Zillow is a home and real estate marketplace that aims to assist homeowners, home buyers, sellers, renters,realestateagents,mortgageprofessionals,landlords,andpropertymanagerslocateandshareinformationabout homes, real estate, and mortgages.Zillow uses a priority formula to estimate home and rental housingmarketvalue,termedaZestimate,usingitsdatabaseofover110millionhomesintheUnitedStates.TheZestimate is calculated from public and user submitted data.In this example we look at Zillow's estimated median sales price of homes in Ames, Iowa recorded in $ persquare foot.The first data entry is in December of 2010.The last data entry is in June of 2016.The vertical lines signify January.Figure (1) shows the predicted sales price of a home based on a quadratictrend(thereisnoapparentseasonalityinthisexamplesonoseasonalityisincludedintheestimatedmodel).In addition we include the output for the estimated AR(1) model.

Figure (1)

Residuals versus Lag Residuals (AR(1) Model) Response Median Sale Price per Square Foot Story Iowa ($/sqft) 50 40 Summary of Fit 30- RSquare 0.649712 20 RSquare Adj 0.638766 10 Story Iowa ($/sqft) Residual Median Sale Price per Square Foot Root Mean Square Error 11.86299 Mean of Response 120.1 -10- Observations (or Sum Wgts) 67 -20 Analysis of Variance -30 40- Sum of 40 -30 -20 1 -10 0 10 20 30 40 50 Source DF Squares Mean Square F Ratio Lag Residuals Model 2 16705.666 8352.83 59.3534 Summary of Fit Error 64 9006.748 140.73 Prob > F RSquare 0.42 C. Total 0.411 66 25712.413 <.0001 rsquare adj root mean square error parameter estimates of response observations sum wgts term estimate std t ratio prob>|t] Parameter Estimates Intercept 82.76 4.48 18.47 <.0001 term estimate std error t ratio prob>/t] Period (t) 1.72 0.30 5.65 <.0001 intercept period lag residuals>