The analysis given below is for data on world population statistics for many cou

Question

The analysis given below is for data on world population statistics for many countries. Density number per area, Urban represents the proportion living in an urban setting, lifeexpf is the life expectancy for females literacy is the proportion of the population that is literate, Babymort is infant mortality rate and GDP Cap is a financial measure(gross domestic product. Latent Roots (Eigenvalues) 3.988 0.339 0.495 0.128 0.033 1.017 Component loadings 0.184 0.957 0.211 DENSITY -0.096 0.101 0.847 URBAN 0.135 -0.102 0.957 LIFEEXPE 0.234 0.228 0.894 LITERACY 0.166 0.097 0.960 BABY MORT 0.593 0.140 0.767 GDP CAP variance Explained by components 0.495 3 1.017 Percent of Total Variance Explained 8.251 66.463

Explanation / Answer

What are the values of the summary statistics marked ???? – note there are two – one for variance explained and the other for proportion variance explained.

Answer:

We observe that first component explained 66.463%, 2nd component explained 16.95% while 3rd explained 8.251% of the variance. So this means that first two components explained appropriate variance.

How would you interpret the first component? What is the significance of the negative loading for birth mortality?

Answer:

Component loading is higher for urban,liefexpf,literacy,babymort,gdp_cap, so first component explain all these variables.

Birth mortality has negative loading because it is negatively correlated with all other variables urban,liefexpf,literacy, ,gdp_cap.

How do you interpret the second component?

Answer:

Second component has high loading on to density indicating it represents this only

How would you interpret the third component?

Answer:

Third component is of no use as it has small compoannet loading with all variables.

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