3. Let's practice time-series forecasting of new home sales. Click here ( https://www.census.gov/constructionrs/historical_data/index.html) to see the newest data in the first table: Houses Sold - Seasonal Factors, Total (Excel file is sold_cust.xls). Look at the monthly data on the "Reg Sold" tab. If you have trouble with the link, I have recreated the data in moodle in the Excel file "A3Q3 Census Housing Data." Only keep the dates beginning in January 2009, so delete the earlier observations, and use the data through April 2019. 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. 2009) to 124 (Apr. 2019); make a t' column 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 to as the independents, 2) seasonally unadjusted monthly as the dependent, and t, t', and D as the independents, 3) seasonally adjusted monthly as the dependent, and t and to as the independents, and 4) seasonally adjusted monthly as the dependent, and t, t', 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 *104-8, which is 0.00000001. State the equation that would be used to forecast sales. Answer: Correlation between N5A monthly and SA monthly which is 0.90902488 by inserting the formal in excel (=CORREL(B2:B125,D2:D125). Correlation 0.90902488 Correlation between NSA monthly and SA monthly which is 0.90902488 The scatter plot between the unadjusted and the adjusted monthly rate is given below