I'm trying to do a linear regression to predict the count of a dataframe based on the count of another dataframe. I am using statsmodels. I have tried the following:
X = df1.count()
Y = df2.count()
from statsmodels.formula.api import ols
fit = ols(Y ~ X, data=kak).fit()
fit.summary()
Using the X and Y variables in the OLS formula is not allowed and I have no idea what to fill in at the data= keyword argument. How would I go about doing this?
Let's assume you have to 1D arrays X and Y:
import numpy as np
X = np.arange(100)
Y = 2*X + 5
Then you can run a linear regression using the line below. There are two important things:
The first argument to ols is a str containing a formula. "Y ~ X" and not Y ~ X (note the double quotes).
The second argument data can be any Python object as long as it has keys data["X"] and data["Y"]. I wrote a dict here, but it would also work with a DataFrame. It basically allows statsmodels to understand who are X and Y in the formula you gave to it.
ols("Y ~ X", {"X": X, "Y": Y}).fit().summary()
Output:
OLS Regression Results
==============================================================================
Dep. Variable: Y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 1.916e+33
Date: Fri, 21 May 2021 Prob (F-statistic): 0.00
Time: 14:01:48 Log-Likelihood: 3055.1
No. Observations: 100 AIC: -6106.
Df Residuals: 98 BIC: -6101.
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 5.0000 2.62e-15 1.91e+15 0.000 5.000 5.000
X 2.0000 4.57e-17 4.38e+16 0.000 2.000 2.000
==============================================================================
Omnibus: 220.067 Durbin-Watson: 0.015
Prob(Omnibus): 0.000 Jarque-Bera (JB): 9.816
Skew: 0.159 Prob(JB): 0.00739
Kurtosis: 1.498 Cond. No. 114.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Related
I am trying to perform multiple linear regression using the statsmodels.formula.api package in python and have listed the code that i have used to perform this regression below.
auto_1= pd.read_csv("Auto.csv")
formula = 'mpg ~ ' + " + ".join(auto_1.columns[1:-1])
results = smf.ols(formula, data=auto_1).fit()
print(results.summary())
The data consists the following variables - mpg, cylinders, displacement, horsepower, weight , acceleration, year, origin and name. When the print result comes up, it shows multiple rows of the horsepower column and the regression results are also not correct. Im not sure why?
screenshot of repeated rows
It's likely because of the data type of the horsepower column. If its values are categories or just strings, the model will use treatment (dummy) coding for them by default, producing the results you are seeing. Check the data type (run auto_1.dtypes) and cast the column to a numeric type (it's best to do it when you are first reading the csv file with the dtype= parameter of the read_csv() method.
Here is an example where a column with numeric values is cast (i.e. converted) to strings (or categories):
import numpy as np
import pandas as pd
import statsmodels.formula.api as smf
df = pd.DataFrame(
{
'mpg': np.random.randint(20, 40, 50),
'horsepower': np.random.randint(100, 200, 50)
}
)
# convert integers to strings (or categories)
df['horsepower'] = (
df['horsepower'].astype('str') # same result with .astype('category')
)
formula = 'mpg ~ horsepower'
results = smf.ols(formula, df).fit()
print(results.summary())
Output (dummy coding):
OLS Regression Results
==============================================================================
Dep. Variable: mpg R-squared: 0.778
Model: OLS Adj. R-squared: -0.207
Method: Least Squares F-statistic: 0.7901
Date: Sun, 18 Sep 2022 Prob (F-statistic): 0.715
Time: 20:17:51 Log-Likelihood: -110.27
No. Observations: 50 AIC: 302.5
Df Residuals: 9 BIC: 380.9
Df Model: 40
Covariance Type: nonrobust
=====================================================================================
coef std err t P>|t| [0.025 0.975]
-------------------------------------------------------------------------------------
Intercept 32.0000 5.175 6.184 0.000 20.294 43.706
horsepower[T.103] -4.0000 7.318 -0.547 0.598 -20.555 12.555
horsepower[T.112] -1.0000 7.318 -0.137 0.894 -17.555 15.555
horsepower[T.116] -9.0000 7.318 -1.230 0.250 -25.555 7.555
horsepower[T.117] 6.0000 7.318 0.820 0.433 -10.555 22.555
horsepower[T.118] 2.0000 7.318 0.273 0.791 -14.555 18.555
horsepower[T.120] -4.0000 6.338 -0.631 0.544 -18.337 10.337
etc.
Now, converting the strings back to integers:
df['horsepower'] = pd.to_numeric(df.horsepower)
# or df['horsepower'] = df['horsepower'].astype('int')
results = smf.ols(formula, df).fit()
print(results.summary())
Output (as expected):
OLS Regression Results
==============================================================================
Dep. Variable: mpg R-squared: 0.011
Model: OLS Adj. R-squared: -0.010
Method: Least Squares F-statistic: 0.5388
Date: Sun, 18 Sep 2022 Prob (F-statistic): 0.466
Time: 20:24:54 Log-Likelihood: -147.65
No. Observations: 50 AIC: 299.3
Df Residuals: 48 BIC: 303.1
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
Intercept 31.7638 3.663 8.671 0.000 24.398 39.129
horsepower -0.0176 0.024 -0.734 0.466 -0.066 0.031
==============================================================================
Omnibus: 3.529 Durbin-Watson: 1.859
Prob(Omnibus): 0.171 Jarque-Bera (JB): 1.725
Skew: 0.068 Prob(JB): 0.422
Kurtosis: 2.100 Cond. No. 834.
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
I get completely different results with the same datasets in R and Python. I cannot understand why it happens.
R:
library(RcppCNPy)
d <- npyLoad("/home/vvkovalchuk/bin/src/python/asks1.npy")
datas = npyLoad('/home/vvkovalchuk/bin/src/python/bids2.npy')
m <- lm(d ~ datas)
summary(m)
Python:
import time
import numpy
import statsmodels.api as sm
from math import log
Y = numpy.load('./asks1.npy', allow_pickle=True)
X = numpy.load('./bids2.npy', allow_pickle=True)
X3 = sm.add_constant(X)
res_ols = sm.OLS(Y, X3).fit()
print(res_ols.params)
What am I doing wrong?
Results:
R:
Call:
lm(formula = d ~ datas)
Residuals:
Min 1Q Median 3Q Max
-6.089e+06 8.797e+07 2.163e+08 2.179e+08 1.122e+10
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -2.561e+00 2.253e+06 0 1
datas 3.809e+03 2.164e+09 0 1
Residual standard error: 208100000 on 14639 degrees of freedom
Multiple R-squared: 0.2735, Adjusted R-squared: 0.2735
F-statistic: 5512 on 1 and 14639 DF, p-value: < 2.2e-16
Python:
OLS Regression Results
Dep. Variable: y R-squared: 0.112
Model: OLS Adj. R-squared: 0.112
Method: Least Squares F-statistic: 1846.
Date: Thu, 25 Mar 2021 Prob (F-statistic): 0.00
Time: 13:08:43 Log-Likelihood: 1.6948e+05
No. Observations: 14641 AIC: -3.390e+05
Df Residuals: 14639 BIC: -3.389e+05
Df Model: 1
Covariance Type: nonrobust
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0004 3.07e-06 126.136 0.000 0.000 0.000
x1 0.1478 0.003 42.969 0.000 0.141 0.155
Omnibus: 3251.130 Durbin-Watson: 0.004
Prob(Omnibus): 0.000 Jarque-Bera (JB): 14606.605
Skew: 1.019 Prob(JB): 0.00
Kurtosis: 7.449 Cond. No. 1.83e+05
I also tried to swap arguments in OLS function. Still getting incorrect results. Could this be related to NAs?
I am trying to build a super dictionary which holds within a number of lower level libraries
Concept
I have interest rates for my retail bank for the last 12 years and I am trying to model the interest rates by using a portfolio of different bonds.
Regression formula
Y_i - Y_i-1 = A + B(X_i - X_i-1) + E
In words, Y_Lag = alpha + beta(X_Lag) + Error term
Data
Note: Y = Historic Rate
df = pd.DataFrame(np.random.randint(low=0, high=10, size=(100,17)),
columns=['Historic Rate', 'Overnight', '1M', '3M', '6M','1Y','2Y','3Y','4Y','5Y','6Y','7Y','8Y','9Y','10Y','12Y','15Y'])
Code thus far
#Import packages required for the analysis
import pandas as pd
import numpy as np
import statsmodels.api as sm
def Simulation(TotalSim,j):
#super dictionary to hold all iterations of the loop
Super_fit_d = {}
for i in range(1,TotalSim):
#Create a introductory loop to run the first set of regressions
#Each loop produces a univariate regression
#Each loop has a fixed lag of i
fit_d = {} # This will hold all of the fit results and summaries
for col in [x for x in df.columns if x != 'Historic Rate']:
Y = df['Historic Rate'] - df['Historic Rate'].shift(1)
# Need to remove the NaN for fit
Y = Y[Y.notnull()]
X = df[col] - df[col].shift(i)
X = X[X.notnull()]
#Y now has more observations than X due to lag, drop rows to match
Y = Y.drop(Y.index[0:i-1])
if j = 1:
X = sm.add_constant(X) # Add a constant to the fit
fit_d[col] = sm.OLS(Y,X).fit()
#append the dictionary for each lag onto the super dictionary
Super_fit_d[lag_i] = fit_d
#Check the output for one column
fit_d['Overnight'].summary()
#Check the output for one column in one segment of the super dictionary
Super_fit_d['lag_5'].fit_d['Overnight'].summary()
Simulation(11,1)
Question
I seem to be overwriting my dictionary with every loop and I'm not evaluating the i properly to index the iteration as lag_1, lag_2, lag_3 etc. How do I fix this?
Thanks in advance
There are a couple of issues here:
you sometimes use i and sometimes lag_i, but only i is defined. I changed all to lag_i for consistency
if j = 1 is incorrect syntax. You need if j == 1
You need to return fit_d so that it persists after your loop
I got it done by applying those changes
import pandas as pd
import numpy as np
import statsmodels.api as sm
df = pd.DataFrame(np.random.randint(low=0, high=10, size=(100,17)),
columns=['Historic Rate', 'Overnight', '1M', '3M', '6M','1Y','2Y','3Y','4Y','5Y','6Y','7Y','8Y','9Y','10Y','12Y','15Y'])
def Simulation(TotalSim,j):
Super_fit_d = {}
for lag_i in range(1,TotalSim):
#Create a introductory loop to run the first set of regressions
#Each loop produces a univariate regression
#Each loop has a fixed lag of i
fit_d = {} # This will hold all of the fit results and summaries
for col in [x for x in df.columns if x != 'Historic Rate']:
Y = df['Historic Rate'] - df['Historic Rate'].shift(1)
# Need to remove the NaN for fit
Y = Y[Y.notnull()]
X = df[col] - df[col].shift(lag_i)
X = X[X.notnull()]
#Y now has more observations than X due to lag, drop rows to match
Y = Y.drop(Y.index[0:lag_i-1])
if j == 1:
X = sm.add_constant(X) # Add a constant to the fit
fit_d[col] = sm.OLS(Y,X).fit()
#append the dictionary for each lag onto the super dictionary
# return fit_d
Super_fit_d[lag_i] = fit_d
return Super_fit_d
test_dict = Simulation(11,1)
First lag
test_dict[1]['Overnight'].summary()
Out[76]:
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: Historic Rate R-squared: 0.042
Model: OLS Adj. R-squared: 0.033
Method: Least Squares F-statistic: 4.303
Date: Fri, 28 Sep 2018 Prob (F-statistic): 0.0407
Time: 11:15:13 Log-Likelihood: -280.39
No. Observations: 99 AIC: 564.8
Df Residuals: 97 BIC: 570.0
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const -0.0048 0.417 -0.012 0.991 -0.833 0.823
Overnight 0.2176 0.105 2.074 0.041 0.009 0.426
==============================================================================
Omnibus: 1.449 Durbin-Watson: 2.756
Prob(Omnibus): 0.485 Jarque-Bera (JB): 1.180
Skew: 0.005 Prob(JB): 0.554
Kurtosis: 2.465 Cond. No. 3.98
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
Second Lag
test_dict[2]['Overnight'].summary()
Out[77]:
<class 'statsmodels.iolib.summary.Summary'>
"""
OLS Regression Results
==============================================================================
Dep. Variable: Historic Rate R-squared: 0.001
Model: OLS Adj. R-squared: -0.010
Method: Least Squares F-statistic: 0.06845
Date: Fri, 28 Sep 2018 Prob (F-statistic): 0.794
Time: 11:15:15 Log-Likelihood: -279.44
No. Observations: 98 AIC: 562.9
Df Residuals: 96 BIC: 568.0
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 0.0315 0.428 0.074 0.941 -0.817 0.880
Overnight 0.0291 0.111 0.262 0.794 -0.192 0.250
==============================================================================
Omnibus: 2.457 Durbin-Watson: 2.798
Prob(Omnibus): 0.293 Jarque-Bera (JB): 1.735
Skew: 0.115 Prob(JB): 0.420
Kurtosis: 2.391 Cond. No. 3.84
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
"""
I was testing some basic category regression using Stats model:
I build up a deterministic model
Y = X + Z
where X can takes 3 values (a, b or c) and Z only 2 (d or e).
At that stage the model is purely deterministic, I setup the weights for each variable as followed
a's weight=1
b's weight=2
c's weight=3
d's weight=1
e's weight=2
Therefore with 1(X=a) being 1 if X=a, 0 otherwise, the model is simply:
Y = 1(X=a) + 2*1(X=b) + 3*1(X=c) + 1(Z=d) + 2*1(Z=e)
Using the following code, to generate the different variables and run the regression
from statsmodels.formula.api import ols
nbData = 1000
rand1 = np.random.uniform(size=nbData)
rand2 = np.random.uniform(size=nbData)
a = 1 * (rand1 <= (1.0/3.0))
b = 1 * (((1.0/3.0)< rand1) & (rand1< (4/5.0)))
c = 1-b-a
d = 1 * (rand2 <= (3.0/5.0))
e = 1-d
weigths = [1,2,3,1,2]
y = a+2*b+3*c+4*d+5*e
df = pd.DataFrame({'y':y, 'a':a, 'b':b, 'c':c, 'd':d, 'e':e})
mod = ols(formula='y ~ a + b + c + d + e - 1', data=df)
res = mod.fit()
print(res.summary())
I end up with the rights results (one has to look at the difference between coef rather than the coef themselfs)
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 1.006e+30
Date: Wed, 16 Sep 2015 Prob (F-statistic): 0.00
Time: 03:05:40 Log-Likelihood: 3156.8
No. Observations: 100 AIC: -6306.
Df Residuals: 96 BIC: -6295.
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
a 1.6000 7.47e-16 2.14e+15 0.000 1.600 1.600
b 2.6000 6.11e-16 4.25e+15 0.000 2.600 2.600
c 3.6000 9.61e-16 3.74e+15 0.000 3.600 3.600
d 3.4000 5.21e-16 6.52e+15 0.000 3.400 3.400
e 4.4000 6.85e-16 6.42e+15 0.000 4.400 4.400
==============================================================================
Omnibus: 11.299 Durbin-Watson: 0.833
Prob(Omnibus): 0.004 Jarque-Bera (JB): 5.720
Skew: -0.381 Prob(JB): 0.0573
Kurtosis: 2.110 Cond. No. 2.46e+15
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 1.67e-29. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.
But when I increase the number of data point to (say) 600, the regression is producing really bad results. I have tried similar regression in Excel and in R and they are producing consistent results whatever the number of data points. Does anyone know if there is some restriction on statsmodel ols explaining such behaviour or am I missing something?
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.167
Model: OLS Adj. R-squared: 0.161
Method: Least Squares F-statistic: 29.83
Date: Wed, 16 Sep 2015 Prob (F-statistic): 1.23e-22
Time: 03:08:04 Log-Likelihood: -701.02
No. Observations: 600 AIC: 1412.
Df Residuals: 595 BIC: 1434.
Df Model: 4
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
a 5.8070 1.15e+13 5.05e-13 1.000 -2.26e+13 2.26e+13
b 6.4951 1.15e+13 5.65e-13 1.000 -2.26e+13 2.26e+13
c 6.9033 1.15e+13 6.01e-13 1.000 -2.26e+13 2.26e+13
d -1.1927 1.15e+13 -1.04e-13 1.000 -2.26e+13 2.26e+13
e -0.1685 1.15e+13 -1.47e-14 1.000 -2.26e+13 2.26e+13
==============================================================================
Omnibus: 67.153 Durbin-Watson: 0.328
Prob(Omnibus): 0.000 Jarque-Bera (JB): 70.964
Skew: 0.791 Prob(JB): 3.89e-16
Kurtosis: 2.419 Cond. No. 7.70e+14
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The smallest eigenvalue is 9.25e-28. This might indicate that there are
strong multicollinearity problems or that the design matrix is singular.
It appears that as mentionned by Mr. F, the main problem is that the statsmodel OLS does not seem to handle the collinearity pb as well as Excel/R in that case, but if instead of defining one variable for each a, b, c, d and e, one define a variable X and one Z which can be equal to a, b or c and d or e resp, then the regression works fine. Ie updating the code with :
df['X'] = ['c']*len(df)
df.X[df.b!=0] = 'b'
df.X[df.a!=0] = 'a'
df['Z'] = ['e']*len(df)
df.Z[df.d!=0] = 'd'
mod = ols(formula='y ~ X + Z - 1', data=df)
leads to the expected results
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 1.000
Model: OLS Adj. R-squared: 1.000
Method: Least Squares F-statistic: 2.684e+27
Date: Thu, 17 Sep 2015 Prob (F-statistic): 0.00
Time: 06:22:43 Log-Likelihood: 2.5096e+06
No. Observations: 100000 AIC: -5.019e+06
Df Residuals: 99996 BIC: -5.019e+06
Df Model: 3
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [95.0% Conf. Int.]
------------------------------------------------------------------------------
X[a] 5.0000 1.85e-14 2.7e+14 0.000 5.000 5.000
X[b] 6.0000 1.62e-14 3.71e+14 0.000 6.000 6.000
X[c] 7.0000 2.31e-14 3.04e+14 0.000 7.000 7.000
Z[T.e] 1.0000 1.97e-14 5.08e+13 0.000 1.000 1.000
==============================================================================
Omnibus: 145.367 Durbin-Watson: 1.353
Prob(Omnibus): 0.000 Jarque-Bera (JB): 9729.487
Skew: -0.094 Prob(JB): 0.00
Kurtosis: 1.483 Cond. No. 2.29
==============================================================================
Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
When it comes to measuring goodness of fit - R-Squared seems to be a commonly understood (and accepted) measure for "simple" linear models.
But in case of statsmodels (as well as other statistical software) RLM does not include R-squared together with regression results.
Is there a way to get it calculated "manually", perhaps in a way similar to how it is done in Stata?
Or is there another measure that can be used / calculated from the results produced by sm.RLS?
This is what Statsmodels is producing:
import numpy as np
import statsmodels.api as sm
# Sample Data with outliers
nsample = 50
x = np.linspace(0, 20, nsample)
x = sm.add_constant(x)
sig = 0.3
beta = [5, 0.5]
y_true = np.dot(x, beta)
y = y_true + sig * 1. * np.random.normal(size=nsample)
y[[39,41,43,45,48]] -= 5 # add some outliers (10% of nsample)
# Regression with Robust Linear Model
res = sm.RLM(y, x).fit()
print(res.summary())
Which outputs:
Robust linear Model Regression Results
==============================================================================
Dep. Variable: y No. Observations: 50
Model: RLM Df Residuals: 48
Method: IRLS Df Model: 1
Norm: HuberT
Scale Est.: mad
Cov Type: H1
Date: Mo, 27 Jul 2015
Time: 10:00:00
No. Iterations: 17
==============================================================================
coef std err z P>|z| [95.0% Conf. Int.]
------------------------------------------------------------------------------
const 5.0254 0.091 55.017 0.000 4.846 5.204
x1 0.4845 0.008 61.555 0.000 0.469 0.500
==============================================================================
Since an OLS return the R2, I would suggest regressing the actual values against the fitted values using simple linear regression. Regardless where the fitted values come from, such an approach would provide you an indication of the corresponding R2.
R2 is not a good measure of goodness of fit for RLM models. The problem is that the outliers have a huge effect on the R2 value, to the point where it is completely determined by outliers. Using weighted regression afterwards is an attractive alternative, but it is better to look at the p-values, standard errors and confidence intervals of the estimated coefficients.
Comparing the OLS summary to RLM (results are slightly different to yours due to different randomization):
OLS Regression Results
==============================================================================
Dep. Variable: y R-squared: 0.726
Model: OLS Adj. R-squared: 0.721
Method: Least Squares F-statistic: 127.4
Date: Wed, 03 Nov 2021 Prob (F-statistic): 4.15e-15
Time: 09:33:40 Log-Likelihood: -87.455
No. Observations: 50 AIC: 178.9
Df Residuals: 48 BIC: 182.7
Df Model: 1
Covariance Type: nonrobust
==============================================================================
coef std err t P>|t| [0.025 0.975]
------------------------------------------------------------------------------
const 5.7071 0.396 14.425 0.000 4.912 6.503
x1 0.3848 0.034 11.288 0.000 0.316 0.453
==============================================================================
Omnibus: 23.499 Durbin-Watson: 2.752
Prob(Omnibus): 0.000 Jarque-Bera (JB): 33.906
Skew: -1.649 Prob(JB): 4.34e-08
Kurtosis: 5.324 Cond. No. 23.0
==============================================================================
Notes:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
Robust linear Model Regression Results
==============================================================================
Dep. Variable: y No. Observations: 50
Model: RLM Df Residuals: 48
Method: IRLS Df Model: 1
Norm: HuberT
Scale Est.: mad
Cov Type: H1
Date: Wed, 03 Nov 2021
Time: 09:34:24
No. Iterations: 17
==============================================================================
coef std err z P>|z| [0.025 0.975]
------------------------------------------------------------------------------
const 5.1857 0.111 46.590 0.000 4.968 5.404
x1 0.4790 0.010 49.947 0.000 0.460 0.498
==============================================================================
If the model instance has been used for another fit with different fit parameters, then the fit options might not be the correct ones anymore .
You can see that the standard errors and size of the confidence interval decreases in going from OLS to RLM for both the intercept and the slope term. This suggests that the estimates are closer to the real values.
Why not use model.predict to obtain the r2? For Example:
r2=1. - np.sum(np.abs(model.predict(X) - y) **2) / np.sum(np.abs(y - np.mean(y)) ** 2)