Question: Human Development Index. The United Nations Development Programme (UNDP) uses the Human Development Index (HDI) in an attempt to summarize in one 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.