Income and housing The Office of Federal HousingEnterprise Oversight (www.ofheo.gov) collects data onvarious aspects of housing costs around the UnitedStates. Here is a scatterplot of the Housing Cost Indexversus the Median Family Income for each of the50 states. The correlation is 0.65. a) Describe the relationship between the Housing CostIndex and the Median Family Income by state. b) If we standardized both variables, what would the corre-lation coefficient between the standardized variables be? c) If we had measured Median Family Income in thou-sands of dollars instead of dollars, how would the correlation change?d) Washington, DC, has a Housing Cost Index of 548and a median income of about $45,000. If we were toinclude DC in the data set, how would that affect thecorrelation coefficient?e) Do these data provide proof that by raising the medianincome in a state, the Housing Cost Index will rise asa result? Explain.
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
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
versus the
50 states. The
Index and the Median Family Income by state.
lation coefficient between the standardized variables be?
sands of dollars instead of dollars, how would the
d) Washington, DC, has a Housing Cost Index of 548
and a median income of about $45,000. If we were to
include DC in the data set, how would that affect the
correlation coefficient?
e) Do these data provide proof that by raising the median
income in a state, the Housing Cost Index will rise as
a result? Explain.
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