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 (hdr.undp.org/en/data#). In 2015, the HDI was as high as 0.94 for Norway and as low as 0.35 for Niger. The gross national income per capita (GNI), by contrast, is often used to summarize the overall economic strength of a country. Is the HDI related to the GNI? Here is a scatterplot of HDI against GNI. (Data in HDI 2015)

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?

HDI 0.9 0.8 0.7 0.6 0.5 0.4+ 0 + 40000 GNI 80000 + 120000