Time series regression fitted model

[hhu]

can someone please help me with locating the parameters and residuals for the fitted model with the seasonal dummy for months.
Also, how to find D12t?
below is my summary for the time series model that I generated in R:

Call:
tslm(formula = arrival_ts ~ trend + season)

Residuals:
** Min 1Q Median 3Q Max **
**-229.310 -39.381 -8.213 31.559 299.215 **

Coefficients:
** Estimate Std. Error t value Pr(>|t|) **
**(Intercept) -47.733662 6.255553 -7.631 4.77e-14 *****
**trend 0.215552 0.004647 46.383 < 2e-16 *****
**season2 2.724638 7.906092 0.345 0.730437 **
**season3 -7.753374 7.906096 -0.981 0.326949 **
**season4 -23.027697 7.886509 -2.920 0.003568 ** **
**season5 -37.784893 7.886502 -4.791 1.87e-06 *****
**season6 -37.379688 7.906158 -4.728 2.54e-06 *****
**season7 -28.093819 7.906140 -3.553 0.000395 *****
**season8 -29.759781 7.906125 -3.764 0.000175 *****
**season9 -28.293453 7.906113 -3.579 0.000359 *****
*season10 -21.454495 7.906103 -2.714 0.006751 ** **
season11 -7.438206 7.906096 -0.941 0.346989 **
season12 24.931742 7.906092 3.153 0.001654 **
---
Signif. codes: 0 ‘’ 0.001 ‘’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 55.9 on 1189 degrees of freedom
**Multiple R-squared: 0.6575, Adjusted R-squared: 0.654 **
F-statistic: 190.2 on 12 and 1189 DF, p-value: < 2.2e-16

Thank you

[clausp]

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[EconProf]

I am replying because there are serious errors in the assignment as it is written. Your difficulty answering the question may be partly due to those errors.

First, D represents a seasonal dummy, which is either one or zero. It is not something that you estimate.

Second, the lower-case delta (the Greek letter just to the left of the D) is the coefficient for a seasonal dummy. The estimated coefficient is usually represented by putting a caret (^) above the delta. The question should be "What is your estimate for delta12?" Adding a caret above the delta would be asking for the estimate of the estimate. Also, if the estimated coefficients (with the carets) are used in the equation, then the error term should also have a caret. That is the difference between the random errors and the residuals.

Third, when using seasonal dummies with monthly data, you leave one out to be the month that all the others are compared to. By using j = 1 to 11, it implies that there are dummies for January to November, so the coefficients represent the differences in y compared to December. In that case, there is no seasonal dummy for December (D12). If you want to use January as the base month, then it would make sense to have j = 2 to 12. Each of the months from February to December would then be compared to January, with delta12 being the estimated difference for December. Note that the default for tslm( ) is to omit the first season (Q1 for quarterly data and January for monthly data).