In: Statistics and Probability
Consider a portion of monthly return data (In %) on 20-year Treasury Bonds from 2006–2010.
| Date | Return | 
| Jan-06 | 4.12 | 
| Feb-06 | 4.44 | 
| Mar-06 | 4.02 | 
| Apr-06 | 4.79 | 
| May-06 | 4.01 | 
| Jun-06 | 3.65 | 
| Jul-06 | 4.07 | 
| Aug-06 | 4.3 | 
| Sep-06 | 5.49 | 
| Oct-06 | 3.6 | 
| Nov-06 | 4.71 | 
| Dec-06 | 3.83 | 
| Jan-07 | 4.14 | 
| Feb-07 | 3.53 | 
| Mar-07 | 3.68 | 
| Apr-07 | 4.19 | 
| May-07 | 3.34 | 
| Jun-07 | 3.51 | 
| Jul-07 | 3.48 | 
| Aug-07 | 3.68 | 
| Sep-07 | 4.96 | 
| Oct-07 | 3.42 | 
| Nov-07 | 4.17 | 
| Dec-07 | 4.25 | 
| Jan-08 | 5.05 | 
| Feb-08 | 3.23 | 
| Mar-08 | 5.34 | 
| Apr-08 | 5.15 | 
| May-08 | 4.58 | 
| Jun-08 | 4.61 | 
| Jul-08 | 4.25 | 
| Aug-08 | 4.49 | 
| Sep-08 | 3.55 | 
| Oct-08 | 4.48 | 
| Nov-08 | 4.38 | 
| Dec-08 | 3.99 | 
| Jan-09 | 3.73 | 
| Feb-09 | 5 | 
| Mar-09 | 3.2 | 
| Apr-09 | 3.87 | 
| May-09 | 5.5 | 
| Jun-09 | 4.6 | 
| Jul-09 | 3.79 | 
| Aug-09 | 3.73 | 
| Sep-09 | 5.35 | 
| Oct-09 | 4.24 | 
| Nov-09 | 3.86 | 
| Dec-09 | 5.38 | 
| Jan-10 | 3.61 | 
| Feb-10 | 4.59 | 
| Mar-10 | 4.22 | 
| Apr-10 | 3.42 | 
| May-10 | 4.54 | 
| Jun-10 | 5.49 | 
| Jul-10 | 4.29 | 
| Aug-10 | 4.49 | 
| Sep-10 | 3.78 | 
| Oct-10 | 3.98 | 
| Nov-10 | 3.44 | 
| Dec-10 | 5.19 | 
Estimate a linear trend model with seasonal dummy variables to make forecasts for the first three months of 2011. (Round intermediate calculations to at least 4 decimal places and final answers to 2 decimal places.)
| Year | Month | y^t | 
| 2011 | Jan | |
| 2011 | Feb | |
| 2011 | Mar | |
| SUMMARY OUTPUT | |||||
| Regression Statistics | |||||
| Multiple R | 0.342473152 | ||||
| R Square | 0.11728786 | ||||
| Adjusted R Square | -0.108085453 | ||||
| Standard Error | 0.667759459 | ||||
| Observations | 60 | ||||
| ANOVA | |||||
| df | SS | MS | F | Significance F | |
| Regression | 12 | 2.784658333 | 0.232054861 | 0.52041592 | 0.890749266 | 
| Residual | 47 | 20.95742667 | 0.445902695 | ||
| Total | 59 | 23.742085 | |||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
| Intercept | 4.38 | 0.350176015 | 12.50799546 | 1.45728E-16 | 3.675536725 | 
| t | 0.004111111 | 0.005079818 | 0.809302785 | 0.42241928 | -0.006108165 | 
| jan | -0.352777778 | 0.426008719 | -0.8280999 | 0.41179927 | -1.209796778 | 
| feb | -0.328888889 | 0.425372229 | -0.773179033 | 0.443287781 | -1.184627436 | 
| march | -0.399 | 0.424795535 | -0.939275408 | 0.35239166 | -1.253578389 | 
| april | -0.211111111 | 0.424278882 | -0.497576288 | 0.621102762 | -1.064650127 | 
| may | -0.105222222 | 0.423822488 | -0.248269559 | 0.805007427 | -0.957843092 | 
| june | -0.131333333 | 0.423426548 | -0.310167924 | 0.757804477 | -0.983157676 | 
| july | -0.531444444 | 0.423091234 | -1.256098927 | 0.215288202 | -1.38259422 | 
| august | -0.373555556 | 0.422816687 | -0.883492934 | 0.381466985 | -1.224153015 | 
| sept | 0.110333333 | 0.422603028 | 0.261080319 | 0.795171202 | -0.739834299 | 
| oct | -0.575777778 | 0.422450348 | -1.362947814 | 0.179393519 | -1.425638257 | 
| nov | -0.411888889 | 0.422358713 | -0.975211061 | 0.334448395 | -1.261565023 | 
| Year | Month | t | y | ||
| 2011 | Jan | 61 | 4.278 | ||
| 2011 | Feb | 62 | 4.306 | ||
| 2011 | Mar | 63 | 4.24 | ||