Income and housing. The Office of Federal Housing Enterprise Oversight (www.ofheo.gov) collects data on various aspects of housing costs around the United States.

Here is a scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states. The correlation is 0.65.

For these data Kendall’s tau is 0.51. Does that provide proof that by raising the median income in a state, the Housing Cost Index will rise as a result? Explain what Kendall’s tau says and does not say.