Income and housing revisited In Chapter 6, Exercise 32, we learned that the Office of Federal Housing Enterprise Oversight (OFHEO) collects data on various aspects of housing costs around the United States. Heres 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. 700 600 500 400 300 200 Housing Cost Index 35 40 45 50 55 60 70 Median Family Income (thousands of dollars) 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?
Inference for Linear Regression: - The idea: o The calculated intercept b0 is a statistic that estimates the population intercept B . The 0 calculated intercept b1 is a statistic that estimates the population intercept B1 . o We can thus perform inference for the two linear parameters (intercept & slope). We are particularly interested in the slope, which indicates whether there is really a linear relationship. o A slope of 0 means no true linear relationship