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Make a new column of seasonally adjusted monthly by dividing the annual data by 12
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. 2007) to 161 (May 2020); make a t2 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 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. When 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.
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