Linear time trend (model 1)

. reg sp500 t Source SS df MS Number of obs = 558 F (1, 556) 1518.39 Model 4362214.78 1 4362214.78 Prob > F 0.0000 Residual 1597339.46 556 2872.9127 R-squared = 0.7320 Adj R-squared 0.7315 Total 5959554.24 557 10699.3793 Root MSE = 53.6 sp500 Coefficient Std. err. t P> It [95% conf. interval] t . 5489004 . 0140864 38.97 0.000 . 5212313 . 5765695 _cons -35. 14424 4.544207 -7.73 0.000 -44. 07015 -26.21833. reg sp500 dl d2 d3 t Source SS df MS Number of obs = 558 F(4, 553) = 378.35 Model 4364681. 41 4 1091170.35 Prob > F = 0.0000 Residual 1594872.83 553 2884.03767 R-squared 0. 7324 Adj R-squared 0. 7304 Total 5959554.24 557 10699.3793 Root MSE 53.703 sp500 Coefficient Std. err. t P> |t| [95% conf. interval] d1 4.002055 6.430769 0.62 0.534 -8. 629666 16.63378 d2 5.494777 6.430629 0.85 0. 393 -7.13667 18.12622 d3 1. 731709 6.465249 0.27 0. 789 -10.96774 14.43116 t . 5489033 . 0141143 38.89 0.000 . 5211792 . 5766275 cons -37.97307 6.052183 -6.27 0.000 -49 . 86115 -26.08499. reg sp500 t tsq Source SS df MS Number of obs = 558 F (2, 555) 2043.45 Model 5247011.49 2 2623505.75 Prob > F = 0.0000 Residual 712542.748 555 1283.86081 R-squared 0. 8804 Adj R-squared 0. 8800 Total 5959554.24 557 10699.3793 Root MSE = 35.831 sp500 Coefficient Std. err. t P> | t [95% conf. interval] t - . 4102524 . 0377303 -10.87 0.000 - . 4843641 - . 3361407 tsq . 0017158 . 0000654 26.25 0.000 . 0015875 . 0018442 cons 54.37669 4.566901 11.91 0.000 45 . 40617 63.34721reg sp500 dl d2 d3 t tsq Source SS df MS Number of obs = 558 F (5, 552) = 814.14 Model 5247915.87 5 1049583.17 Prob > F = 0.0000 I Residual 711638.375 552 1289.19995 R-squared = 0.8806 Adj R-squared = 0. 8795 Total 5959554.24 557 10699.3793 Root MSE 35.905 sp500 Coefficient Std. err. t [95% conf. interval] d1 2. 088319 4.300167 0.49 0. 627 -6.358374 10.53501 d2 3.581042 4. 300074 0.83 0. 405 -4. 865468 12.02755 d3 1. 731709 4. 322599 0.40 0. 689 -6.759045 10.22246 t - . 4096794 . 0378191 -10.83 0.000 - . 4839663 - . 3353925 tsq . 0017148 . 0000655 26.17 0.000 . 0015861 . 0018435 _cons 52.46181 5. 320822 9.86 0.000 42.01027 62.91334