#~~~~~~~~
res2 = OLS(y, X).fit()
#print "estimated parameters: x d1-d0 d2-d0 constant"
print(res2.params)
#print "standard deviation of parameter estimates"
print(res2.bse)
prstd, iv_l, iv_u = wls_prediction_std(res2)
#print res.summary()
#plot
#~~~~
plt.figure()
plt.plot(x1, y, 'o', x1, y_true, 'b-')
plt.plot(x1, res2.fittedvalues, 'r--.')
plt.plot(x1, iv_u, 'r--')
plt.plot(x1, iv_l, 'r--')
plt.title('3 groups: different intercepts, common slope; blue: true, red: OLS')
plt.show()
#Test hypothesis that all groups have same intercept
#~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
R = [[0, 1, 0, 0], [0, 0, 1, 0]]
# F test joint hypothesis R * beta = 0
# i.e. coefficient on both dummy variables equal zero
print "Test hypothesis that all groups have same intercept"
print res2.f_test(R)
