Income and housing Here is a scatterplot of the Housing Cost Index vs. the Median Family Income for 10 regions in a country. The correlation is 0.66.

a) Describe the relationship between the Housing Cost Index and the Median Family Income by region.

b) If we standardized both variables, what would the correlation coefficient between the standardized variables be?

c) If we had measured Median Family Income in thousands of dollars instead of dollars, how would the correlation change?

d) One region of the country has a housing cost index of 225 and a median income of about $45,000. If we were to include this region in the dataset, how would that affect the correlation coefficient?

e) Do these data provide proof that by raising the median family income in a state, the housing cost index will rise as a result? Explain.
*f) For these data, Kendall’s tau is 0.58. Does that provide proof that by raising the median income in a region the Housing Cost Index will rise as a result? Explain what Kendall’s tau says and does not say.

Housing Cost Index 800 500 200 30,000 45,000 60,000 Median Family Income ($)