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. Figure (1) is the time series plot by month of the Median home sales price in Ames ($/sqft) over the past 5 plus years. The rst data entry is in December of 2010. The last data entry is in June of 2016. The vertical lines signify J anuary. Figure (2) shows the predicted sales price of home based on a quadratic trend (there is no visual seasonality in this example so no seasonality is included in the estimated model). In addition we include the output for the estimated AR(1) model. (a) What is the predicted median sales price for Ames homes ($/sqft) for June 2016 based on the model accounting for trend? Show all your work to receive full credit. (b) What is the predicted median sales price for Ames homes ($/sqft) for July 2016 based on the model accounting for trend? Show all your work to receive full credit. (c) In June of 2016 the median sales price for Ames homes ($/sqft) was 133 ($/sqft). Find the residual median home value per square foot. (d) of the variability in the median sales prices of homes ($/sqft) in Ames is explained by the quadratic trend over time. (c) Based on your estimated AR(1) model, provide a prediction for the residual for July of 2016. (f) Find the updated forecast for median sales price for Ames homes ($/sqft) for July of 2016 using the information from the previous parts of this problem. This update should be based on the quadratic trend and the correlation (serial correlation) between observations. Show your work for full credit