Hello,

i am quite new in the world of statistical problems I have read some lecture notes and books to solve my current problem, but i am note sure whether the results are appropriate. So perhaps somebody of you can help me a little bit.

Situation

I calculated the percentage change of 10 key performance indicators (KPI) for 37 enterprises over 5 years. I want to know whether one or more of these KPIs are in context with the percentage change of the enterprise value.

So We are talking about panel data

I conducted the pooled, fixed effect and random effect regression.

I am using the statistical software "R"

Code: 
> File <- plm.data(File, index=c("NAME", "PERIOD"))
> pool <- plm(formula = AK ~ UMS + EBT + EBIT + EPS + EKRBT + EKR + GKRBT + EBITM + CFM + KGV, data = File, model = "pooling")
> summary(pool)
Oneway (individual) effect Pooling Model

Call:
plm(formula = AK ~ UMS + EBT + EBIT + EPS + EKRBT + EKR + GKRBT + 
    EBITM + CFM + KGV, data = File, model = "pooling")

Balanced Panel: n=37, T=5, N=185

Residuals :
   Min. 1st Qu.  Median 3rd Qu.    Max. 
-0.6910 -0.1680 -0.0155  0.1380  1.0200 

Coefficients :
               Estimate  Std. Error t-value  Pr(>|t|)    
(Intercept) -0.06074457  0.02731679 -2.2237  0.027455 *  
UMS          0.02155862  0.02469945  0.8728  0.383954    
EBT          0.45960162  0.14602370  3.1474  0.001938 ** 
EBIT        -0.03481862  0.01558743 -2.2338  0.026773 *  
EPS          0.32004201  0.08267234  3.8712  0.000153 ***
EKRBT       -0.29844106  0.12857144 -2.3212  0.021435 *  
EKR         -0.13300907  0.03053158 -4.3564 2.254e-05 ***
GKRBT       -0.14772221  0.06619797 -2.2315  0.026924 *  
EBITM       -0.01143662  0.00711142 -1.6082  0.109603    
CFM         -0.00148743  0.00094323 -1.5770  0.116622    
KGV          0.01584729  0.00707191  2.2409  0.026299 *  
---
Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1

Total Sum of Squares:    16.875
Residual Sum of Squares: 11.25
R-Squared      :  0.33335 
      Adj. R-Squared :  0.31352 
F-statistic: 8.70046 on 10 and 174 DF, p-value: 1.7308e-11
The results of the Pooled Regression:
- The KPIs: EBT, EBIT, EPS, EKRBT, EKR, GKRBT und KGV are in context with the enterprise value
- The model explains 33,3% of the variance

Code: 
> FEM <- plm(formula = AK ~ UMS + EBT + EBIT + EPS + EKRBT + EKR + GKRBT + EBITM + CFM + KGV, data = File, model ="within", effect = "individual")
> summary(FEM)
Oneway (individual) effect Within Model

Call:
plm(formula = AK ~ UMS + EBT + EBIT + EPS + EKRBT + EKR + GKRBT + 
    EBITM + CFM + KGV, data = File, effect = "individual", model = "within")

Balanced Panel: n=37, T=5, N=185

Residuals :
    Min.  1st Qu.   Median  3rd Qu.     Max. 
-0.71700 -0.15200 -0.00857  0.13400  0.90800 

Coefficients :
        Estimate Std. Error t-value Pr(>|t|)   
UMS    0.0314726  0.0299581  1.0506 0.295300   
EBT    0.2993271  0.1983570  1.5090 0.133577   
EBIT  -0.0271353  0.0189801 -1.4297 0.155071   
EPS    0.3242736  0.0992487  3.2673 0.001370 **
EKRBT -0.1619534  0.1769449 -0.9153 0.361643   
EKR   -0.1158079  0.0377384 -3.0687 0.002589 **
GKRBT -0.2066635  0.0801468 -2.5786 0.010969 * 
EBITM -0.0005839  0.0093656 -0.0623 0.950378   
CFM   -0.0019884  0.0011233 -1.7701 0.078925 . 
KGV    0.0176208  0.0083009  2.1228 0.035560 * 
---
Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1

Total Sum of Squares:    13.506
Residual Sum of Squares: 9.9266
R-Squared      :  0.265 
      Adj. R-Squared :  0.19768 
F-statistic: 4.97549 on 10 and 138 DF, p-value: 3.7582e-06
The results of the Fixed Effect model:
- The KPIs: EPS, EKR, GKRBT, CFM und KGV are in context with the enterprise value
- The model explains 26,5% of the variance

Code: 
> pFtest(FEM, pool)

        F test for individual effects

data:  AK ~ UMS + EBT + EBIT + EPS + EKRBT + EKR + GKRBT + EBITM + CFM +  ...
F = 0.51098, df1 = 36, df2 = 138, p-value = 0.9895
alternative hypothesis: significant effects
The Result of the F-Test is that there is no subject specific influence, so the pooled OLS is better then the Fixed Effect model.

No subject specific influence while using 37 enterprises ???

Code: 
> REM <- plm(formula = AK ~ UMS + EBT + EBIT + EPS + EKRBT + EKR + GKRBT + EBITM + CFM + KGV, data = File, model ="random", effect = "individual", random.method="amemiya")
> summary(REM)
Oneway (individual) effect Random Effect Model 
   (Amemiya's transformation)

Call:
plm(formula = AK ~ UMS + EBT + EBIT + EPS + EKRBT + EKR + GKRBT + 
    EBITM + CFM + KGV, data = File, effect = "individual", model = "random", 
    random.method = "amemiya")

Balanced Panel: n=37, T=5, N=185

Effects:
                  var std.dev share
idiosyncratic 0.07193 0.26820     1
individual    0.00000 0.00000     0
theta:  0  

Residuals :
   Min. 1st Qu.  Median 3rd Qu.    Max. 
-0.6910 -0.1680 -0.0155  0.1380  1.0200 

Coefficients :
               Estimate  Std. Error t-value  Pr(>|t|)    
(Intercept) -0.06074457  0.02731679 -2.2237  0.027455 *  
UMS          0.02155862  0.02469945  0.8728  0.383954    
EBT          0.45960162  0.14602370  3.1474  0.001938 ** 
EBIT        -0.03481862  0.01558743 -2.2338  0.026773 *  
EPS          0.32004201  0.08267234  3.8712  0.000153 ***
EKRBT       -0.29844106  0.12857144 -2.3212  0.021435 *  
EKR         -0.13300907  0.03053158 -4.3564 2.254e-05 ***
GKRBT       -0.14772221  0.06619797 -2.2315  0.026924 *  
EBITM       -0.01143662  0.00711142 -1.6082  0.109603    
CFM         -0.00148743  0.00094323 -1.5770  0.116622    
KGV          0.01584729  0.00707191  2.2409  0.026299 *  
---
Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1

Total Sum of Squares:    16.875
Residual Sum of Squares: 11.25
R-Squared      :  0.33335 
      Adj. R-Squared :  0.31352 
F-statistic: 8.70046 on 10 and 174 DF, p-value: 1.7308e-11
The results of the Random Effect Model Regression:
- The KPIs: EBT, EBIT, EPS, EKRBT, EKR, GKRBT und KGV are in context with the enterprise value
- The model explains 33,3% of the variance

Code: 
> phtest(FEM, REM)

        Hausman Test

data:  AK ~ UMS + EBT + EBIT + EPS + EKRBT + EKR + GKRBT + EBITM + CFM +  ...
chisq = 7.246, df = 10, p-value = 0.702
alternative hypothesis: one model is inconsistent
The result of the Hausman Test is, that the random effect model is more usefull then fixed effect model

Code: 
> summary(fixef(FEM))
                               Estimate Std. Error t-value Pr(>|t|)  
UNTERNEHMEN -0.1623027  0.1219950 -1.3304  0.18339  
UNTERNEHMEN       -0.1951134  0.1493709 -1.3062  0.19147  
UNTERNEHMEN       -0.0803891  0.1277292 -0.6294  0.52911  
UNTERNEHMEN  -0.0383305  0.1219140 -0.3144  0.75321  
UNTERNEHMEN            -0.0033085  0.1222359 -0.0271  0.97841  
UNTERNEHMEN  0.0503065  0.1286474  0.3910  0.69577  
UNTERNEHMEN -0.0541861  0.1232551 -0.4396  0.66021  
UNTERNEHMEN -0.0403202  0.1400175 -0.2880  0.77337  
UNTERNEHMEN     0.0191747  0.1263086  0.1518  0.87934  
UNTERNEHMEN -0.0220647  0.1226561 -0.1799  0.85724  
UNTERNEHMEN   -0.1586823  0.1222933 -1.2976  0.19444  
UNTERNEHMEN   -0.0469532  0.1215327 -0.3863  0.69924  
UNTERNEHMEN                    0.0280940  0.1519753  0.1849  0.85334  
UNTERNEHMEN             -0.0634890  0.1230360 -0.5160  0.60584  
UNTERNEHMEN                -0.1812572  0.1241798 -1.4596  0.14439  
UNTERNEHMEN  0.1237957  0.1451925  0.8526  0.39386  
UNTERNEHMEN    -0.1403343  0.1222436 -1.1480  0.25097  
UNTERNEHMEN    0.1207582  0.1276013  0.9464  0.34396  
UNTERNEHMEN     -0.0298196  0.1220226 -0.2444  0.80694  
UNTERNEHMEN       -0.0384329  0.1218950 -0.3153  0.75254  
UNTERNEHMEN  -0.0624917  0.1294618 -0.4827  0.62931  
UNTERNEHMEN         -0.1491432  0.1367685 -1.0905  0.27550  
UNTERNEHMEN              0.1604043  0.1271040  1.2620  0.20695  
UNTERNEHMEN              -0.2342410  0.1214463 -1.9288  0.05376 .
UNTERNEHMEN                  0.0850191  0.1298292  0.6549  0.51256  
UNTERNEHMEN                  0.0513719  0.1215813  0.4225  0.67264  
UNTERNEHMEN      -0.0909503  0.1233526 -0.7373  0.46093  
UNTERNEHMEN       -0.0893145  0.1219306 -0.7325  0.46386  
UNTERNEHMEN    -0.0176131  0.1345790 -0.1309  0.89587  
UNTERNEHMEN             0.1099560  0.1217784  0.9029  0.36657  
UNTERNEHMEN              -0.0715216  0.1221160 -0.5857  0.55809  
UNTERNEHMEN      0.0244789  0.1210396  0.2022  0.83973  
UNTERNEHMEN    -0.0506230  0.1215979 -0.4163  0.67718  
UNTERNEHMEN         0.0394862  0.1399703  0.2821  0.77786  
UNTERNEHMEN -0.1121713  0.1229228 -0.9125  0.36149  
UNTERNEHMEN -0.0533292  0.1225155 -0.4353  0.66336  
UNTERNEHMEN          -0.1082216  0.1362796 -0.7941  0.42713  
---
Signif. codes:  0 *** 0.001 ** 0.01 * 0.05 . 0.1   1
I am very confused about the non subject influence influence in this model. Did i do anaything wrong?

Moreover the results of the pooled model and random effect model are exactly the same. That looks also very strange.