Human Development Index.
The United Nations Development Programme (UNDP) collects data in the developing world to help countries solve global and national development challenges. In the UNDP annual Human Development Report, you can find data on over 100 variables for each of 177 countries worldwide. One summary measure used by the agency is the Human Development Index (HDI), which attempts to summarize in a single number the progress in health, education, and economics of a country.
In 2006, the HDI was as high as 0.965 for Norway and as low as 0.331 for Niger. The gross domestic product per capita (GDPPC), by contrast, is often used to summarize the overall economic strength of a country. Is the HDI related to the GDPPC? Here is a scatterplot of HDI against GDPPC.
a) Explain why fitting a linear model to these data might be misleading.
b) If you fit a linear model to the data, what do you think a scatterplot of residuals versus predicted HDI will look like?
c) There is an outlier (Luxembourg) with a GDPPC of around $70,000. Will setting this point aside improve the model substantially? Explain.