The closer the R2 value is to the 1 value the more reliable the regression line is as an index, and if it is equal to 1 it represents a perfect fit. For my data, I have regressed my dependent variable against all my independent variables and computed the R2 to be 0.9933 (99.33%), which shows a strong correlation between...