python - confidence and prediction intervals with StatsModels

Question

I do this linear regression with StatsModels:

import numpy as np
import statsmodels.api as sm
from statsmodels.sandbox.regression.predstd import wls_prediction_std

n = 100

x = np.linspace(0, 10, n)
e = np.random.normal(size=n)
y = 1 + 0.5*x + 2*e
X = sm.add_constant(x)

re = sm.OLS(y, X).fit()
print(re.summary())

prstd, iv_l, iv_u = wls_prediction_std(re)

My questions are, iv_l and iv_u are the upper and lower confidence intervals or prediction intervals?

How I get others?

I need the confidence and prediction intervals for all points, to do a plot.

Answer 1

For test data you can try to use the following.

predictions = result.get_prediction(out_of_sample_df)
predictions.summary_frame(alpha=0.05)

I found the summary_frame() method buried here and you can find the get_prediction() method here. You can change the significance level of the confidence interval and prediction interval by modifying the "alpha" parameter.

I am posting this here because this was the first post that comes up when looking for a solution for confidence & prediction intervals – even though this concerns itself with test data rather.

Here's a function to take a model, new data, and an arbitrary quantile, using this approach:

def ols_quantile(m, X, q):
  # m: OLS model.
  # X: X matrix.
  # q: Quantile.
  #
  # Set alpha based on q.
  a = q * 2
  if q > 0.5:
    a = 2 * (1 - q)
  predictions = m.get_prediction(X)
  frame = predictions.summary_frame(alpha=a)
  if q > 0.5:
    return frame.obs_ci_upper
  return frame.obs_ci_lower