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 |