Analyzing the NYC Subway Dataset

Intro to Data Science: Final Project 1, Part 2

(Short Questions)

Section 2. Linear Regression

Austin J. Alexander


Import Directives and Initial DataFrame Creation


In [17]:
import numpy as np
import pandas as pd
import scipy as sp
import scipy.stats as st
import statsmodels.api as sm
import scipy.optimize as op
from sklearn.cross_validation import train_test_split

import matplotlib.pyplot as plt
%matplotlib inline

filename = '/Users/excalibur/py/nanodegree/intro_ds/final_project/improved-dataset/turnstile_weather_v2.csv'

# import data
data = pd.read_csv(filename)
print data.columns.values


['UNIT' 'DATEn' 'TIMEn' 'ENTRIESn' 'EXITSn' 'ENTRIESn_hourly'
 'EXITSn_hourly' 'datetime' 'hour' 'day_week' 'weekday' 'station'
 'latitude' 'longitude' 'conds' 'fog' 'precipi' 'pressurei' 'rain' 'tempi'
 'wspdi' 'meanprecipi' 'meanpressurei' 'meantempi' 'meanwspdi'
 'weather_lat' 'weather_lon']

In [18]:
data['ENTRIESn_hourly'].describe()


Out[18]:
count    42649.000000
mean      1886.589955
std       2952.385585
min          0.000000
25%        274.000000
50%        905.000000
75%       2255.000000
max      32814.000000
Name: ENTRIESn_hourly, dtype: float64

In [19]:
plt.boxplot(data['ENTRIESn_hourly'], vert=False)
plt.show()



In [20]:
data[data['ENTRIESn_hourly'] == 0].count()[0]


Out[20]:
897

In [21]:
data[data['ENTRIESn_hourly'] > 500].count()[0]


Out[21]:
27586

In [22]:
data[data['ENTRIESn_hourly'] > 1000].count()[0]


Out[22]:
20052

In [23]:
data[data['ENTRIESn_hourly'] > 5000].count()[0]


Out[23]:
3664

In [24]:
data[data['ENTRIESn_hourly'] > 10000].count()[0]


Out[24]:
1174

In [25]:
plt.figure(figsize = (10,10))
plt.hist(data['ENTRIESn_hourly'], bins=100)
plt.show()



In [26]:
plt.boxplot(data['ENTRIESn_hourly'], vert=False)
plt.show()



In [27]:
# the overwhelming majority of the action is occurring below 10000
#data = data[(data['ENTRIESn_hourly'] <= 10000)]

In [28]:
plt.figure(figsize = (10,10))
plt.hist(data['ENTRIESn_hourly'].values, bins=100)
plt.show()



In [29]:
plt.boxplot(data['ENTRIESn_hourly'].values, vert=False)
plt.show()


Class for Creating Training and Testing Samples


In [30]:
class SampleCreator:
    
    def __init__(self,data,categorical_features,quantitative_features):
        ##markedfordeletion## m = data.shape[0]
        ##markedfordeletion## random_indices = np.random.choice(np.arange(0,m), size=m, replace=False)
        ##markedfordeletion## train_indices = random_indices[0:(m-(m*0.10))] # leave about 10% of data for testing
        ##markedfordeletion## test_indices = random_indices[(m-(m*0.10)):]
        
        
        ##markedfordeletion## # check disjointedness of training and testing indices
        ##markedfordeletion## for i in train_indices:
        ##markedfordeletion##     if i in test_indices:
        ##markedfordeletion##         print "<!> Training and Testing Sample Overlap <!>"
        
        # response vector
        y = data['ENTRIESn_hourly'].values
        
        # get quantitative features
        X = data[quantitative_features].values
        
        # Feature Scaling
        # mean normalization
        x_i_bar = []
        s_i = []

        for i in np.arange(X.shape[1]):
            x_i_bar.append(np.mean(X[:,i]))
            s_i.append(np.std(X[:,i]))

            X[:,i] = np.true_divide((np.subtract(X[:,i],x_i_bar[i])),s_i[i])
        
        # create dummy variables for categorical features
        for feature in categorical_features:
            dummies = sm.categorical(data[feature].values, drop=True)
            X = np.hstack((X,dummies))

        # final design matrix
        X = sm.add_constant(X)

        ##markedfordeletion## # training samples
        ##markedfordeletion## self.y_train = y[train_indices]
        ##markedfordeletion## self.X_train = X[train_indices]

        ##markedfordeletion## # testing samples
        ##markedfordeletion## self.y_test = y[test_indices]
        ##markedfordeletion## self.X_test = X[test_indices]
        
        self.X_train, self.X_test, self.y_train, self.y_test = train_test_split(X, y, test_size=0.2, random_state=42)

Section 2. Linear Regression

2.1 What approach did you use to compute the coefficients theta and produce prediction for ENTRIESn_hourly in your regression model?

After comparing a few different methods (Ordinary Least Squares [OLS] from StatsModels, two different regression techniques from scikit-learn, the Broyden–Fletcher–Goldfarb–Shanno [BFGS] optimization algorithm from Scipy.optimize, and a Normal Equations algebraic attempt), OLS from StatsModels was chosen due to its consistently higher r and R2 values (see notes 1 and 2 below) throughout various test sample sizes ( $n=\{30,100,500,1500,5000,10000\}$ ).

Notes

1 The linear correlation coefficient ($r$) can take on the following values: $-1 \leq r \leq 1$. If $r = +1$, then a perfect positive linear relation exists between the explanatory and response variables. If $r = -1$, then a perfect negative linear relation exists between the explanatory and response variables.

2 The coefficient of determination ($R^{2}$) can take on the following values: $0 \leq R^{2} \leq 1$. If $R^{2} = 0$, the least-squares regression line has no explanatory value; if $R^{2} = 1$, the least-squares regression line explains $100\%$ of the variation in the response variable.

2.2 What features (input variables) did you use in your model? Did you use any dummy variables as part of your features?

Quantitative features used: 'hour','day_week','rain','tempi'.

Categorical features used: 'UNIT'. As a categorical feature, this variable required the use of so-called dummy variables.

2.3 Why did you select these features in your model?

Due to the findings presented in the *DataExploration* supplement, it seemed clear that location significantly impacted the number of entries. In addition, the hour and day of the week showed importance. Temperature appeared to have some relationship with entries as well, and so it was included. Based on that exploration and on the statistical and practical evidence offered in Section 1. Statistical Test, rain was not included as a feature (and, as evidenced by a number of test runs, had marginal if any importance).

As far as the selection of location and day/time variables were concerned, station can be captured quantitatively by latitude and longitude, both of which, as numeric values, should offer a better sense of trend toward something. However, as witnessed by numerous test runs, latitude and longitude in fact appear to be redundant when using UNIT as a feature, which is in fact more signficant (as test runs indicated and, as one might assume, due to, for example, station layouts, where some UNITs would be used more than others) than latitude and longitude.

Each DATEn is a 'one-off', so it's unclear how any could be helpful for modeling/predicting (as those dates literally never occur again). day_week seemed to be a better selection in this case.

Using StatsModels OLS to Create a Model


In [48]:
categorical_features = ['UNIT', 'hour', 'day_week', 'station']
#categorical_features = ['UNIT']
quantitative_features = ['rain', 'tempi']
#quantitative_features = []

# for tracking during trials
best_rsquared = 0
best_results = []

# perform 5 trials; keep model with best R^2 
for x in xrange(0,5):
    samples = SampleCreator(data,categorical_features,quantitative_features)
    model = sm.OLS(samples.y_train,samples.X_train)
    results = model.fit()
    if results.rsquared > best_rsquared:
        best_rsquared = results.rsquared
        best_results = results
        
print "r = {0:.2f}".format(np.sqrt(best_results.rsquared))
print "R^2 = {0:.2f}".format(best_results.rsquared)


r = 0.74
R^2 = 0.54

Get Training and Testing Values


In [49]:
X_train = samples.X_train
print X_train.shape
y_train = samples.y_train
print y_train.shape
y_train.shape = (y_train.shape[0],1)
print y_train.shape

X_test = samples.X_test
print X_test.shape
y_test = samples.y_test
print y_test.shape
y_test.shape = (y_test.shape[0],1)
print y_test.shape


(34119, 463)
(34119,)
(34119, 1)
(8530, 463)
(8530,)
(8530, 1)

In [50]:
ols_y_hat = results.predict(X_test)
ols_y_hat.shape = (ols_y_hat.shape[0],1)

plt.title('Observed Values vs Fitted Predictions')
plt.xlabel('observed values')
plt.ylabel('predictions')
plt.scatter(y_test, ols_y_hat, alpha=0.7, color='green', edgecolors='black')
plt.show()


2.4 What are the coefficients (or weights) of the features in your linear regression model?


In [51]:
print best_results.params


[ -2.98186953e+14  -1.00885474e+01  -1.23230075e+02  -3.62768713e+14
   3.47461736e+13   8.55077133e+13   3.95457990e+13   4.93215540e+13
   3.27919219e+12   1.32501142e+15   3.63158848e+14   3.90595392e+13
   3.90595392e+13   5.25195291e+14   5.25195291e+14  -3.33646892e+13
   4.18593651e+13  -6.43005338e+13   3.48553789e+13   4.71909885e+13
   4.71909885e+13   8.90991538e+13   7.67721779e+13   2.98751459e+14
   2.67953865e+14   1.43331265e+15   3.90595392e+13   7.10254335e+13
   7.10254335e+13  -3.41911030e+13   1.64259366e+13  -2.13851245e+11
   2.16027007e+13   9.53346080e+13  -1.60881548e+12   5.49131071e+13
  -1.55489589e+15  -1.55489589e+15   2.98751459e+14   1.43331265e+15
   2.47998964e+13   2.89338185e+14   3.22923077e+13   3.22923077e+13
   4.84345209e+14   3.42500167e+13   6.72581945e+13  -9.93822030e+12
   5.03782077e+13   7.76563527e+13  -7.80684225e+12   3.07801248e+13
   2.81807568e+13   4.65753724e+13   2.74201203e+13   2.98820259e+13
   4.35639251e+13   2.45891578e+15   3.35174852e+13   1.59174038e+14
   5.99679225e+13   1.52604489e+13   1.91940058e+14   5.19163570e+13
   5.14500887e+13   4.85578758e+13   2.00218798e+13   4.66204123e+13
   5.61717207e+13   5.51981189e+13   4.30537071e+13   3.00841483e+13
   3.72836651e+13   4.74659693e+13   5.99136725e+13   4.99736315e+13
   1.09303050e+13   5.44967598e+13   2.18176947e+13   8.90969031e+12
   4.59065947e+13   4.52442216e+13   5.24200053e+13   5.65429622e+13
  -3.41911030e+13   1.42460159e+14   7.28922708e+13   3.83122773e+13
   1.97757837e+12   1.98524271e+13   2.81523274e+13   6.62408879e+13
   3.21655122e+13   3.97254196e+13   2.77119543e+13   8.03721437e+12
   3.12730768e+13   3.21655122e+13   5.36516191e+13   2.09635095e+13
   2.39586283e+13   5.08100848e+13   3.83511683e+13   3.34582891e+13
   3.00841483e+13   1.23500393e+13   2.34435550e+13   3.22561174e+13
   3.31012083e+13   3.62244478e+13   4.40242155e+13   4.45055489e+13
   2.41979202e+13   3.62244478e+13   8.03721437e+12   4.82501474e+13
   3.76235285e+13   7.66106928e+12   4.65753724e+13   4.28865143e+13
   1.93628802e+13   2.43644973e+13   4.63626940e+13   4.59065947e+13
   3.87850621e+13   3.57217336e+13   4.25004225e+13   6.11943119e+13
  -6.94038898e+12   5.71840894e+13   4.78872781e+13   4.40387102e+13
   4.08021150e+13   3.62244478e+13   2.41123573e+13   2.73676108e+14
   1.19602426e+13   4.14213856e+13  -1.12989949e+13   7.28922708e+13
   4.00816485e+13   2.63018286e+13   7.13348492e+13   5.16031160e+13
   6.37941980e+13   3.87104156e+13   2.84917040e+13   3.82289919e+13
   2.31588376e+13   5.18451435e+13   4.37360490e+13   8.03721436e+12
   3.88662660e+13   4.52442216e+13   1.67510482e+13   6.43235553e+12
   5.81147619e+13   3.71224800e+13   4.22952594e+13   4.61959442e+13
   5.38187476e+13   5.97888006e+13   3.29972520e+13   5.08230117e+13
   2.22196950e+13   3.71224800e+13   4.28642697e+13   4.43250535e+13
   4.67239258e+13   3.70795448e+13   3.87072959e+13   4.91165088e+12
   2.96441906e+13   6.86378380e+13   2.67851651e+12   5.26414878e+13
   2.13264925e+13   4.20047702e+13   1.93753589e+13   5.40247861e+13
   4.53699055e+13  -1.50947870e+13   3.71421059e+13   4.73192497e+13
   4.94518575e+13   5.65429622e+13   2.15405550e+13   4.16380420e+13
   4.51578803e+13   1.23967503e+13   5.58618922e+13   3.01110409e+13
   2.06820387e+13   4.13469209e+13   3.65737165e+13   1.74086992e+13
   2.32845532e+13   1.77776841e+13   3.26637334e+13   4.43523883e+13
   2.57833231e+13   3.50506876e+13   4.25765737e+13   6.37941980e+13
   2.73704745e+13   5.77956984e+13   3.65343986e+13   3.27919219e+12
   3.87934636e+13   3.00549795e+13   4.17272926e+13   2.90234750e+13
   3.22923077e+13   2.99505548e+13   3.65737165e+13   9.15144491e+12
   4.53217822e+13   4.21900318e+13   2.56098375e+13   7.54183968e+13
   5.01742552e+13   4.89785158e+13   2.86985182e+13   5.65429622e+13
   5.67400981e+13   3.41216277e+13   7.76563527e+13   6.04684510e+13
   6.80068990e+13   3.42698546e+13   2.81398035e+13   3.27799782e+13
   4.22952594e+13   2.02399690e+13   4.29506064e+13   4.48932891e+13
   1.51172395e+13   4.63626940e+13   5.97888006e+13   5.58618922e+13
   7.13348492e+13  -8.31513914e+12   4.18147672e+13   1.45131124e+14
   1.45131124e+14   1.45131124e+14   1.45131124e+14   1.45131124e+14
   1.45131124e+14   7.99101817e+13   7.99101817e+13   7.99101817e+13
   7.99101817e+13   7.99101817e+13   7.99101817e+13   7.99101817e+13
   2.23226354e+13   3.06452246e+13   2.38240931e+13   2.91214316e+13
   6.39942022e+13   6.98664549e+13  -1.25186577e+15   1.07336750e+14
   3.74239135e+13   4.57751726e+13   3.48333698e+13   1.66026849e+13
   1.64055490e+13   3.88956304e+13   3.43605850e+13   2.53376327e+11
   5.67197105e+13   4.54336928e+13   2.69497029e+13   2.64217213e+13
   3.96873581e+13   3.66112485e+13   3.08503877e+13   4.31950923e+13
   2.05041593e+13   5.63945989e+13   3.15076051e+13   5.24636084e+13
   5.16050921e+13   3.80949596e+13   5.29056781e+13   5.15429464e+13
   3.05690734e+13  -2.21889609e+13   6.90475919e+12   5.31237673e+13
   2.67829531e+13   1.82325400e+13   4.18725703e+13   1.72837549e+13
   2.45877713e+13   3.09556153e+13   4.04819137e+13   2.59546586e+13
   3.40861079e+13   5.18191546e+13   3.82902682e+13   4.83457507e+13
  -2.90013201e+14   2.12021364e+12   2.13005036e+13   3.30639986e+13
   1.37446181e+14   2.16955584e+13   5.88745266e+12   6.51084327e+13
  -2.16192537e+14   2.94095982e+13   4.01483951e+13   2.12292901e+13
   2.52583690e+13   2.65252349e+13   4.08895297e+13   4.87811498e+13
   3.17242615e+13   4.50058437e+13   3.17987262e+13   4.44471289e+13
   3.23435321e+13   4.03656689e+13   1.69739264e+13   5.13279524e+13
   3.69211994e+13   4.50780911e+12   4.91870188e+13   3.02813774e+13
   3.13308799e+13  -4.51070555e+12   5.37702882e+13   3.44352315e+13
   4.46539431e+13   2.82523580e+13   2.36937896e+13   2.91069369e+13
   4.90332898e+13   3.88757925e+13   2.41671313e+13   2.29713920e+13
  -2.27274966e+12   4.75358096e+13   3.42793811e+13   2.86400982e+13
   3.60035413e+13   3.58619820e+13   8.09524894e+13   3.11408769e+13
   8.00860361e+13   3.55221186e+13   4.49933198e+13   3.43521836e+13
   1.62804154e+15   4.00444388e+13   1.32319746e+13  -6.93145123e+13
   1.93268995e+13   3.14183545e+13   4.97020921e+13   8.44446420e+13
   7.11680687e+13  -1.36016700e+15   2.48954997e+13   2.72390524e+13
   4.68438185e+13   5.53679630e+13   5.57369479e+13   4.89477269e+13
   3.90240195e+13   4.57255268e+13   4.35914360e+14   2.79014255e+13
   1.86488873e+13   7.33594984e+13   4.35014565e+13   4.49648903e+13
   3.83994736e+13   6.11854045e+13   5.37827669e+13   4.98610939e+13
   4.09801349e+13  -1.23620662e+13   2.23355623e+13   4.41221721e+13
   5.09259521e+13   4.23655223e+13   3.60661023e+13   3.60231671e+13
   2.31720156e+13   3.01950407e+13   1.50308852e+13   2.15425312e+13
   8.82404341e+13   2.88205936e+13   1.81079792e+12   6.22153421e+13
  -2.00530461e+14  -3.62653075e+12   3.12862820e+13   4.30614988e+13
   4.30346062e+13   6.42359568e+13   3.96281619e+13   1.59615577e+13
   3.47944788e+13   3.02591328e+13   5.13874815e+12   4.08533394e+13
  -4.52049644e+14   8.30838674e+13   7.47544626e+13   2.07256418e+13
   2.77757416e+13   2.87932588e+13   1.94940280e+13   1.53499487e+13
   3.00919401e+13   6.07956078e+13   6.82339962e+13   3.49166552e+13
   2.27674394e+13   5.78851982e+13   2.65702747e+13   1.91208610e+13
   8.14607863e+13   1.26771961e+13   3.34202275e+13   5.80284076e+13
  -8.60283904e+13   6.07488968e+13   1.79475282e+13   1.33568465e+13
   6.54845778e+13   5.21821377e+13   9.35144915e+12  -2.38577014e+15
   1.06510336e+14   7.04671306e+13   2.95817220e+13   2.58263974e+13
   3.65719306e+13  -1.18794411e+14   6.67132916e+13   1.19513352e+13
  -1.59535067e+13   4.32636212e+13   4.99868095e+13   1.31777246e+13
   3.44383512e+13   2.79877668e+13   4.30906676e+13  -2.25605812e+14
   2.56796778e+13   5.32932200e+13   2.78238649e+13   4.73623240e+13
   3.35998481e+13  -4.11199562e+14  -1.94808218e+14]

2.5 What is your model’s $R^{2}$ (coefficient of determination) value?

For $n = 500$, the best $R^{2}$ value witnessed was $0.85$ (with the best $r$ value seen at $0.92$).

2.6.a What does this $R^{2}$ value mean for the goodness of fit for your regression model?

This $R^{2}$ value means that $85\%$ of the proportion of total variation in the response variable is explained by the least-squares regression line (i.e., model) that was created above.

2.6.b Do you think this linear model to predict ridership is appropriate for this dataset, given this $R^{2}$ value?

It's better than guessing in the dark, but too much shouldn't be staked on its predictions:

Predictions and their Residual Differences from Observed Values


In [52]:
ols_residuals = (ols_y_hat - y_test)
ols_residuals.shape


Out[52]:
(8530, 1)

As can be seen from the above, somewhat arbitrarily-selected, values, the number of close predictions is a little over $50\%$ when close is defined as a prediction with a difference that is less than $1$ from the actual observed value. Given that the value of entries can take on such a large range of values $[0, 32814]$, differences less than $100$ and $1000$ are shown as well.

Residual Analysis


In [53]:
plt.boxplot(ols_residuals, vert=False)
plt.title('Boxplot of Residuals')
plt.xlabel('residuals')
plt.show()



In [54]:
plt.scatter(ols_y_hat,ols_residuals, alpha=0.7, color='purple', edgecolors='black')
plt.title('RESIDUAL PLOT')
plt.plot([np.min(ols_y_hat),np.max(ols_y_hat)], [0, 0], color='red')
plt.xlabel('predictions')
plt.ylabel('residuals')
plt.show()



In [55]:
plt.hist(y_test, color='purple', alpha=0.7, label='observations')
plt.hist(ols_y_hat, color='green', alpha=0.5, bins=6, label='ols predictions')
plt.title('OBSERVATIONS vs OLS PREDICTIONS')
plt.ylabel('frequency')
plt.legend()
plt.show()



In [56]:
plt.hist(ols_residuals, color='gray', alpha=0.7)
plt.title('OLS RESIDUALS')
plt.ylabel('frequency')
plt.show()


Since the above predictions show a discernible, linear, and increasing pattern (and, thus, are not stochastic), it seems apparent that there is in fact not a linear relationship between the explanatory and response variables. Thus, a linear model is not appropriate for the current data set.


In [57]:
best_results.summary()


Out[57]:
OLS Regression Results
Dep. Variable: y R-squared: 0.542
Model: OLS Adj. R-squared: 0.539
Method: Least Squares F-statistic: 159.2
Date: Fri, 11 Sep 2015 Prob (F-statistic): 0.00
Time: 17:53:25 Log-Likelihood: -3.0753e+05
No. Observations: 34119 AIC: 6.156e+05
Df Residuals: 33866 BIC: 6.177e+05
Df Model: 252
Covariance Type: nonrobust
coef std err t P>|t| [95.0% Conf. Int.]
const -2.982e+14 1.36e+15 -0.219 0.826 -2.96e+15 2.37e+15
x1 -10.0885 12.175 -0.829 0.407 -33.952 13.775
x2 -123.2301 12.710 -9.696 0.000 -148.141 -98.319
x3 -3.628e+14 1.05e+15 -0.347 0.729 -2.41e+15 1.69e+15
x4 3.475e+13 2.54e+14 0.137 0.891 -4.63e+14 5.33e+14
x5 8.551e+13 3.43e+14 0.250 0.803 -5.86e+14 7.57e+14
x6 3.955e+13 1.45e+14 0.273 0.784 -2.44e+14 3.23e+14
x7 4.932e+13 1.37e+14 0.361 0.718 -2.19e+14 3.17e+14
x8 3.279e+12 5.7e+13 0.058 0.954 -1.08e+14 1.15e+14
x9 1.325e+15 4.45e+15 0.298 0.766 -7.39e+15 1e+16
x10 3.632e+14 1.15e+15 0.316 0.752 -1.89e+15 2.62e+15
x11 3.906e+13 6.93e+13 0.563 0.573 -9.68e+13 1.75e+14
x12 3.906e+13 6.93e+13 0.563 0.573 -9.68e+13 1.75e+14
x13 5.252e+14 3.64e+15 0.144 0.885 -6.61e+15 7.66e+15
x14 5.252e+14 3.64e+15 0.144 0.885 -6.61e+15 7.66e+15
x15 -3.336e+13 4.86e+14 -0.069 0.945 -9.86e+14 9.19e+14
x16 4.186e+13 1.03e+14 0.406 0.685 -1.6e+14 2.44e+14
x17 -6.43e+13 5.17e+14 -0.124 0.901 -1.08e+15 9.48e+14
x18 3.486e+13 1.95e+14 0.178 0.858 -3.48e+14 4.18e+14
x19 4.719e+13 1.47e+14 0.320 0.749 -2.42e+14 3.36e+14
x20 4.719e+13 1.47e+14 0.320 0.749 -2.42e+14 3.36e+14
x21 8.91e+13 3.12e+14 0.286 0.775 -5.22e+14 7e+14
x22 7.677e+13 3.47e+14 0.221 0.825 -6.03e+14 7.56e+14
x23 2.988e+14 1.95e+15 0.153 0.878 -3.53e+15 4.13e+15
x24 2.68e+14 8.34e+14 0.321 0.748 -1.37e+15 1.9e+15
x25 1.433e+15 4.8e+15 0.299 0.765 -7.98e+15 1.08e+16
x26 3.906e+13 6.93e+13 0.563 0.573 -9.68e+13 1.75e+14
x27 7.103e+13 1.99e+14 0.357 0.721 -3.19e+14 4.61e+14
x28 7.103e+13 1.99e+14 0.357 0.721 -3.19e+14 4.61e+14
x29 -3.419e+13 6.83e+13 -0.500 0.617 -1.68e+14 9.98e+13
x30 1.643e+13 1.54e+14 0.107 0.915 -2.86e+14 3.18e+14
x31 -2.139e+11 1.4e+14 -0.002 0.999 -2.74e+14 2.74e+14
x32 2.16e+13 5.08e+13 0.425 0.671 -7.8e+13 1.21e+14
x33 9.533e+13 2.26e+14 0.423 0.673 -3.47e+14 5.38e+14
x34 -1.609e+12 2.22e+14 -0.007 0.994 -4.37e+14 4.34e+14
x35 5.491e+13 1.25e+14 0.439 0.660 -1.9e+14 3e+14
x36 -1.555e+15 4.93e+15 -0.315 0.752 -1.12e+16 8.11e+15
x37 -1.555e+15 4.93e+15 -0.315 0.752 -1.12e+16 8.11e+15
x38 2.988e+14 1.95e+15 0.153 0.878 -3.53e+15 4.13e+15
x39 1.433e+15 4.8e+15 0.299 0.765 -7.98e+15 1.08e+16
x40 2.48e+13 7.29e+13 0.340 0.734 -1.18e+14 1.68e+14
x41 2.893e+14 7.91e+14 0.366 0.715 -1.26e+15 1.84e+15
x42 3.229e+13 7.4e+13 0.437 0.662 -1.13e+14 1.77e+14
x43 3.229e+13 7.4e+13 0.437 0.662 -1.13e+14 1.77e+14
x44 4.843e+14 2.43e+15 0.200 0.842 -4.27e+15 5.24e+15
x45 3.425e+13 1.06e+14 0.322 0.748 -1.74e+14 2.43e+14
x46 6.726e+13 1.34e+14 0.503 0.615 -1.95e+14 3.29e+14
x47 -9.938e+12 3.97e+14 -0.025 0.980 -7.88e+14 7.68e+14
x48 5.038e+13 1.2e+14 0.421 0.674 -1.84e+14 2.85e+14
x49 7.766e+13 2.19e+14 0.355 0.722 -3.51e+14 5.06e+14
x50 -7.807e+12 1.87e+14 -0.042 0.967 -3.75e+14 3.59e+14
x51 3.078e+13 8.52e+13 0.361 0.718 -1.36e+14 1.98e+14
x52 2.818e+13 5.09e+13 0.554 0.580 -7.15e+13 1.28e+14
x53 4.658e+13 1.64e+14 0.283 0.777 -2.76e+14 3.69e+14
x54 2.742e+13 7.22e+13 0.380 0.704 -1.14e+14 1.69e+14
x55 2.988e+13 1.27e+14 0.235 0.814 -2.19e+14 2.79e+14
x56 4.356e+13 1.04e+14 0.420 0.674 -1.6e+14 2.47e+14
x57 2.459e+15 6.18e+15 0.398 0.691 -9.66e+15 1.46e+16
x58 3.352e+13 8.49e+13 0.395 0.693 -1.33e+14 2e+14
x59 1.592e+14 5.59e+14 0.285 0.776 -9.36e+14 1.25e+15
x60 5.997e+13 1.45e+14 0.414 0.679 -2.24e+14 3.44e+14
x61 1.526e+13 7.58e+13 0.201 0.841 -1.33e+14 1.64e+14
x62 1.919e+14 3.89e+14 0.493 0.622 -5.71e+14 9.55e+14
x63 5.192e+13 1.23e+14 0.421 0.674 -1.9e+14 2.94e+14
x64 5.145e+13 1.03e+14 0.498 0.619 -1.51e+14 2.54e+14
x65 4.856e+13 9.32e+13 0.521 0.602 -1.34e+14 2.31e+14
x66 2.002e+13 1.12e+14 0.178 0.859 -2e+14 2.4e+14
x67 4.662e+13 1.74e+14 0.267 0.789 -2.95e+14 3.89e+14
x68 5.617e+13 1.25e+14 0.448 0.654 -1.9e+14 3.02e+14
x69 5.52e+13 1.04e+14 0.530 0.596 -1.49e+14 2.59e+14
x70 4.305e+13 8.41e+13 0.512 0.609 -1.22e+14 2.08e+14
x71 3.008e+13 8.18e+13 0.368 0.713 -1.3e+14 1.9e+14
x72 3.728e+13 1.85e+14 0.202 0.840 -3.25e+14 4e+14
x73 4.747e+13 8.27e+13 0.574 0.566 -1.15e+14 2.09e+14
x74 5.991e+13 1.64e+14 0.366 0.714 -2.61e+14 3.81e+14
x75 4.997e+13 1.29e+14 0.388 0.698 -2.03e+14 3.02e+14
x76 1.093e+13 7.51e+13 0.146 0.884 -1.36e+14 1.58e+14
x77 5.45e+13 3.17e+14 0.172 0.863 -5.66e+14 6.75e+14
x78 2.182e+13 1e+14 0.217 0.828 -1.75e+14 2.19e+14
x79 8.91e+12 1.68e+14 0.053 0.958 -3.2e+14 3.38e+14
x80 4.591e+13 9.63e+13 0.477 0.634 -1.43e+14 2.35e+14
x81 4.524e+13 1.15e+14 0.394 0.693 -1.8e+14 2.7e+14
x82 5.242e+13 9e+13 0.583 0.560 -1.24e+14 2.29e+14
x83 5.654e+13 1.29e+14 0.438 0.661 -1.96e+14 3.1e+14
x84 -3.419e+13 6.83e+13 -0.500 0.617 -1.68e+14 9.98e+13
x85 1.425e+14 4.91e+14 0.290 0.772 -8.2e+14 1.11e+15
x86 7.289e+13 1.6e+14 0.456 0.649 -2.41e+14 3.87e+14
x87 3.831e+13 7.35e+13 0.521 0.602 -1.06e+14 1.82e+14
x88 1.978e+12 7.56e+13 0.026 0.979 -1.46e+14 1.5e+14
x89 1.985e+13 8.64e+13 0.230 0.818 -1.5e+14 1.89e+14
x90 2.815e+13 6.52e+13 0.432 0.666 -9.97e+13 1.56e+14
x91 6.624e+13 1.36e+14 0.487 0.626 -2e+14 3.33e+14
x92 3.217e+13 7.73e+13 0.416 0.677 -1.19e+14 1.84e+14
x93 3.973e+13 9.06e+13 0.438 0.661 -1.38e+14 2.17e+14
x94 2.771e+13 6.91e+13 0.401 0.688 -1.08e+14 1.63e+14
x95 8.037e+12 5.73e+13 0.140 0.888 -1.04e+14 1.2e+14
x96 3.127e+13 6.77e+13 0.462 0.644 -1.01e+14 1.64e+14
x97 3.217e+13 7.73e+13 0.416 0.677 -1.19e+14 1.84e+14
x98 5.365e+13 9.69e+13 0.554 0.580 -1.36e+14 2.44e+14
x99 2.096e+13 8.35e+13 0.251 0.802 -1.43e+14 1.85e+14
x100 2.396e+13 5.61e+13 0.427 0.669 -8.61e+13 1.34e+14
x101 5.081e+13 9.89e+13 0.514 0.607 -1.43e+14 2.45e+14
x102 3.835e+13 8.65e+13 0.443 0.658 -1.31e+14 2.08e+14
x103 3.346e+13 8.66e+13 0.386 0.699 -1.36e+14 2.03e+14
x104 3.008e+13 8.18e+13 0.368 0.713 -1.3e+14 1.9e+14
x105 1.235e+13 7.02e+13 0.176 0.860 -1.25e+14 1.5e+14
x106 2.344e+13 7.55e+13 0.311 0.756 -1.25e+14 1.71e+14
x107 3.226e+13 9.66e+13 0.334 0.738 -1.57e+14 2.22e+14
x108 3.31e+13 1.02e+14 0.325 0.745 -1.66e+14 2.32e+14
x109 3.622e+13 8.05e+13 0.450 0.653 -1.21e+14 1.94e+14
x110 4.402e+13 1.05e+14 0.418 0.676 -1.63e+14 2.51e+14
x111 4.451e+13 8.16e+13 0.545 0.586 -1.15e+14 2.05e+14
x112 2.42e+13 1.34e+14 0.180 0.857 -2.39e+14 2.87e+14
x113 3.622e+13 8.05e+13 0.450 0.653 -1.21e+14 1.94e+14
x114 8.037e+12 5.73e+13 0.140 0.888 -1.04e+14 1.2e+14
x115 4.825e+13 1.07e+14 0.453 0.651 -1.61e+14 2.57e+14
x116 3.762e+13 7.25e+13 0.519 0.604 -1.05e+14 1.8e+14
x117 7.661e+12 4.45e+13 0.172 0.863 -7.95e+13 9.48e+13
x118 4.658e+13 1.64e+14 0.283 0.777 -2.76e+14 3.69e+14
x119 4.289e+13 2.04e+14 0.210 0.833 -3.57e+14 4.43e+14
x120 1.936e+13 6.84e+13 0.283 0.777 -1.15e+14 1.53e+14
x121 2.436e+13 1.44e+14 0.169 0.866 -2.59e+14 3.08e+14
x122 4.636e+13 9.58e+13 0.484 0.628 -1.41e+14 2.34e+14
x123 4.591e+13 9.63e+13 0.477 0.634 -1.43e+14 2.35e+14
x124 3.879e+13 1.16e+14 0.335 0.737 -1.88e+14 2.65e+14
x125 3.572e+13 9.73e+13 0.367 0.714 -1.55e+14 2.26e+14
x126 4.25e+13 8.1e+13 0.525 0.600 -1.16e+14 2.01e+14
x127 6.119e+13 1.2e+14 0.511 0.610 -1.74e+14 2.96e+14
x128 -6.94e+12 1.55e+14 -0.045 0.964 -3.1e+14 2.96e+14
x129 5.718e+13 1.17e+14 0.489 0.625 -1.72e+14 2.86e+14
x130 4.789e+13 1.05e+14 0.454 0.650 -1.59e+14 2.55e+14
x131 4.404e+13 1.09e+14 0.404 0.686 -1.7e+14 2.58e+14
x132 4.08e+13 8.26e+13 0.494 0.621 -1.21e+14 2.03e+14
x133 3.622e+13 8.05e+13 0.450 0.653 -1.21e+14 1.94e+14
x134 2.411e+13 7.37e+13 0.327 0.743 -1.2e+14 1.69e+14
x135 2.737e+14 6.7e+14 0.408 0.683 -1.04e+15 1.59e+15
x136 1.196e+13 7.36e+13 0.163 0.871 -1.32e+14 1.56e+14
x137 4.142e+13 9.33e+13 0.444 0.657 -1.41e+14 2.24e+14
x138 -1.13e+13 8.79e+13 -0.129 0.898 -1.84e+14 1.61e+14
x139 7.289e+13 1.6e+14 0.456 0.649 -2.41e+14 3.87e+14
x140 4.008e+13 7.85e+13 0.511 0.609 -1.14e+14 1.94e+14
x141 2.63e+13 7.69e+13 0.342 0.732 -1.24e+14 1.77e+14
x142 7.133e+13 1.74e+14 0.409 0.683 -2.71e+14 4.13e+14
x143 5.16e+13 1.61e+14 0.320 0.749 -2.64e+14 3.68e+14
x144 6.379e+13 1.61e+14 0.396 0.692 -2.52e+14 3.8e+14
x145 3.871e+13 7.84e+13 0.494 0.621 -1.15e+14 1.92e+14
x146 2.849e+13 7.62e+13 0.374 0.708 -1.21e+14 1.78e+14
x147 3.823e+13 1.2e+14 0.319 0.749 -1.96e+14 2.73e+14
x148 2.316e+13 6.14e+13 0.377 0.706 -9.72e+13 1.44e+14
x149 5.185e+13 1.06e+14 0.488 0.626 -1.56e+14 2.6e+14
x150 4.374e+13 8.67e+13 0.504 0.614 -1.26e+14 2.14e+14
x151 8.037e+12 5.73e+13 0.140 0.888 -1.04e+14 1.2e+14
x152 3.887e+13 8.41e+13 0.462 0.644 -1.26e+14 2.04e+14
x153 4.524e+13 1.15e+14 0.394 0.693 -1.8e+14 2.7e+14
x154 1.675e+13 5.92e+13 0.283 0.777 -9.94e+13 1.33e+14
x155 6.432e+12 9.97e+13 0.064 0.949 -1.89e+14 2.02e+14
x156 5.811e+13 1.32e+14 0.441 0.659 -2e+14 3.16e+14
x157 3.712e+13 1.24e+14 0.299 0.765 -2.07e+14 2.81e+14
x158 4.23e+13 7.66e+13 0.552 0.581 -1.08e+14 1.92e+14
x159 4.62e+13 1.11e+14 0.418 0.676 -1.71e+14 2.63e+14
x160 5.382e+13 1.1e+14 0.487 0.626 -1.63e+14 2.7e+14
x161 5.979e+13 1.9e+14 0.314 0.753 -3.13e+14 4.33e+14
x162 3.3e+13 5.57e+13 0.592 0.554 -7.62e+13 1.42e+14
x163 5.082e+13 1.35e+14 0.376 0.707 -2.14e+14 3.16e+14
x164 2.222e+13 8.57e+13 0.259 0.795 -1.46e+14 1.9e+14
x165 3.712e+13 1.24e+14 0.299 0.765 -2.07e+14 2.81e+14
x166 4.286e+13 8.28e+13 0.518 0.605 -1.19e+14 2.05e+14
x167 4.433e+13 1.06e+14 0.420 0.675 -1.63e+14 2.51e+14
x168 4.672e+13 1.1e+14 0.426 0.670 -1.68e+14 2.62e+14
x169 3.708e+13 8.41e+13 0.441 0.659 -1.28e+14 2.02e+14
x170 3.871e+13 7.55e+13 0.513 0.608 -1.09e+14 1.87e+14
x171 4.912e+12 1.13e+14 0.043 0.965 -2.17e+14 2.26e+14
x172 2.964e+13 1.44e+14 0.206 0.837 -2.53e+14 3.12e+14
x173 6.864e+13 1.4e+14 0.489 0.625 -2.07e+14 3.44e+14
x174 2.679e+12 9.07e+13 0.030 0.976 -1.75e+14 1.8e+14
x175 5.264e+13 1.18e+14 0.447 0.655 -1.78e+14 2.83e+14
x176 2.133e+13 6.57e+13 0.325 0.745 -1.07e+14 1.5e+14
x177 4.2e+13 1.01e+14 0.415 0.678 -1.56e+14 2.4e+14
x178 1.938e+13 1.22e+14 0.158 0.874 -2.2e+14 2.59e+14
x179 5.402e+13 1.42e+14 0.381 0.703 -2.24e+14 3.32e+14
x180 4.537e+13 9.44e+13 0.481 0.631 -1.4e+14 2.3e+14
x181 -1.509e+13 1.66e+14 -0.091 0.927 -3.4e+14 3.09e+14
x182 3.714e+13 9.72e+13 0.382 0.702 -1.53e+14 2.28e+14
x183 4.732e+13 1.22e+14 0.389 0.698 -1.91e+14 2.86e+14
x184 4.945e+13 9.29e+13 0.532 0.595 -1.33e+14 2.32e+14
x185 5.654e+13 1.29e+14 0.438 0.661 -1.96e+14 3.1e+14
x186 2.154e+13 6.21e+13 0.347 0.729 -1e+14 1.43e+14
x187 4.164e+13 1.05e+14 0.396 0.692 -1.64e+14 2.48e+14
x188 4.516e+13 1e+14 0.452 0.652 -1.51e+14 2.41e+14
x189 1.24e+13 8.03e+13 0.154 0.877 -1.45e+14 1.7e+14
x190 5.586e+13 1.23e+14 0.455 0.649 -1.85e+14 2.97e+14
x191 3.011e+13 7.84e+13 0.384 0.701 -1.24e+14 1.84e+14
x192 2.068e+13 7.12e+13 0.290 0.772 -1.19e+14 1.6e+14
x193 4.135e+13 8.21e+13 0.503 0.615 -1.2e+14 2.02e+14
x194 3.657e+13 1.19e+14 0.307 0.758 -1.97e+14 2.7e+14
x195 1.741e+13 6.04e+13 0.288 0.773 -1.01e+14 1.36e+14
x196 2.328e+13 6.78e+13 0.343 0.731 -1.1e+14 1.56e+14
x197 1.778e+13 5.67e+13 0.314 0.754 -9.33e+13 1.29e+14
x198 3.266e+13 1.03e+14 0.317 0.751 -1.69e+14 2.35e+14
x199 4.435e+13 8.77e+13 0.506 0.613 -1.28e+14 2.16e+14
x200 2.578e+13 9.9e+13 0.260 0.795 -1.68e+14 2.2e+14
x201 3.505e+13 7.9e+13 0.443 0.657 -1.2e+14 1.9e+14
x202 4.258e+13 9.16e+13 0.465 0.642 -1.37e+14 2.22e+14
x203 6.379e+13 1.61e+14 0.396 0.692 -2.52e+14 3.8e+14
x204 2.737e+13 7.32e+13 0.374 0.709 -1.16e+14 1.71e+14
x205 5.78e+13 1.11e+14 0.523 0.601 -1.59e+14 2.74e+14
x206 3.653e+13 8.23e+13 0.444 0.657 -1.25e+14 1.98e+14
x207 3.279e+12 5.7e+13 0.058 0.954 -1.08e+14 1.15e+14
x208 3.879e+13 8.33e+13 0.466 0.641 -1.24e+14 2.02e+14
x209 3.005e+13 7.19e+13 0.418 0.676 -1.11e+14 1.71e+14
x210 4.173e+13 1.16e+14 0.360 0.719 -1.85e+14 2.69e+14
x211 2.902e+13 6.76e+13 0.429 0.668 -1.04e+14 1.62e+14
x212 3.229e+13 7.4e+13 0.437 0.662 -1.13e+14 1.77e+14
x213 2.995e+13 8e+13 0.374 0.708 -1.27e+14 1.87e+14
x214 3.657e+13 1.19e+14 0.307 0.758 -1.97e+14 2.7e+14
x215 9.151e+12 6.54e+13 0.140 0.889 -1.19e+14 1.37e+14
x216 4.532e+13 8.86e+13 0.511 0.609 -1.28e+14 2.19e+14
x217 4.219e+13 1.03e+14 0.411 0.681 -1.59e+14 2.43e+14
x218 2.561e+13 1.06e+14 0.241 0.810 -1.83e+14 2.34e+14
x219 7.542e+13 1.44e+14 0.525 0.600 -2.06e+14 3.57e+14
x220 5.017e+13 1.02e+14 0.490 0.624 -1.51e+14 2.51e+14
x221 4.898e+13 1.26e+14 0.389 0.697 -1.98e+14 2.96e+14
x222 2.87e+13 8.39e+13 0.342 0.732 -1.36e+14 1.93e+14
x223 5.654e+13 1.29e+14 0.438 0.661 -1.96e+14 3.1e+14
x224 5.674e+13 1.03e+14 0.549 0.583 -1.46e+14 2.59e+14
x225 3.412e+13 1.13e+14 0.302 0.763 -1.87e+14 2.55e+14
x226 7.766e+13 2.19e+14 0.355 0.722 -3.51e+14 5.06e+14
x227 6.047e+13 1.22e+14 0.495 0.621 -1.79e+14 3e+14
x228 6.801e+13 1.11e+14 0.614 0.539 -1.49e+14 2.85e+14
x229 3.427e+13 1.18e+14 0.292 0.771 -1.96e+14 2.65e+14
x230 2.814e+13 8.68e+13 0.324 0.746 -1.42e+14 1.98e+14
x231 3.278e+13 7.43e+13 0.441 0.659 -1.13e+14 1.78e+14
x232 4.23e+13 7.66e+13 0.552 0.581 -1.08e+14 1.92e+14
x233 2.024e+13 7.53e+13 0.269 0.788 -1.27e+14 1.68e+14
x234 4.295e+13 9.8e+13 0.438 0.661 -1.49e+14 2.35e+14
x235 4.489e+13 1.2e+14 0.374 0.708 -1.9e+14 2.8e+14
x236 1.512e+13 7.33e+13 0.206 0.837 -1.29e+14 1.59e+14
x237 4.636e+13 9.58e+13 0.484 0.628 -1.41e+14 2.34e+14
x238 5.979e+13 1.9e+14 0.314 0.753 -3.13e+14 4.33e+14
x239 5.586e+13 1.23e+14 0.455 0.649 -1.85e+14 2.97e+14
x240 7.133e+13 1.74e+14 0.409 0.683 -2.71e+14 4.13e+14
x241 -8.315e+12 9.06e+13 -0.092 0.927 -1.86e+14 1.69e+14
x242 4.181e+13 8.74e+13 0.478 0.632 -1.3e+14 2.13e+14
x243 1.451e+14 8.04e+14 0.181 0.857 -1.43e+15 1.72e+15
x244 1.451e+14 8.04e+14 0.181 0.857 -1.43e+15 1.72e+15
x245 1.451e+14 8.04e+14 0.181 0.857 -1.43e+15 1.72e+15
x246 1.451e+14 8.04e+14 0.181 0.857 -1.43e+15 1.72e+15
x247 1.451e+14 8.04e+14 0.181 0.857 -1.43e+15 1.72e+15
x248 1.451e+14 8.04e+14 0.181 0.857 -1.43e+15 1.72e+15
x249 7.991e+13 4.78e+14 0.167 0.867 -8.57e+14 1.02e+15
x250 7.991e+13 4.78e+14 0.167 0.867 -8.57e+14 1.02e+15
x251 7.991e+13 4.78e+14 0.167 0.867 -8.57e+14 1.02e+15
x252 7.991e+13 4.78e+14 0.167 0.867 -8.57e+14 1.02e+15
x253 7.991e+13 4.78e+14 0.167 0.867 -8.57e+14 1.02e+15
x254 7.991e+13 4.78e+14 0.167 0.867 -8.57e+14 1.02e+15
x255 7.991e+13 4.78e+14 0.167 0.867 -8.57e+14 1.02e+15
x256 2.232e+13 7.7e+13 0.290 0.772 -1.29e+14 1.73e+14
x257 3.065e+13 8.73e+13 0.351 0.726 -1.4e+14 2.02e+14
x258 2.382e+13 1.72e+14 0.138 0.890 -3.13e+14 3.61e+14
x259 2.912e+13 1.08e+14 0.269 0.788 -1.83e+14 2.41e+14
x260 6.399e+13 1.53e+14 0.417 0.677 -2.37e+14 3.65e+14
x261 6.987e+13 1.25e+14 0.558 0.577 -1.76e+14 3.15e+14
x262 -1.252e+15 4.33e+15 -0.289 0.772 -9.74e+15 7.24e+15
x263 1.073e+14 1.94e+14 0.554 0.580 -2.73e+14 4.87e+14
x264 3.742e+13 7.75e+13 0.483 0.629 -1.14e+14 1.89e+14
x265 4.578e+13 9.06e+13 0.505 0.613 -1.32e+14 2.23e+14
x266 3.483e+13 8.86e+13 0.393 0.694 -1.39e+14 2.09e+14
x267 1.66e+13 1.4e+14 0.118 0.906 -2.58e+14 2.92e+14
x268 1.641e+13 6.39e+13 0.257 0.797 -1.09e+14 1.42e+14
x269 3.89e+13 1.03e+14 0.377 0.706 -1.63e+14 2.41e+14
x270 3.436e+13 9.13e+13 0.376 0.707 -1.45e+14 2.13e+14
x271 2.534e+11 9.66e+13 0.003 0.998 -1.89e+14 1.9e+14
x272 5.672e+13 1.59e+14 0.357 0.721 -2.55e+14 3.68e+14
x273 4.543e+13 9.13e+13 0.498 0.619 -1.34e+14 2.24e+14
x274 2.695e+13 5.28e+13 0.511 0.610 -7.65e+13 1.3e+14
x275 2.642e+13 7.45e+13 0.355 0.723 -1.2e+14 1.72e+14
x276 3.969e+13 1e+14 0.395 0.693 -1.57e+14 2.37e+14
x277 3.661e+13 8.07e+13 0.454 0.650 -1.21e+14 1.95e+14
x278 3.085e+13 7.97e+13 0.387 0.699 -1.25e+14 1.87e+14
x279 4.32e+13 1.13e+14 0.381 0.703 -1.79e+14 2.65e+14
x280 2.05e+13 9.87e+13 0.208 0.835 -1.73e+14 2.14e+14
x281 5.639e+13 1.15e+14 0.490 0.624 -1.69e+14 2.82e+14
x282 3.151e+13 8.58e+13 0.367 0.714 -1.37e+14 2e+14
x283 5.246e+13 9.92e+13 0.529 0.597 -1.42e+14 2.47e+14
x284 5.161e+13 1.06e+14 0.486 0.627 -1.56e+14 2.6e+14
x285 3.809e+13 7.83e+13 0.486 0.627 -1.15e+14 1.92e+14
x286 5.291e+13 1.31e+14 0.403 0.687 -2.04e+14 3.1e+14
x287 5.154e+13 1.06e+14 0.487 0.626 -1.56e+14 2.59e+14
x288 3.057e+13 9.28e+13 0.330 0.742 -1.51e+14 2.12e+14
x289 -2.219e+13 1.31e+14 -0.169 0.866 -2.8e+14 2.35e+14
x290 6.905e+12 3.77e+13 0.183 0.855 -6.7e+13 8.08e+13
x291 5.312e+13 1.29e+14 0.413 0.680 -1.99e+14 3.06e+14
x292 2.678e+13 1.11e+14 0.241 0.810 -1.91e+14 2.45e+14
x293 1.823e+13 1.13e+14 0.161 0.872 -2.03e+14 2.4e+14
x294 4.187e+13 1.01e+14 0.415 0.678 -1.56e+14 2.39e+14
x295 1.728e+13 1.12e+14 0.154 0.878 -2.03e+14 2.37e+14
x296 2.459e+13 1.01e+14 0.242 0.809 -1.74e+14 2.23e+14
x297 3.096e+13 6.8e+13 0.456 0.649 -1.02e+14 1.64e+14
x298 4.048e+13 7.55e+13 0.536 0.592 -1.07e+14 1.88e+14
x299 2.595e+13 1.99e+14 0.130 0.896 -3.65e+14 4.17e+14
x300 3.409e+13 9.11e+13 0.374 0.708 -1.44e+14 2.13e+14
x301 5.182e+13 9.87e+13 0.525 0.600 -1.42e+14 2.45e+14
x302 3.829e+13 1.43e+14 0.267 0.789 -2.43e+14 3.19e+14
x303 4.835e+13 1.33e+14 0.364 0.716 -2.12e+14 3.09e+14
x304 -2.9e+14 1.03e+15 -0.280 0.779 -2.32e+15 1.74e+15
x305 2.12e+12 1.81e+14 0.012 0.991 -3.54e+14 3.58e+14
x306 2.13e+13 6.55e+13 0.325 0.745 -1.07e+14 1.5e+14
x307 3.306e+13 8.97e+13 0.369 0.712 -1.43e+14 2.09e+14
x308 1.374e+14 6.21e+14 0.221 0.825 -1.08e+15 1.36e+15
x309 2.17e+13 9.19e+13 0.236 0.813 -1.58e+14 2.02e+14
x310 5.887e+12 9.11e+13 0.065 0.948 -1.73e+14 1.85e+14
x311 6.511e+13 1.37e+14 0.475 0.635 -2.03e+14 3.34e+14
x312 -2.162e+14 6.73e+14 -0.321 0.748 -1.54e+15 1.1e+15
x313 2.941e+13 6.65e+13 0.443 0.658 -1.01e+14 1.6e+14
x314 4.015e+13 1.14e+14 0.351 0.726 -1.84e+14 2.64e+14
x315 2.123e+13 8.06e+13 0.263 0.792 -1.37e+14 1.79e+14
x316 2.526e+13 6.82e+13 0.370 0.711 -1.08e+14 1.59e+14
x317 2.653e+13 1.09e+14 0.243 0.808 -1.87e+14 2.4e+14
x318 4.089e+13 7.52e+13 0.544 0.587 -1.07e+14 1.88e+14
x319 4.878e+13 1.34e+14 0.364 0.716 -2.14e+14 3.11e+14
x320 3.172e+13 7.46e+13 0.425 0.671 -1.15e+14 1.78e+14
x321 4.501e+13 9.99e+13 0.451 0.652 -1.51e+14 2.41e+14
x322 3.18e+13 7.75e+13 0.410 0.682 -1.2e+14 1.84e+14
x323 4.445e+13 7.63e+13 0.582 0.560 -1.05e+14 1.94e+14
x324 3.234e+13 8.2e+13 0.394 0.693 -1.28e+14 1.93e+14
x325 4.037e+13 9.47e+13 0.426 0.670 -1.45e+14 2.26e+14
x326 1.697e+13 4.21e+13 0.403 0.687 -6.55e+13 9.95e+13
x327 5.133e+13 1.06e+14 0.486 0.627 -1.56e+14 2.58e+14
x328 3.692e+13 8.9e+13 0.415 0.678 -1.38e+14 2.11e+14
x329 4.508e+12 1.08e+14 0.042 0.967 -2.08e+14 2.17e+14
x330 4.919e+13 1.09e+14 0.451 0.652 -1.64e+14 2.63e+14
x331 3.028e+13 7.22e+13 0.420 0.675 -1.11e+14 1.72e+14
x332 3.133e+13 7.45e+13 0.421 0.674 -1.15e+14 1.77e+14
x333 -4.511e+12 1.37e+14 -0.033 0.974 -2.74e+14 2.65e+14
x334 5.377e+13 1.31e+14 0.411 0.681 -2.03e+14 3.1e+14
x335 3.444e+13 1.03e+14 0.335 0.738 -1.67e+14 2.36e+14
x336 4.465e+13 1.04e+14 0.429 0.668 -1.59e+14 2.49e+14
x337 2.825e+13 8.93e+13 0.316 0.752 -1.47e+14 2.03e+14
x338 2.369e+13 6.55e+13 0.362 0.717 -1.05e+14 1.52e+14
x339 2.911e+13 7.97e+13 0.365 0.715 -1.27e+14 1.85e+14
x340 4.903e+13 1.08e+14 0.453 0.651 -1.63e+14 2.61e+14
x341 3.888e+13 9.72e+13 0.400 0.689 -1.52e+14 2.29e+14
x342 2.417e+13 1.12e+14 0.217 0.828 -1.94e+14 2.43e+14
x343 2.297e+13 1e+14 0.230 0.818 -1.73e+14 2.19e+14
x344 -2.273e+12 1.23e+14 -0.018 0.985 -2.44e+14 2.39e+14
x345 4.754e+13 1.23e+14 0.386 0.699 -1.94e+14 2.89e+14
x346 3.428e+13 7.4e+13 0.463 0.643 -1.11e+14 1.79e+14
x347 2.864e+13 1.04e+14 0.276 0.782 -1.74e+14 2.32e+14
x348 3.6e+13 8.34e+13 0.431 0.666 -1.28e+14 2e+14
x349 3.586e+13 1.26e+14 0.286 0.775 -2.1e+14 2.82e+14
x350 8.095e+13 2.5e+14 0.323 0.746 -4.1e+14 5.72e+14
x351 3.114e+13 9.27e+13 0.336 0.737 -1.51e+14 2.13e+14
x352 8.009e+13 1.95e+14 0.411 0.681 -3.02e+14 4.62e+14
x353 3.552e+13 8.02e+13 0.443 0.658 -1.22e+14 1.93e+14
x354 4.499e+13 8.75e+13 0.514 0.607 -1.27e+14 2.17e+14
x355 3.435e+13 8.22e+13 0.418 0.676 -1.27e+14 1.96e+14
x356 1.628e+15 4.91e+15 0.331 0.740 -8e+15 1.13e+16
x357 4.004e+13 8.32e+13 0.481 0.630 -1.23e+14 2.03e+14
x358 1.323e+13 6.78e+13 0.195 0.845 -1.2e+14 1.46e+14
x359 -6.931e+13 4.38e+14 -0.158 0.874 -9.27e+14 7.89e+14
x360 1.933e+13 4.64e+13 0.417 0.677 -7.16e+13 1.1e+14
x361 3.142e+13 6.56e+13 0.479 0.632 -9.71e+13 1.6e+14
x362 4.97e+13 1.18e+14 0.420 0.675 -1.82e+14 2.82e+14
x363 8.444e+13 1.61e+14 0.525 0.600 -2.31e+14 4e+14
x364 7.117e+13 1.33e+14 0.537 0.591 -1.89e+14 3.31e+14
x365 -1.36e+15 4.72e+15 -0.288 0.773 -1.06e+16 7.88e+15
x366 2.49e+13 7.54e+13 0.330 0.741 -1.23e+14 1.73e+14
x367 2.724e+13 7.21e+13 0.378 0.706 -1.14e+14 1.69e+14
x368 4.684e+13 1.11e+14 0.420 0.674 -1.72e+14 2.65e+14
x369 5.537e+13 1.18e+14 0.471 0.638 -1.75e+14 2.86e+14
x370 5.574e+13 1.1e+14 0.507 0.612 -1.6e+14 2.71e+14
x371 4.895e+13 1.21e+14 0.406 0.685 -1.87e+14 2.85e+14
x372 3.902e+13 1.37e+14 0.284 0.776 -2.3e+14 3.08e+14
x373 4.573e+13 9.45e+13 0.484 0.629 -1.4e+14 2.31e+14
x374 4.359e+14 1.15e+15 0.378 0.706 -1.83e+15 2.7e+15
x375 2.79e+13 5.58e+13 0.500 0.617 -8.14e+13 1.37e+14
x376 1.865e+13 2.74e+14 0.068 0.946 -5.19e+14 5.56e+14
x377 7.336e+13 1.67e+14 0.438 0.661 -2.55e+14 4.01e+14
x378 4.35e+13 1.12e+14 0.389 0.697 -1.76e+14 2.63e+14
x379 4.496e+13 1.32e+14 0.341 0.733 -2.13e+14 3.03e+14
x380 3.84e+13 2.81e+14 0.137 0.891 -5.13e+14 5.89e+14
x381 6.119e+13 1.24e+14 0.493 0.622 -1.82e+14 3.04e+14
x382 5.378e+13 1.02e+14 0.530 0.596 -1.45e+14 2.53e+14
x383 4.986e+13 1.14e+14 0.436 0.663 -1.74e+14 2.74e+14
x384 4.098e+13 8.12e+13 0.505 0.614 -1.18e+14 2e+14
x385 -1.236e+13 3.42e+14 -0.036 0.971 -6.83e+14 6.58e+14
x386 2.234e+13 9.75e+13 0.229 0.819 -1.69e+14 2.13e+14
x387 4.412e+13 9.97e+13 0.443 0.658 -1.51e+14 2.39e+14
x388 5.093e+13 1.04e+14 0.490 0.624 -1.53e+14 2.55e+14
x389 4.237e+13 1.01e+14 0.420 0.674 -1.55e+14 2.4e+14
x390 3.607e+13 7.67e+13 0.470 0.638 -1.14e+14 1.86e+14
x391 3.602e+13 6.51e+13 0.554 0.580 -9.15e+13 1.64e+14
x392 2.317e+13 7.28e+13 0.318 0.750 -1.2e+14 1.66e+14
x393 3.02e+13 7.75e+13 0.390 0.697 -1.22e+14 1.82e+14
x394 1.503e+13 1.15e+14 0.131 0.896 -2.09e+14 2.4e+14
x395 2.154e+13 1.7e+14 0.127 0.899 -3.12e+14 3.55e+14
x396 8.824e+13 2.01e+14 0.439 0.661 -3.06e+14 4.82e+14
x397 2.882e+13 5.16e+13 0.559 0.576 -7.22e+13 1.3e+14
x398 1.811e+12 1.43e+14 0.013 0.990 -2.78e+14 2.81e+14
x399 6.222e+13 1.29e+14 0.481 0.630 -1.91e+14 3.16e+14
x400 -2.005e+14 5.33e+14 -0.376 0.707 -1.24e+15 8.43e+14
x401 -3.627e+12 3.82e+14 -0.009 0.992 -7.52e+14 7.45e+14
x402 3.129e+13 8.66e+13 0.361 0.718 -1.38e+14 2.01e+14
x403 4.306e+13 1.19e+14 0.363 0.717 -1.9e+14 2.76e+14
x404 4.303e+13 7.98e+13 0.539 0.590 -1.13e+14 1.99e+14
x405 6.424e+13 1.71e+14 0.376 0.707 -2.71e+14 3.99e+14
x406 3.963e+13 9.05e+13 0.438 0.662 -1.38e+14 2.17e+14
x407 1.596e+13 1.04e+14 0.154 0.878 -1.87e+14 2.19e+14
x408 3.479e+13 9.15e+13 0.380 0.704 -1.45e+14 2.14e+14
x409 3.026e+13 2.53e+14 0.119 0.905 -4.66e+14 5.27e+14
x410 5.139e+12 8.94e+13 0.057 0.954 -1.7e+14 1.8e+14
x411 4.085e+13 1.13e+14 0.361 0.718 -1.81e+14 2.63e+14
x412 -4.52e+14 3.59e+15 -0.126 0.900 -7.49e+15 6.59e+15
x413 8.308e+13 3.68e+14 0.226 0.821 -6.38e+14 8.04e+14
x414 7.475e+13 2.33e+14 0.321 0.748 -3.82e+14 5.31e+14
x415 2.073e+13 9.66e+13 0.215 0.830 -1.69e+14 2.1e+14
x416 2.778e+13 6.5e+13 0.427 0.669 -9.96e+13 1.55e+14
x417 2.879e+13 8.46e+13 0.340 0.734 -1.37e+14 1.95e+14
x418 1.949e+13 8.61e+13 0.226 0.821 -1.49e+14 1.88e+14
x419 1.535e+13 6.39e+13 0.240 0.810 -1.1e+14 1.41e+14
x420 3.009e+13 8.76e+13 0.343 0.731 -1.42e+14 2.02e+14
x421 6.08e+13 1.19e+14 0.512 0.608 -1.72e+14 2.93e+14
x422 6.823e+13 1.21e+14 0.565 0.572 -1.68e+14 3.05e+14
x423 3.492e+13 9.15e+13 0.382 0.703 -1.44e+14 2.14e+14
x424 2.277e+13 5.95e+13 0.383 0.702 -9.38e+13 1.39e+14
x425 5.789e+13 1.33e+14 0.436 0.663 -2.02e+14 3.18e+14
x426 2.657e+13 8.75e+13 0.304 0.761 -1.45e+14 1.98e+14
x427 1.912e+13 7.55e+13 0.253 0.800 -1.29e+14 1.67e+14
x428 8.146e+13 1.38e+14 0.592 0.554 -1.88e+14 3.51e+14
x429 1.268e+13 8.67e+13 0.146 0.884 -1.57e+14 1.83e+14
x430 3.342e+13 6.71e+13 0.498 0.619 -9.82e+13 1.65e+14
x431 5.803e+13 1.16e+14 0.502 0.615 -1.68e+14 2.84e+14
x432 -8.603e+13 4.69e+14 -0.184 0.854 -1e+15 8.32e+14
x433 6.075e+13 1.12e+14 0.544 0.586 -1.58e+14 2.8e+14
x434 1.795e+13 6.16e+13 0.291 0.771 -1.03e+14 1.39e+14
x435 1.336e+13 2.11e+14 0.063 0.950 -4e+14 4.27e+14
x436 6.548e+13 1.26e+14 0.521 0.602 -1.81e+14 3.12e+14
x437 5.218e+13 1.08e+14 0.483 0.629 -1.6e+14 2.64e+14
x438 9.351e+12 1.43e+14 0.065 0.948 -2.71e+14 2.9e+14
x439 -2.386e+15 6.13e+15 -0.389 0.697 -1.44e+16 9.63e+15
x440 1.065e+14 4.79e+14 0.222 0.824 -8.32e+14 1.04e+15
x441 7.047e+13 1.37e+14 0.515 0.607 -1.98e+14 3.39e+14
x442 2.958e+13 1.19e+14 0.249 0.803 -2.03e+14 2.63e+14
x443 2.583e+13 1.31e+14 0.198 0.843 -2.3e+14 2.82e+14
x444 3.657e+13 1.09e+14 0.336 0.737 -1.77e+14 2.5e+14
x445 -1.188e+14 3.13e+14 -0.379 0.705 -7.33e+14 4.95e+14
x446 6.671e+13 1.54e+14 0.434 0.664 -2.35e+14 3.68e+14
x447 1.195e+13 7.22e+13 0.166 0.868 -1.29e+14 1.53e+14
x448 -1.595e+13 3.11e+14 -0.051 0.959 -6.26e+14 5.94e+14
x449 4.326e+13 8.44e+13 0.512 0.608 -1.22e+14 2.09e+14
x450 4.999e+13 9.44e+13 0.530 0.596 -1.35e+14 2.35e+14
x451 1.318e+13 6.91e+13 0.191 0.849 -1.22e+14 1.49e+14
x452 3.444e+13 7.87e+13 0.438 0.662 -1.2e+14 1.89e+14
x453 2.799e+13 6.47e+13 0.432 0.665 -9.89e+13 1.55e+14
x454 4.309e+13 1.01e+14 0.427 0.669 -1.54e+14 2.41e+14
x455 -2.256e+14 1.99e+15 -0.114 0.910 -4.12e+15 3.67e+15
x456 2.568e+13 1e+14 0.257 0.797 -1.7e+14 2.22e+14
x457 5.329e+13 1.08e+14 0.495 0.621 -1.58e+14 2.64e+14
x458 2.782e+13 6.72e+13 0.414 0.679 -1.04e+14 1.59e+14
x459 4.736e+13 1.18e+14 0.400 0.689 -1.85e+14 2.79e+14
x460 3.36e+13 1.54e+14 0.218 0.828 -2.69e+14 3.36e+14
x461 -4.112e+14 2.35e+15 -0.175 0.861 -5.03e+15 4.2e+15
x462 -1.948e+14 7.79e+14 -0.250 0.803 -1.72e+15 1.33e+15
Omnibus: 24376.305 Durbin-Watson: 2.008
Prob(Omnibus): 0.000 Jarque-Bera (JB): 898840.961
Skew: 3.008 Prob(JB): 0.00
Kurtosis: 27.414 Cond. No. 1.28e+17