def run_simple_regression(n=1000,k=1,feature='X0'):
(coefs,df)=gen_simplemodel_data(n=n,k=k)
# logging.debug(df.head())
df.sort(feature,inplace=True)
lr=lin_model.LinModel()
X=df[df.columns[df.columns!='y']]
y=df.y
lr.fit(X=X,y=y)
lr.summary()
df_ci=lr.get_confidence_interval_for_mean(X)
df_pi=lr.get_prediction_interval(X)
(fig,ax)=plt.subplots(nrows=2,ncols=1,figsize=[14,12])
cols=sns.color_palette('husl',n_colors=4)
ax[0].scatter(X[feature],y,label='y',color=cols[3],alpha=0.4)
ax[0].plot(X[feature],df_pi['upper_pred'],label='pred',color=cols[1],alpha=0.5)
ax[0].plot(X[feature],df_pi['lower_pred'],color=cols[1],alpha=0.5)
ax[0].plot(X[feature],df_ci['upper_mean'],color=cols[2],alpha=0.5)
ax[0].plot(X[feature],df_ci['lower_mean'],label='mean_ci',color=cols[2],alpha=0.5)
ax[0].scatter(X[feature],df_pi['y_hat'],label='y_hat',color=cols[0],alpha=0.5)
ax[0].legend(loc='best')
ax[1].scatter(X[feature],y,label='y',color=cols[3],alpha=0.4)
ax[1].scatter(X[feature],df_ci['y_hat'],label='y_hat',color=cols[0],alpha=0.5)
ax[1].legend(loc='best')
def test_pred_interval(show_plot=False):
from ml_ext import examples
(coefs,df)=examples.gen_simplemodel_data(n=50,k=3)
df.sort('X1',inplace=True)
lr=LinModel()
X=df[df.columns[df.columns!='y']]
y=df.y
lr.fit(X=X,y=y)
lr.summary()
df_ci=lr.get_confidence_interval_for_mean(X)
df_pi=lr.get_prediction_interval(X)
#Now use statsmodels to compare
from statsmodels.sandbox.regression.predstd import wls_prediction_std
import statsmodels.api as sm
re = sm.OLS(y, X).fit()
prstd, iv_l, iv_u = wls_prediction_std(re)
if show_plot:
(fig,ax)=plt.subplots(nrows=2,ncols=1,figsize=[14,12])
cols=sns.color_palette('husl',n_colors=4)
ax[0].scatter(X.X1,y,label='y',color=cols[3],alpha=0.4)
ax[0].plot(X.X1,df_pi['upper_pred'],label='pred',color=cols[1],alpha=0.5)
ax[0].plot(X.X1,df_pi['lower_pred'],color=cols[1],alpha=0.5)
ax[0].plot(X.X1,df_ci['upper_mean'],color=cols[2],alpha=0.5)
ax[0].plot(X.X1,df_ci['lower_mean'],label='mean_ci',color=cols[2],alpha=0.5)
ax[0].scatter(X.X1,df_pi['y_hat'],label='y_hat',color=cols[0],alpha=0.5)
ax[0].legend(loc='best')
ax[1].scatter(X.X1,y,label='y',color=cols[3],alpha=0.4)
ax[1].scatter(X.X1,df_ci['y_hat'],label='y_hat',color=cols[0],alpha=0.5)
ax[1].plot(X.X1,iv_u,label='wls',color=cols[1],alpha=0.5)
ax[1].plot(X.X1,iv_l,color=cols[1],alpha=0.5)
ax[1].legend(loc='best')
#get difference between uppers from each and check they are within 1%
overall_diff=100*numpy.sum(iv_u-df_pi['upper_pred'])/numpy.sum(iv_u)
logging.debug("Overall % difference in prediction ranges for upper bound: {}".format(overall_diff))
assert overall_diff<0.1