Inferential Statistics Concepts

Introduction to Linear Modeling in Python

Jason Vestuto

Data Scientist

Probability Distribution

Histogram plot of day count versus temperature bins, Daily high temperatures in August

Populations and Statistics

Histogram plot of day count versus temperature bins, Daily high temperatures in August

Sampling the Population

Population statistics vs Sample statistics

print( len(month_of_temps), month_of_temps.mean(), month_of_temps.std() )
print( len(decade_of_temps), decade_of_temps.mean(), decade_of_temps.std() )

Draw a Random Sample from a Population

month_of_temps = np.random.choice(decade_of_temps, size=31)

Visualizing Distributions

2 histograms, one for sample one for population, both of day count versus temperature bins, with sample bins being much shorter

Visualizing Distributions

2 histograms, one for sample one for population, both of normalized day count versus temperature bins, with sample bin bars being about the same height as population bin bars

Probability and Inference

Histogram plot of day count versus temperature bins, Daily high temperatures in August

Visualizing Distributions

2 histograms, one for each of two different samples, both of normalized day count versus temperature bins, both with similar bin bar heights, but differing slightly from bin to bin

Resampling

# Resampling as Iteration
num_samples = 20
for ns in range(num_samples):
    sample = np.random.choice(population, num_pts)
    distribution_of_means[ns] = sample.mean()

# Sample Distribution Statistics
mean_of_means = np.mean(distribution_of_means)
stdev_of_means = np.std(distribution_of_means)

Let's practice!

Introduction to Linear Modeling in Python