Binning groups observations into intervals, then summarizes each interval. For example, bird-strike records can be grouped into 100-foot height ranges and counted. section 7.12
Bird strikes by altitude
A dataset records each bird strike, but not a ready-made count of strikes at each altitude. Creating 100-foot HEIGHT bins produces one count per interval, which can be plotted and analyzed. The resulting Pearson correlation is weak before transformation, while extreme near-ground outliers challenge the assumptions of linear analysis. section 7.12
A practical binning workflow uses:
- Remove records with missing height values. section 7.12
- Create 100-foot intervals with pandas.cut() and count records in each interval. section 7.12
- Plot the counts before applying correlation or regression, and inspect skew and outliers first. section 7.12
import pandas as pd
import numpy as np
from scipy.stats import linregress
import matplotlib.pyplot as plt
df = pd.read_csv('birdstrike.csv')
df = df[df['HEIGHT'].isna() == False] #1
max_height = int(df['HEIGHT'].max() \
// 100 + 1) * 100 #2
bins = list(range(0, max_height + 100, 100)) #2
df['HEIGHT_BIN'] = pd.cut(df['HEIGHT'],
bins=bins, right=False) #2
incidents_by_bin = df['HEIGHT_BIN']
.value_counts().sort_index() #2
x = np.arange(start=0, stop=max_height, step=100) #3
y = incidents_by_bin.to_numpy() #3
slope, intercept, r_value, p_value, std_err \
= linregress(x, y) #4
x_line = np.linspace(min(x), max(x), 100) #5
y_line = slope * x_line + intercept #5
plt.scatter(x, y, label='Data points') #6
plt.plot(x_line, #7
y_line, #7
color='red', #7
label=f'Fit: y = {slope:.2f}x '
f'{'-' if intercept < 0 else '+'}'
f' {abs(intercept):.2f}')#7
plt.title("Bird Strikes by Height") #8
plt.xlabel("Bird Strike Height (feet)") #8
plt.ylabel("Bird Strike Count") #8
plt.legend() #8
plt.show() #9
print(f"Slope: {slope:.8f}") #10
print(f"Intercept: {intercept:.8f}") #10
print(f"Pearson Correlation: {r_value:.4f}") #10
print(f"P-value (for slope): {p_value:.10f}") #10
print(f"Standard error of slope: {std_err:.4f}") #10
"""
Slope: -0.03924224
Intercept: 851.05028927
Pearson Correlation: -0.1672
P-value (for slope): 0.0026550029
Standard error of slope: 0.0130
"""
Python code demonstrates interval construction, counting, plotting, and linear regression on binned observations. section 7.12
