Let's practice time-series forecasting of new home sales. Click here ( https://www.census.gov/construction/nrs/historical_data/index.html ) to see...

Let's practice time-series forecasting of new home sales. Click here (https://www.census.gov/construction/nrs/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 CSV file "A3Q3 Census Housing Data."

Only keep the dates beginning in January 2010, so delete the earlier observations, and use the data through Feb. 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. 2010) to 98 (Feb. 2018); make a t^2 column too (since, if you look at the data, you can see sales are slightly 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 connectors) of both.

Question 12Question text

Do you think making a seasonal adjustment will be useful, given what you observe at this point?

Select one:

a. Yes, since the seasonally unadjusted data traces a smoother path (graphically speaking) than the seasonally adjusted data.

b. No; even though the unadjusted is more volatile than the adjusted, it is expected to be and thus making the adjustment will not improve the analysis.

c. Yes, since even though they follow the same general trend, the seasonally unadjusted data is predictably more volatile than the seasonally adjusted data.

d. No, since there is no discernible difference between the two data series, as far as is evident in the graph.

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Run four regressions:

1. seasonally unadjusted monthly as the dependent, and t and t^2 as the independents
2. seasonally unadjusted monthly as the dependent, and t, t^2 and D as the independents
3. seasonally adjusted monthly as the dependent, and t and t^2 as the independents, and
4. seasonally adjusted monthly as the dependent, and t, t^2 and D as the independents

In interpreting your p-values, remember that, say, 1.0E-08 is 1.0×10^−8, which is 0.00000001

Question 13Question text

In comparing the regression results between model 1 and 2 (the unadjusted sales), it is notable that including the extra variable D in model 2

Select one:

a. dramatically improves the explanatory power of the model.

b. makes the t and t^2 variables statistically insignificant in model 2, whereas they were significant in model 1.

c. increases the R^2, but it is insignificant and has an unexpected sign.

d. increases the R^2 as expected but reduces the adjusted R^2, suggesting that D does not contribute to the explanatory power of the model.

Question 14Question text

In comparing the regression results between models 2 and 3, it is notable that

Select one:

a. the D variable in model 2 does a decent job of capturing the seasonal effect, since the results between the two models are not hugely different and D has the expected sign and is statistically significant.

b. including the D variable in model 2 results in a much larger adjusted R^2, suggesting that the inclusion of the dummy variable is necessary to boost predictive power.

c. the coefficient estimates for t and t^2 change dramatically, even though the models are very comparable (unadjusted with a seasonal dummy is pretty close to seasonally adjusted).

d. dropping the D variable in model 3 pulls the R^2 down, which is unexpected since D in model 2 is statistically insignificant.

Question 15Question text

The regression results for model 4 are notable because

Select one:

a. adding a redundant seasonal dummy to already seasonally-adjusted data results in the D variable being insignificant, as expected, and the model's explanatory power is essentially the same as model 3.

b. adding the redundant D variable to the seasonally adjusted data causes the coefficient estimates for t and t^2

to be dramatically different than they were in models 2 and 3.

c. the adjusted R^2 is higher than in the comparable model 3 (without the D).

d. making the seasonal adjustment in the dependent variable, in addition to adding the D dummy, yields the best results in terms of significant coefficients, explanatory power, and expected signs.