Relationships

• Exploring relationships
  • PMF of age
  • Scatter plot
  • Jittering
• Visualizing relationships
  • Height and weight
  • Distribution of income
  • Income and height
• Correlation
  • Computing correlations
• Simple regression
  • Income and vegetables
  • Fit a line

Exploring relationships

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from empiricaldist import Pmf, Cdf

brfss_original = pd.read_hdf('./dataset/brfss.hdf5', 'brfss')

PMF of age

age = Pmf.from_seq(brfss_original['AGE'])

# Plot the PMF
age.bar()

# Label the axes
plt.xlabel('Age in years')
plt.ylabel('PMF')

Text(0, 0.5, 'PMF')

Scatter plot

brfss = brfss_original[:1000]

# Extract age and weight
age = brfss['AGE']
weight = brfss['WTKG3']

# Make a scatter plot
plt.plot(age, weight, 'o', alpha=0.1)

plt.xlabel('Age in years')
plt.ylabel('Weight in kg')

Text(0, 0.5, 'Weight in kg')

Jittering

brfss = brfss_original[:1000]

# Add jittering to age
age = brfss['AGE'] + np.random.normal(0, 2.5, size=len(brfss))
# Extract weight
weight = brfss['WTKG3']

# Make a scatter plot
plt.plot(age, weight, 'o', markersize=5, alpha=0.2)

plt.xlabel('Age in years')
plt.ylabel('Weight in kg')

Text(0, 0.5, 'Weight in kg')

Visualizing relationships

Height and weight

data = brfss_original.dropna(subset=['_HTMG10', 'WTKG3'])

# Make a box plot
sns.boxplot(x='_HTMG10', y='WTKG3', data=data, whis=10)

# Plot the y-axis on a log scale
plt.yscale('log')

# Remove unneeded lines and label axes
sns.despine(left=True, bottom=True)
plt.xlabel('Height in cm')
plt.ylabel('Weight in kg')
plt.savefig('../images/brfss-boxplot.png')

Distribution of income

income = brfss_original['INCOME2']

# Plot the PMF
Pmf.from_seq(income).bar()

# Label the axes
plt.xlabel('Income level')
plt.ylabel('PMF')

Text(0, 0.5, 'PMF')

Income and height

data = brfss_original.dropna(subset=['INCOME2', 'HTM4'])

# Make a violin plot
sns.violinplot(x = 'INCOME2', y='HTM4', data=data, inner=None)

# Remove unneeded lines and label axes
sns.despine(left=True, bottom=True)
plt.xlabel('Income level')
plt.ylabel('Height in cm')

Text(0, 0.5, 'Height in cm')

Correlation

Computing correlations

columns = ['AGE', 'INCOME2', '_VEGESU1']
subset = brfss_original[columns]

# Compute the correlation matrix
print(subset.corr())

               AGE   INCOME2  _VEGESU1
AGE       1.000000 -0.015158 -0.009834
INCOME2  -0.015158  1.000000  0.119670
_VEGESU1 -0.009834  0.119670  1.000000

Simple regression

Income and vegetables

from scipy.stats import linregress

subset = brfss_original.dropna(subset=['INCOME2', '_VEGESU1'])
xs = subset['INCOME2']
ys = subset['_VEGESU1']

# Compute the linear regression
res = linregress(xs, ys)
print(res)

LinregressResult(slope=0.06988048092105248, intercept=1.5287786243362973, rvalue=0.11967005884864361, pvalue=1.3785039162157718e-238, stderr=0.002110976356332355)

Fit a line

plt.figure(figsize=(10, 10))
# Plot the scatter plot
x_jitter = xs + np.random.normal(0, 0.15, len(xs))
plt.plot(x_jitter, ys, 'o', alpha=0.2)

# Plot the line of best fit
fx = np.array([xs.min(), xs.max()])
fy = res.intercept + res.slope * fx
plt.plot(fx, fy, '-', alpha=0.7)

plt.xlabel('Income code')
plt.ylabel('Vegetable servings per day')
plt.ylim([0, 6])

(0, 6)