Omnibus and R square improvements for OLS model

Checking on this community if any one can help with this problem posted on Cross Validated.

Detailed question is as below:

                             OLS Regression Results
===============================================================================
Dep. Variable:     Losses in Thousands   R-squared:                       0.305
Model:                             OLS   Adj. R-squared:                  0.304
Method:                  Least Squares   F-statistic:                     1171.
Date:                 Fri, 20 Dec 2019   Prob (F-statistic):               0.00
Time:                         11:12:52   Log-Likelihood:                -72503.
No. Observations:                10703   AIC:                         1.450e+05
Df Residuals:                    10698   BIC:                         1.451e+05
Df Model:                            4
Covariance Type:             nonrobust
======================================================================================
coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------
const                539.6565      7.950     67.884      0.000     524.074     555.239
Age                   -6.1490      0.112    -54.971      0.000      -6.368      -5.930
Number of Vehicles    -1.7906      2.151     -0.832      0.405      -6.007       2.426
M                     97.2349      4.094     23.750      0.000      89.210     105.260
Single               136.7923      4.094     33.410      0.000     128.767     144.818
==============================================================================
Omnibus:                     7898.559   Durbin-Watson:                   2.010
Prob(Omnibus):                  0.000   Jarque-Bera (JB):           403312.043
Skew:                           3.029   Prob(JB):                         0.00
Kurtosis:                      32.456   Cond. No.                         187.
==============================================================================


Shown above are the results of an OLS model I ran in Python.

Below are my few understandings:

• Omnibus : value close to Zero, to indicate normal distribution of error

• Prob(Omnibus): Value must be close to 1 for normal error distribution

• Skew : Same as above, close to zero

• Condition Number – Indicates multicollinearity, so it must be relatively small number,something below 30. In below results, it is way above 30 but with correlation function, i couldn't see any correlation(i found one but i dropped the variable so nothing left now)

Results after logarithmic transformation of y variable.

OLS Regression Results

    Dep. Variable:     Losses in Thousands   R-squared:                       0.326
Model:                             OLS   Adj. R-squared:                  0.326
Method:                  Least Squares   F-statistic:                     1295.
Date:                 Fri, 20 Dec 2019   Prob (F-statistic):               0.00
Time:                         14:34:13   Log-Likelihood:                -9712.2
No. Observations:                10703   AIC:                         1.943e+04
Df Residuals:                    10698   BIC:                         1.947e+04
Df Model:                            4
Covariance Type:             nonrobust
======================================================================================
coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------------
const                  6.3490      0.023    281.983      0.000       6.305       6.393
Age                   -0.0203      0.000    -64.137      0.000      -0.021      -0.020
Number of Vehicles     0.0007      0.006      0.118      0.906      -0.011       0.013
M                      0.2137      0.012     18.429      0.000       0.191       0.236
Single                 0.3159      0.012     27.240      0.000       0.293       0.339
==============================================================================
Omnibus:                     1231.182   Durbin-Watson:                   1.998
Prob(Omnibus):                  0.000   Jarque-Bera (JB):             1943.765
Skew:                          -0.825   Prob(JB):                         0.00
Kurtosis:                       4.279   Cond. No.                         187.
=============================================================================


 Correlation Matrix:

    Ac_No   Age Years of Experience Number of Vehicles  Losses in Thousands Losses in Thousands_log
Ac_No   1.000000    0.008291    0.008437    -0.003056   -0.000794   -0.001057
Age 0.008291    1.000000    0.997161    0.008366    -0.442962   -0.509823
Yr Exp  0.008437    0.997161    1.000000    0.008545    -0.442115   -0.511495
No Veh  -0.003056   0.008366    0.008545    1.000000    -0.011553   -0.004839
Loss    -0.000794   -0.442962   -0.442115   -0.011553   1.000000    0.849515
Loss_l  -0.001057   -0.509823   -0.511495   -0.004839   0.849515    1.000000


Describe():

Age Number of Vehicles  M   Single
count   10703.000000    10703.000000    10703.000000    10703.000000
mean    42.519761   2.497804    0.492292    0.490984
std 18.298802   0.951530    0.499964    0.499942
min 16.000000   1.000000    0.000000    0.000000
25% 24.000000   2.000000    0.000000    0.000000
50% 42.000000   2.000000    0.000000    0.000000
75% 61.000000   3.000000    1.000000    1.000000
max 70.000000   4.000000    1.000000    1.000000
`

R-Square is also very poor in this case (0.33) though there were slight improvement with log transformation(from 0.31 to 0.33).

To get a good model and to get the values of "Omnibus" and other parameters in limit, what other things I can do?

• Thanks for putting in the work to make the question better. Reopened it. Welcome to the site :) Jan 7, 2020 at 4:59
• Thanks Dawny33.
– SKB
Jan 7, 2020 at 5:30