How do home prices vary with square footage, age, and a variety of other factors? The Data and Story Library (DASL) contains data, including the sale price, for a random sample of 117 homes sold in Albuquerque, New Mexico. Go to the DASL website (lib.stat. cmu.edu/DASL/) and retrieve the home price data set. To do this, select Data subjects. Economics, Home Prices or go directly to lib.stat.cmu.edu/DASL/ Datafiles/homedat.html. There are a number of ways to capture the home price data from the DASL site. One simple way is to select just the rows containing the data values (and not the labels), copy, paste directly into an Excel or MINITAB worksheet, add your own variable la¬bels, and save the resulting worksheet. It is possible to copy the variable labels from DASL as well, but the differences in alignment and the intervening blank line add to the difficulty (data sets: AlbHome.xIsx, AlbHome.mtw).
a. Construct plots of PRICE versus SQFT and PRICE versus AGE. Describe the nature and apparent strength of the relationships between PRICE and the variables SQFT and AGE. Construct box plots of PRICE versus each of the qualitative/dummy variables NE (north-east location), CUST (custom built), and COR (corner location). What do the box plots suggest about the effect of these features on home prices?
b. Using MINITAB, Excel, or other available statistical software, develop a multiple regression model of the dependent variable PRICE versus independent variables SQFT, AGE, NE, CUST, and COR. Report and interpret the key summary measures: R2, the standard error, and the F-statistic from the ANOVA table. Report and interpret the p-values for the estimated regression coefficients. Which of the independent variables appear to be most important for predicting Albuquerque home prices? Compute and interpret a point prediction and a 95 percent prediction interval for a five-year-old, 2,500 square foot, custom-built home located in the northeast sector of the city (not on a corner lot). Prepare a brief summary of your observations.