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Question 1

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

Select one:

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

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

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

d. 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.

Run four regressions:

  1. seasonally unadjusted monthly as the dependent, and tt and t2t2 as the independents,
  2. seasonally unadjusted monthly as the dependent, and tt, t2t2, and DD as the independents,
  3. seasonally adjusted monthly as the dependent, and tt and t2t2 as the independents, and
  4. seasonally adjusted monthly as the dependent, and tt, t2t2, and DD as the independents.

In interpreting your p-values, remember that, say, 1.0E-08 is 1.0×10−81.0×10−8, which is 0.00000001

Question 2

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

Select one:

a. increases the R2R2, but DD is insignificant and has an unexpected sign.

b. makes the tt and t2t2 variables statistically insignificant in model 2, whereas they were significant in model 1.

c. increases the R2R2 as expected but reduces the adjusted R2R2, suggesting that DD does not contribute to the explanatory power of the model.

d. noticeably improves the explanatory power of the model.

Question 3

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

Select one:

a. the DD 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 DD has the expected sign and is statistically significant.

b. the coefficient estimates for tt and t2t2 change dramatically, even though the models are very comparable (unadjusted with a seasonal dummy is pretty close to seasonally adjusted).

c. including the DD variable in model 2 results in a much larger adjusted R2R2, suggesting that the inclusion of the dummy variable is necessary to boost predictive power.

d. dropping the DD variable in model 3 pulls the R2R2 down, which is unexpected since DDin model 2 is statistically insignificant.

Question 4

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 DDvariable being insignificant, as expected, and the model’s explanatory power is almost the same as model 3.

b. the adjusted R2R2 is higher than in the comparable model 3 (without the DD).

c. adding the redundant DD variable to the seasonally adjusted data causes the coefficient estimates for both tt and t2t2 to be of opposite signs than they were in models 2 and 3.

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


Look at the monthly data on the “Reg Sold” tab.

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 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.

Houses Sold by Region