Multivariable Linear Regression Coefficient

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I have a dataset something like this:

A       B     C      D      E         coef to A
1900  0.23   0.98   0.55    1         B  51
1530  0.47   0.76   0.46    1         C  62
2300  0.26   0.86   0.13    0         D  53
1430  0.24   0.66   0.76    0         E  55
2440  0.05   0.88   0.45    1     

And when I form my model (with StatsModels Python) to predict A

I get E with a 100+ number for a coefficient, others around 51-56. E is a bivariable (0, 1) but not sure how I should transform it if I should at all. How should I handle this? Figure With E

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                tuition   R-squared (uncentered):                   0.927
Model:                            OLS   Adj. R-squared (uncentered):              0.927
Method:                 Least Squares   F-statistic:                              3659.
Date:                Tue, 10 Dec 2019   Prob (F-statistic):                        0.00
Time:                        14:30:59   Log-Likelihood:                         -10794.
No. Observations:                1155   AIC:                                  2.160e+04
Df Residuals:                    1151   BIC:                                  2.162e+04
Df Model:                           4                                                  
Covariance Type:            nonrobust                                                  
==================================================================================
                     coef    std err          t      P>|t|      [0.025      0.975]
----------------------------------------------------------------------------------
pcttop25          51.4044      4.607     11.157      0.000      42.365      60.444
graduat           57.3034      4.684     12.235      0.000      48.114      66.493
alumni            56.7086      8.162      6.948      0.000      40.695      72.723
public/private  3120.7245    192.468     16.214      0.000    2743.097    3498.352
==============================================================================
Omnibus:                       16.130   Durbin-Watson:                   1.461
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               23.647
Skew:                           0.127   Prob(JB):                     7.33e-06
Kurtosis:                       3.653   Cond. No.                         204.
==============================================================================

Without E

                                 OLS Regression Results                                
=======================================================================================
Dep. Variable:                tuition   R-squared (uncentered):                   0.910
Model:                            OLS   Adj. R-squared (uncentered):              0.910
Method:                 Least Squares   F-statistic:                              3903.
Date:                Tue, 10 Dec 2019   Prob (F-statistic):                        0.00
Time:                        14:23:06   Log-Likelihood:                         -10913.
No. Observations:                1155   AIC:                                  2.183e+04
Df Residuals:                    1152   BIC:                                  2.185e+04
Df Model:                           3                                                  
Covariance Type:            nonrobust                                                  
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
pcttop25      43.3553      5.075      8.544      0.000      33.399      53.312
graduat       85.6925      4.813     17.806      0.000      76.250      95.135
alumni        90.4125      8.744     10.340      0.000      73.256     107.569
==============================================================================
Omnibus:                       16.562   Durbin-Watson:                   1.479
Prob(Omnibus):                  0.000   Jarque-Bera (JB):               17.476
Skew:                           0.257   Prob(JB):                     0.000160
Kurtosis:                       3.314   Cond. No.                         8.65
==============================================================================