In Problem 19 in Chapter 5 and Problem 14 in Chapter 8, data from the 1990 Census for 26 randomly selected Metropolitan Statistical Areas (MSAs) were discussed. Of interest were factors potentially associated with the rate of owner occupancy of
OWNEROCC: Proportion of housing units that are owner-occupied (as opposed to renter occupied)
OWNCOST: Median selected monthly ownership costs, in dollars
URBAN: Proportion of population living in urban areas
It is also of interest to see whether the average owner occupancy rate differs between metropolitan areas where 75% or more of the population lives in urban areas and metropolitan areas where less than 75% of the population lives in urban areas, while controlling for ownership costs. For this purpose, the following additional variable is defined:
a. State an ANACOVA regression model that can be used to compare the two MSA types, controlling for average monthly ownership costs.
b. State the model that should be used to check whether the ANACOVA model in part (a) is appropriate. Using the computer output given next, carry out the appropriate test.
c. Using ANACOVA methods and the accompanying output, determine adjusted mean owner occupancy rates for the two types of MSAs, and test whether they significantly differ from one another. (The unadjusted average owner occupancy rate for MSAs where at least 75% of the population lives in urban areas = 64.5%; the unadjusted average owner occupancy rate for MSAs where less than 75% of the population lives in urban areas = 69.25%.)
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f proportion of population living in urban areas a otherwise 0 Regression of OWNEROCC on OWNCOST, Z, and OWNCOST Z ANALYSIS OF VARIANCE Sum of DFI squares Mean SquareF Value Pr>F Source Model Error Corrected Total 4.06 0.0194 3 214.1949671.39832 22 386.76658 1758030 25 600.96154 Regression of OWNEROCC on OWNCOST and Z ANALYSIS OF VARIANCE Sum of Mean Square 106.74930 16.84621 DF Squares F Value Pr> F Source Model Error Corrected Total 2 213 49860 6.34 0.0064 23 387 46294 1 25 600.98154 PARAMETER ESTIMATES Parameter Standard Variable Intercept OWNCOST DF Estimate Error t Value Pr> It 68.66546 0.01267 0.00553 -3.90 147336 46.60 <0001 2.290.0314 -2.19 0.0388 567 1.78250 219 00388
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a Let X denote OWNCOST and Y denote OWNEROCC Y 0 1 X 2 Z E b Y 0 1 X 2 …View the full answer
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