In the analysis of housing prices, researchers often specify an econometric model of the following form: 5. Iprice, = B, + B,S, + ByN; + BspSD, +€, where Iprice, denotes the log of the sale price of house i, S, is a set of structural attributes of house i (such as living area, presence of a view, and number of bathrooms), N, is a set of neighborhood/community characteristics (such as the crime rate and air quality), SD,is a set of school district dummy variables that take the value of one if the ith house is located in that school distriet and €, is a random disturbance term. In a recent study, this specification was used to estimate the determinants of housing values using data on homes that sold within Los Angeles and Orange County. Definitions of the variables used in the study are reported below. Variable Definition Units of Measurement Structural Attributes PRICE Sale Price Dollars BATH Number of Bathrooms Number LIVAREA Interior Living Space Square Feet POOL Presence of Pool Zero/One VIEW Presence of a View Zero/One Neighborhood/Community Attributes BEACH Distance to Nearest Beach Miles BEACHSQ Distance to Beach Squared Miles CRIME Per Capita FBI Crime Index Crimes/Population TWORK Time to Work Minutes AIRQ Air Quality Miles of Visibility SCHOOL DISTRICT Location in Specific School Districts Zero/One Estimated Hedonic Equations Dependent Variable = Ln(Home Sale Price) Variable (Coefficient) Coefficient (St. Error) Structural Attributes BATH ( BI) .06 (.002) POOL (B2) .07 (.05) LIVAREA (B) 00035 (000002) VIEW (B4) .09 (.01) Neighborhood/Community Attributes BEACH (Bs) -015 4002) BEACHSQ (B6 ) 0.0002 (.0001) CRIME (B7) -.001 (.0001) TWORK (B) -.015 (.001) AIRQ (B») .02 (.001) School District Beverly Hills (Bi0) 39 (.002) Compton ( B1) 22 (.06) Orange (B12) .07 (05) Laguna Beach ( B13) .43 (.10) INTERCEPT ( Bo) 12.79 R-Square .55 Number of Observations 41,852

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Set Theory

Every field in the present world involves a set. The theory of sets was developed by German mathematician Georg Cantor while working on the “problems of trigonometric series”.