https://www.census.gov/construction/nrs/historical_data/index.html

Data was too large to post but can be accessed at the above link. The "Houses Sold - Seasonal Factors" tab - select the "Total Excel XLS file".

Only keep the dates beginning in January 2005, so delete the earlier observations, and use the data through May 2018. Keep only the US data, both the seasonally unadjusted monthly (column B) and the seasonally adjusted annual (column G). Make a new column of seasonally adjusted monthly by dividing the annual data by 12. Make a column called t where t will go from 1 (Jan. 2005) to 161 (May 2018); make a t2column too (since, if you look at the data, you can see sales are U-shaped; hence the quadratic). Also make a column D that is a dummy variable equal to one during the spring and summer months of March through August.

Determine the correlation between the unadjusted and the adjusted monthly data (=CORREL(unadjust., adjust.) in Excel), and produce scatterplots (with straight lines) of both. Do you think making a seasonal adjustment will be useful, given what you observe at this point?

Run four regressions: 1) seasonally unadjusted monthly as the dependent, and t and t2 as the independents, 2) seasonally unadjusted monthly as the dependent, and t, t2, and D as the independents, 3) seasonally adjusted monthly as the dependent, and t and t2 as the independents, and 4) seasonally adjusted monthly as the dependent, and t, t2, and D as the independents. Discuss your findings, and determine which of the four models is the best for forecasting new home sales. In interpreting your p-values, remember that, say, 1.0E-08 is 1.0 * 10^-8, which is 0.00000001. State the equation that would be used to forecast sales.