Show confidence limits and prediction limits in scatter plot

Question

I have two arrays of data as hight and weight:

import numpy as np, matplotlib.pyplot as plt

heights = np.array([50,52,53,54,58,60,62,64,66,67,68,70,72,74,76         


        

Answer 1

For a project of mine, I needed to create intervals for time-series modeling, and to make the procedure more efficient I created tsmoothie: A python library for time-series smoothing and outlier detection in a vectorized way.

It provides different smoothing algorithms together with the possibility to computes intervals.

In the case of linear regression:

import numpy as np
import matplotlib.pyplot as plt
from tsmoothie.smoother import *
from tsmoothie.utils_func import sim_randomwalk

# generate 10 randomwalks of length 50
np.random.seed(33)
data = sim_randomwalk(n_series=10, timesteps=50, 
                      process_noise=10, measure_noise=30)

# operate smoothing
smoother = PolynomialSmoother(degree=1)
smoother.smooth(data)

# generate intervals
low_pi, up_pi = smoother.get_intervals('prediction_interval', confidence=0.05)
low_ci, up_ci = smoother.get_intervals('confidence_interval', confidence=0.05)

# plot the first smoothed timeseries with intervals
plt.figure(figsize=(11,6))
plt.plot(smoother.smooth_data[0], linewidth=3, color='blue')
plt.plot(smoother.data[0], '.k')
plt.fill_between(range(len(smoother.data[0])), low_pi[0], up_pi[0], alpha=0.3, color='blue')
plt.fill_between(range(len(smoother.data[0])), low_ci[0], up_ci[0], alpha=0.3, color='blue')

In the case of regression with order bigger than 1:

# operate smoothing
smoother = PolynomialSmoother(degree=5)
smoother.smooth(data)

# generate intervals
low_pi, up_pi = smoother.get_intervals('prediction_interval', confidence=0.05)
low_ci, up_ci = smoother.get_intervals('confidence_interval', confidence=0.05)

# plot the first smoothed timeseries with intervals
plt.figure(figsize=(11,6))
plt.plot(smoother.smooth_data[0], linewidth=3, color='blue')
plt.plot(smoother.data[0], '.k')
plt.fill_between(range(len(smoother.data[0])), low_pi[0], up_pi[0], alpha=0.3, color='blue')
plt.fill_between(range(len(smoother.data[0])), low_ci[0], up_ci[0], alpha=0.3, color='blue')

I point out also that tsmoothie can carry out the smoothing of multiple time-series in a vectorized way. Hope this can help someone