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MATH05, Regression analysis

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Ordinary Least Squares

import statsmodels.api as sm

X = range(1,8)
X = sm.add_constant(X)
Y = [1,3,4,5,2,3,4]

model = sm.OLS(Y,X)
results = model.fit()
results.summary()
OUTPUT 1

image

OUTPUT 2

RegressionResults 


results.tvalues

array([ 1.87867287,  0.98019606])



results.t_test([1, 0])

<class 'statsmodels.stats.contrast.ContrastResults'>
                             Test for Constraints                             
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
c0             2.1429      1.141      1.879      0.119      -0.789       5.075
==============================================================================



import numpy as np

results.f_test(np.identity(2))

<class 'statsmodels.stats.contrast.ContrastResults'>
<F test: F=array([[19.46078431]]), p=0.004372505910945688, df_denom=5, df_num=2>




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OUTPUT