F-test

[Sabrina Solanki]

i just ran the following regression. what does the F-test tell me?

xtreg tscorek small, fe

Fixed-effects (within) regression Number of obs = 5,786
Group variable: schidkn Number of groups = 79

R-sq: Obs per group:
within = 0.0111 min = 34
between = 0.0073 avg = 73.2
overall = 0.0073 max = 137

F(1,5706) = 64.19
corr(u_i, Xb) = -0.0186 Prob > F = 0.0000

------------------------------------------------------------------------------
tscorek | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
small | 15.15738 1.891813 8.01 0.000 11.4487 18.86605
_cons | 917.7757 1.027697 893.04 0.000 915.7611 919.7904
-------------+----------------------------------------------------------------
sigma_u | 35.38274
sigma_e | 65.134565
rho | .22785507 (fraction of variance due to u_i)
------------------------------------------------------------------------------
F test that all u_i=0: F(78, 5706) = 21.23 Prob > F = 0.0000

[Clyde Schechter]

In general, the overall F statistic tests the hypothesis that all of the regression coefficients for all of your model predictors are zero. In your particular situation, there is only one predictor, so in this case, it tests the same hypothesis as the t-statistic in the output for variable small. Not coincidentally, it is exactly the same test, because an F with 1 numerator df is the square of a t with the same number of denominator df. And, indeed, except for a little rounding error, 64.19 is almost exactly 8.01^2.

Or were you referring to the F test at the very bottom? That one tests the hypothesis that all of the u_i fixed effects are zero, just as it says. When that test is not significant one can consider simplifying the model to pooled ordinary least squares regression. Since, however, it is highly statistically significant in your case, it tells you that the use of a two-level model is mandatory, and pooled OLS is not acceptable for this data.

[Sabrina Solanki]

Yes, I was referring to the F test at the very bottom. Sorry, I should have been more specific. Thank you, this helps.