1) Zillow is a home and real estate marketplace that aims to assist homeowners, home buyers, sellers, renters, real estate agents, mortgage professionals, landlords, and property managers locate and share information about homes, real estate, and mortgages. Zillow uses a priority formula to estimate home and rental housing market value, termed a Zestimate, using its database of over 110 million homes in the United States. The Zestimate 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 $ per square foot. The first data entry is in December of 2010. The last data entry is in June of 2016. The vertical lines signify January.

Assume the time period number starts as 1 in December of 2010 and monthly data is collected until June of 2016. The time period t increases by 1 integer for each consecutive month.

What is the time period (value for t) for June of 2016?

2) 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 below 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.

Response Median Sale Price per Square Foot Story Iowa ($lsqft) Summary of Fit RSquare 0.649712 RSquare Adj 0.638766 Root Mean Square Error 11.86299 Mean of Response 120.1 Observations (or Sum Wgts) 67 Analysis of Variance Sum of Source DF Squares Mean Square F Ratio Model 2 16705.666 8352.83 59.3534 Error 64 9006.748 140.73 Prob > F C. Total 66 25712.413 |t| |t| Intercept 41.159 1.11 41.14 0.8863 Lag Residuals 0.645 0.095 6.81