The Office of Federal Housing Enterprise Oversight collects data on various aspects of housing costs around the United States. A scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states is provided. The correlation is 0.649. Complete parts a through e below. ✔ Click the icon to view the scatterplot. a) Describe the relationship between the Housing Cost Index and the Median Family Income by state. (Consider a correlation between -0.5 and 0.5 to be weak. Consider a correlation less than -0.75 or greater than 0.75 to be strong.) There is a moderate positive linear relationship between Housing Cost Index and the Median Family Income. b) If both variables are standardized, what would the correlation coefficient between the standardized variables be? r= (Round to the nearest thousandth as needed.) c) If Median Family Income had been measured The correlation would d) A state that is not represented in the scatterplot has a housing cost index of 548 and a median income of about $45,000. If this state were included in the dataset, how would that affect the correlation coefficient? The correlation would 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. thousands of dollars instead of dollars, how would the correlation change? ▼
The Office of Federal Housing Enterprise Oversight collects data on various aspects of housing costs around the United States. A scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states is provided. The correlation is 0.649. Complete parts a through e below. ✔ Click the icon to view the scatterplot. a) Describe the relationship between the Housing Cost Index and the Median Family Income by state. (Consider a correlation between -0.5 and 0.5 to be weak. Consider a correlation less than -0.75 or greater than 0.75 to be strong.) There is a moderate positive linear relationship between Housing Cost Index and the Median Family Income. b) If both variables are standardized, what would the correlation coefficient between the standardized variables be? r= (Round to the nearest thousandth as needed.) c) If Median Family Income had been measured The correlation would d) A state that is not represented in the scatterplot has a housing cost index of 548 and a median income of about $45,000. If this state were included in the dataset, how would that affect the correlation coefficient? The correlation would 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. thousands of dollars instead of dollars, how would the correlation change? ▼
Chapter1: Introducing The Economic Way Of Thinking
Section1.A: Applying Graphics To Economics
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Transcribed Image Text:The Office of Federal Housing Enterprise Oversight collects data on various aspects of housing costs around the United States. A scatterplot of the Housing Cost Index versus the Median Family Income for each of the 50 states
is provided. The correlation is 0.649. Complete parts a through e below.
Click the icon to view the scatterplot.
a) Describe the relationship between the Housing Cost Index and the Median Family Income by state. (Consider a correlation between -0.5 and 0.5 to be weak. Consider a correlation less than -0.75 or greater than 0.75 to be
strong.)
There is a moderate positive linear relationship between Housing Cost Index and the Median Family Income.
b) If both variables are standardized, what would the correlation coefficient between the standardized variables be?
(Round to the nearest thousandth as needed.)
c) If Median Family Income had been measured in thousands of dollars instead of dollars, how would the correlation change?
The correlation would
d) A state that is not represented in the scatterplot has a housing cost index of 548 and a median income of about $45,000. If this state were included in the dataset, how would that affect the correlation coefficient?
The correlation would
e) Do these data provide proof that by raising the median family income in a state, the housing cost index will rise as a result? Explain.
O A. No, but they do provide proof that by raising housing costs in a state, that state's median family income will also rise.
OB. Yes, because the correlation coefficient is large enough to prove that raising the median family income in a region raises the housing cost index in that state.
O C. No, because one can only claim that higher median incomes are associated with higher housing costs.
O D. No, because the correlation coefficient is not large enough to claim any sort of association between median family income and housing cost index.
Housing Scatterplot
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Median Family Income ($)
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