I am trying to get the numerator and denominator used to get a F-statistic of a joint significance test of some of the model's regressors.
In case of a single regressor (or if we want to test the joint significance), this shows up in the regression output. The F-stat is the ratio between MS(Model) and MS(Residual).
What would be the numerator and denominator of the F-statistic below, when we test the join significance of some (but not all) regressors?
I copied below the corresponding detailed -anova- output, but I still don't know how to find out the numerator and denominator
In case of a single regressor (or if we want to test the joint significance), this shows up in the regression output. The F-stat is the ratio between MS(Model) and MS(Residual).
Code:
. sysuse auto.dta, clear (1978 automobile data) . reg price mpg Source | SS df MS Number of obs = 74 -------------+---------------------------------- F(1, 72) = 20.26 Model | 139449474 1 139449474 Prob > F = 0.0000 Residual | 495615923 72 6883554.48 R-squared = 0.2196 -------------+---------------------------------- Adj R-squared = 0.2087 Total | 635065396 73 8699525.97 Root MSE = 2623.7 ------------------------------------------------------------------------------ price | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- mpg | -238.8943 53.07669 -4.50 0.000 -344.7008 -133.0879 _cons | 11253.06 1170.813 9.61 0.000 8919.088 13587.03 ------------------------------------------------------------------------------ . display 139449474/6883554.48 // I get the same Fstat as displayed in regression output 20.258353
Code:
. reg price mpg weight foreign Source | SS df MS Number of obs = 74 -------------+---------------------------------- F(3, 70) = 23.29 Model | 317252881 3 105750960 Prob > F = 0.0000 Residual | 317812515 70 4540178.78 R-squared = 0.4996 -------------+---------------------------------- Adj R-squared = 0.4781 Total | 635065396 73 8699525.97 Root MSE = 2130.8 ------------------------------------------------------------------------------ price | Coefficient Std. err. t P>|t| [95% conf. interval] -------------+---------------------------------------------------------------- mpg | 21.8536 74.22114 0.29 0.769 -126.1758 169.883 weight | 3.464706 .630749 5.49 0.000 2.206717 4.722695 foreign | 3673.06 683.9783 5.37 0.000 2308.909 5037.212 _cons | -5853.696 3376.987 -1.73 0.087 -12588.88 881.4934 ------------------------------------------------------------------------------ . test mpg weight // how can I get the numerator and denominator used to calculate this F-sta > tistic? ( 1) mpg = 0 ( 2) weight = 0 F( 2, 70) = 34.77 Prob > F = 0.0000 .
Code:
. anova price c.mpg c.weight foreign Number of obs = 74 R-squared = 0.4996 Root MSE = 2130.77 Adj R-squared = 0.4781 Source | Partial SS df MS F Prob>F -----------+---------------------------------------------------- Model | 3.173e+08 3 1.058e+08 23.29 0.0000 | mpg | 393607.95 1 393607.95 0.09 0.7693 weight | 1.370e+08 1 1.370e+08 30.17 0.0000 foreign | 1.309e+08 1 1.309e+08 28.84 0.0000 | Residual | 3.178e+08 70 4540178.8 -----------+---------------------------------------------------- Total | 6.351e+08 73 8699526 . test mpg weight ( 1) mpg = 0 ( 2) weight = 0 F( 2, 70) = 34.77 Prob > F = 0.0000
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