Interpretation of output - Regression Random Effects Model

#1
Hello,
can someone help to interpret the end of this Stata output for a random effects model?
What does sigma_u and sigma_e mean exactly?

furthermore:
rho | .51380409 (fraction of variance due to u_i)

rho should be the correlation coefficient, u_i refers to the indep. var. in the model? Thus, the indep.var. explain 51% of variation in the dep.var?


Random-effects GLS regression Number of obs = 3316
Group variable: gvkey Number of groups = 594

R-sq: within = 0.9861 Obs per group: min = 1
between = 0.9898 avg = 5.6
overall = 0.9906 max = 10

Wald chi2(82) = 255618.02
corr(u_i, X) = 0 (assumed) Prob > chi2 = 0.0000

------------------------------------------------------------------------------
ebit | Coef. Std. Err. z P>|z| [95% Conf. Interval]
-------------+----------------------------------------------------------------
blankcheck | -18.77437 15.49914 -1.21 0.226 -49.15213 11.60339
classifboard | -13.09287 10.39391 -1.26 0.208 -33.46457 7.278822
limabmeeting | 3.085954 8.646161 0.36 0.721 -13.86021 20.03212
limabconsent | -14.10836 10.32817 -1.37 0.172 -34.3512 6.134476
compensplan | 11.80877 8.946295 1.32 0.187 -5.725641 29.34319
direcindemn | 4.204275 12.85933 0.33 0.744 -20.99955 29.40811
indemncont~t | -8.493403 17.03869 -0.50 0.618 -41.88861 24.90181
direcliab | -28.47976 12.28121 -2.32 0.020 -52.55049 -4.409038
cumvot | -.7138307 15.37581 -0.05 0.963 -30.84986 29.4222
limabbylaws | 14.15925 12.90114 1.10 0.272 -11.12652 39.44502
limabcharter | 15.43622 27.95228 0.55 0.581 -39.34925 70.22169
secrballot | (omitted)
supermajme~r | 17.81152 12.18287 1.46 0.144 -6.06647 41.68951
unequalvot~g | 10.5995 35.14885 0.30 0.763 -58.29098 79.48997
execsevera~e | -8.76017 12.67634 -0.69 0.490 -33.60534 16.085
antigreenm~l | -1.544717 23.71169 -0.07 0.948 -48.01878 44.92935
directduties | 33.44969 17.9182 1.87 0.062 -1.669344 68.56872
fairprice | .864597 12.10377 0.07 0.943 -22.85836 24.58755
pensionpar~e | 32.34659 36.27229 0.89 0.373 -38.74578 103.439
poisonpill | -7.023224 8.561382 -0.82 0.412 -23.80323 9.756777
silverpara~e | -3.156402 24.90082 -0.13 0.899 -51.96111 45.64831
buscomblaw | -.9687104 16.97601 -0.06 0.954 -34.24107 32.30365
cashoutlaw | -10.08382 53.66264 -0.19 0.851 -115.2607 95.09302
controlsha~w | -6.001288 16.83404 -0.36 0.721 -38.99541 26.99283
directordu~w | -19.18761 42.81866 -0.45 0.654 -103.1107 64.73543
fairpricelaw | 26.84789 18.88682 1.42 0.155 -10.1696 63.86537
recaptprof~w | 2.282536 19.43598 0.12 0.907 -35.81129 40.37636
sp500return | -36.25719 11.98639 -3.02 0.002 -59.75008 -12.7643
beta | -.3551128 .4074893 -0.87 0.384 -1.153777 .4435515
totaldebt | .0016537 .0012455 1.33 0.184 -.0007875 .0040949
roe | .0052857 .0157554 0.34 0.737 -.0255943 .0361657
peratio | .015965 .0172759 0.92 0.355 -.0178951 .0498251
liquidity | -.2929525 .8821644 -0.33 0.740 -2.021963 1.436058
currentratio | 2.384161 1.618004 1.47 0.141 -.787068 5.555391
yrendmarke~p | .0003492 .0001541 2.27 0.023 .0000471 .0006513
salesoneyr~_ | 9.302141 7.277687 1.28 0.201 -4.961863 23.56615
salesthree~h | -7.779762 16.22615 -0.48 0.632 -39.58244 24.02292
salesfivey~h | -2.039143 17.0578 -0.12 0.905 -35.47183 31.39354
opmargin | -.7747464 .4562289 -1.70 0.089 -1.668939 .1194458
ebitmargin | .6298818 .7379244 0.85 0.393 -.8164234 2.076187
ebitdamargin | .1954472 .6371915 0.31 0.759 -1.053425 1.444319
netmargin | .0990261 .2283691 0.43 0.665 -.3485691 .5466213
markettobo~o | .0964123 .2227244 0.43 0.665 -.3401196 .5329441
roa | (omitted)
currentass~s | -.0028879 .0058149 -0.50 0.619 -.0142849 .0085091
netsales | .001462 .0008586 1.70 0.089 -.0002209 .0031448
assets | .0712838 .0119957 5.94 0.000 .0477727 .0947948
bookvaluep~e | .738355 .5043415 1.46 0.143 -.2501361 1.726846
liquidatio~e | -.1109864 .0121406 -9.14 0.000 -.1347815 -.0871914
cash | -.0091562 .0058973 -1.55 0.121 -.0207148 .0024024
cashandsho~m | .0702596 .0067532 10.40 0.000 .0570236 .0834956
commshares~t | -.1115409 .0121497 -9.18 0.000 -.1353539 -.0877279
longtermdebt | -.0163349 .0052332 -3.12 0.002 -.0265919 -.006078
currentliab | -.0166132 .0059785 -2.78 0.005 -.0283309 -.0048956
totalliab | -.0709934 .0120215 -5.91 0.000 -.0945552 -.0474316
workingcap | (omitted)
dividends | -.0346647 .0190356 -1.82 0.069 -.0719738 .0026444
ebitda | .9307281 .0072418 128.52 0.000 .9165344 .9449217
netincome | .1220222 .003745 32.58 0.000 .1146821 .1293623
capex | -.1798691 .0080132 -22.45 0.000 -.1955747 -.1641634
netcashflow | -.0692219 .0083794 -8.26 0.000 -.0856452 -.0527986
marketvalue | .0013092 .0071448 0.18 0.855 -.0126943 .0153126
hhisales | 48.90659 124.8096 0.39 0.695 -195.7158 293.5289
hhiassets | 32.61442 96.56859 0.34 0.736 -156.6565 221.8854
netincome~ts | -382.2562 34.79183 -10.99 0.000 -450.4469 -314.0654
ebitdabyas~s | -3396.412 158.0025 -21.50 0.000 -3706.091 -3086.733
ebitbyassets | 3609.022 160.9161 22.43 0.000 3293.633 3924.412
netincome~es | -1.206331 4.394728 -0.27 0.784 -9.819839 7.407177
mvassets | -.0004871 .007151 -0.07 0.946 -.0145028 .0135286
bvassets | (omitted)
tobinsq | -2.322463 1.442243 -1.61 0.107 -5.149206 .5042807
divbybooke~y | 1.790651 29.69044 0.06 0.952 -56.40154 59.98284
divbynetin~e | -.7153984 1.013262 -0.71 0.480 -2.701355 1.270558
capexbyass~s | 525.8223 72.74172 7.23 0.000 383.2512 668.3935
cashandsho~s | -117.7088 36.1777 -3.25 0.001 -188.6158 -46.80181
liabbymvas~s | .4934939 .3073977 1.61 0.108 -.1089945 1.095982
longtermde~e | .5511297 1.747929 0.32 0.753 -2.874748 3.977007
totalliabb~e | .4336966 1.080608 0.40 0.688 -1.684256 2.55165
liquidity2 | -54.77267 32.11517 -1.71 0.088 -117.7173 8.171909
mvequbybvequ | -.6410019 .5380964 -1.19 0.234 -1.695651 .4136476
logmvcomms~k | 32.42151 12.40698 2.61 0.009 8.104271 56.73876
logbvassets | -64.33212 16.40679 -3.92 0.000 -96.48884 -32.1754
opnetcfbya~s | 128.9108 50.76875 2.54 0.011 29.40588 228.4157
SDopnetcfb~s | 508.3243 7965.52 0.06 0.949 -15103.81 16120.46
SDebitbyas~s | -1005.745 11906.24 -0.08 0.933 -24341.55 22330.06
SDebitdaby~s | 9941.857 16834.27 0.59 0.555 -23052.71 42936.42
_cons | 225.3514 45.47711 4.96 0.000 136.2179 314.4849
-------------+----------------------------------------------------------------
sigma_u | 99.400236
sigma_e | 96.692834
rho | .51380409 (fraction of variance due to u_i)