Income and housing revisited In Chapter, Exercise, we

Chapter 6, Problem 49E

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Problem 49E

Income and housing revisited In Chapter, Exercise, we learned that the Office of Federal Housing Enterprise Oversight (OFHEO) collects data on various aspects of housing costs around the United States. Here’s a scatterplot (by state) of the Housing Cost Index (HCI) versus the Median Family Income (MFI) for the 50 states. The correlation is r = 0.65. The mean HCI is 338.2, with a standard deviation of 116.55. The mean MFI is $46,234, with a standard deviation of $7072.47.

a) Is a regression analysis appropriate? Explain.

b) What is the equation that predicts Housing Cost Index from median family income?

c) For a state with MFI = +44,993, what would be the predicted HCI?

d) Washington, DC, has an MFI of $44,993 and an HCI of 548.02. How far off is the prediction in c) from the actual HCI?

e) If we standardized both variables, what would be the regression equation that predicts standardized HCI from standardized MFI?

f) If we standardized both variables, what would be the regression equation that predicts standardized MFI from standardized HCI?