Factor Analysis

The Factor analysis summarizes many variables by few factors and helps to understand the structure of a correlation matrix. It accounts for multi-collinearity among a large number of interrelated independent quantitative variables by grouping the variables into a few factors and reduces correlations.  
In our case, we have countries as the units of observations. We have data on different aspects of these countries like population, density, percentage of people living in cities, religion, life expectancy, literacy rates, daily calorie intake, number of people affected from aids, fertility, death rates etc. Now, for the purpose of this lab we are taking LIFEXPF (Female Life Expectancy) as a dependent variable and running regression on that. However, before doing that we are running a factor analysis on other independent variables and grouping them into few factors and use these factor scores as independent variables for regression. This will help in reducing correlations among independent variables present in the model. The outputs from factor analysis are analyzed below in different sections followed by interpretation of the regression analysis.

1) The suitability of the data set for factor analysis (mention the correlation matrix & Bartlett's)

Here, I want to explain more about the data set I am using for factor analysis. The data set has a lot of missing information for independent as well as dependent variable. Thus, I exclude all the observations with missing cases to improve the analysis and the model.
First of all, I ran correlation matrix for all the independent variables to examine their strength of the relationship with the dependent variable LIFEXPF. From the correlation matrix, I find that variables like Population in thousand, N ...
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