Visualising Relationships

import pandas as pd
import numpy as np

# Fitness app users — 16 users, 5 features + upgrade outcome
df = pd.DataFrame({
    'user_id':      range(1, 17),
    'daily_steps':  [4200, 9800, 3100, 11200, 5400, 10500, 2800, 9200,
                     4800, 8900, 3500, 10800, 6100, 9500, 2500, 11500],
    'active_mins':  [28,   72,   18,   88,    35,   80,    15,   68,
                     30,   65,   22,   85,    40,   74,    12,   91  ],
    'sleep_hours':  [5.2,  7.8,  5.5,  8.1,   6.2,  7.5,   5.1,  7.2,
                     5.8,  7.0,  5.3,  8.3,   6.8,  7.6,   4.9,  8.0 ],
    'sessions_pw':  [3,    8,    2,    10,    4,    9,    1,    7,
                     3,    7,    2,    9,     5,    8,    1,    11  ],
    'upgraded':     [0,    1,    0,    1,     0,    1,    0,    1,
                     0,    1,    0,    1,     0,    1,    0,    1   ]
})

print(df.to_string(index=False))

What just happened?

Even just scanning the table, a pattern jumps out: users who upgraded (1) consistently have higher step counts, more active minutes, better sleep, and more sessions. Let's make that pattern impossible to miss with charts.

def text_scatter(df, x_col, y_col, width=50, height=15):
    """Draws a simple text scatter plot in the terminal."""
    x = df[x_col]
    y = df[y_col]

    # Normalise both axes to fit within the grid size
    x_norm = ((x - x.min()) / (x.max() - x.min()) * (width - 1)).round().astype(int)
    y_norm = ((y - y.min()) / (y.max() - y.min()) * (height - 1)).round().astype(int)

    # Build an empty grid of dots
    grid = [['·'] * width for _ in range(height)]

    # Place each data point onto the grid
    # Use '●' for upgraded users, '○' for non-upgraded
    for i, row in df.iterrows():
        xi = x_norm.iloc[i]
        yi = height - 1 - y_norm.iloc[i]   # flip y axis so higher = higher on screen
        marker = '●' if row['upgraded'] == 1 else '○'
        grid[yi][xi] = marker

    print(f"{y_col} ↑")
    for row in grid:
        print('  ' + ''.join(row))
    print(f"  {'─' * width}→ {x_col}")
    print(f"  ○ = not upgraded   ● = upgraded\n")

text_scatter(df, 'daily_steps', 'active_mins')

What just happened?

The function normalises both columns onto a grid using simple maths — subtract the minimum, divide by the range, scale to grid size. pandas' .iterrows() loops through each row to place its dot on the grid.

The separation is crystal clear: all the filled circles (●, upgraded users) are in the top-right — high steps and high active minutes. All the empty circles (○, non-upgraders) are in the bottom-left. This is a strong positive relationship with perfect group separation. A correlation number of 0.99 would tell you the same thing — but seeing the two groups literally occupy different corners of the chart makes it viscerally obvious.

Daily Steps vs Active Minutes — by Upgrade Status

Daily Steps

from scipy import stats

features = ['daily_steps', 'active_mins', 'sleep_hours', 'sessions_pw']

print("How strongly does each feature relate to upgrading?\n")
print(f"{'Feature':<15} {'Correlation':>12}  {'Strength':>12}  Visual")
print("─" * 60)

for feat in features:
    r, p = stats.pearsonr(df[feat], df['upgraded'])

    # Plain-English strength label
    if abs(r) >= 0.8:   strength = "Very strong"
    elif abs(r) >= 0.6: strength = "Strong"
    elif abs(r) >= 0.4: strength = "Moderate"
    else:               strength = "Weak"

    # A simple visual bar scaled to the correlation value
    bar = '█' * int(abs(r) * 20)

    print(f"  {feat:<13} {r:>+12.3f}  {strength:>12}  {bar}")

What just happened?

scipy's stats.pearsonr() gives us both the correlation and its p-value in one call. We loop over all four features and rank them by relationship strength with the target (upgraded).

All four features are very strongly correlated with upgrading — r above 0.95 for all of them. That's excellent news for the modelling team: any of these features would be a powerful predictor. But it also raises the multicollinearity question from Lesson 25 — if they're all this correlated with upgrading, they're probably also correlated with each other. Let's check that next.

# Build a feature-vs-feature correlation matrix
# This is the "numbers behind the pair plot"
pair_corr = df[features].corr(method='pearson').round(2)

print("Feature pair correlations (the numbers behind a pair plot):\n")
print(pair_corr)
print()

# Find the two features that are most correlated WITH EACH OTHER
# (potential multicollinearity — Lesson 25!)
max_r = 0
max_pair = ('', '')
for i in range(len(features)):
    for j in range(i + 1, len(features)):
        r = abs(pair_corr.iloc[i, j])
        if r > max_r:
            max_r   = r
            max_pair = (features[i], features[j])

print(f"Most correlated pair: {max_pair[0]}  ×  {max_pair[1]}  (r = {max_r:.2f})")
print("→ If building a linear model, consider dropping one of these two.")

What just happened?

pandas' .corr() builds the full matrix in one call. We then loop the upper triangle to find the most correlated pair automatically — connecting back to the multicollinearity lesson.

All four features are heavily correlated with each other (0.95–0.99). They're essentially four different ways of measuring the same thing: "how active is this user?" For a tree-based model this is fine. For a linear model, we'd want to keep just one or two. The pair plot correlation grid gives you this picture in seconds.

Pair Plot — Feature Correlation Grid

Teacher's Note

Always look at the scatter plot before trusting the correlation number. A correlation of 0.7 could mean a clean diagonal line of points — or it could mean a U-shaped curve where Pearson is giving you the wrong answer. The number alone can't tell you which one it is.

And coloured scatter plots — where the dots are coloured by a category like "upgraded" vs "not upgraded" — are one of the most powerful EDA tools you have. When two groups separate cleanly in a scatter plot, you've found a signal your model will love. When they overlap completely, that feature probably won't help much.

Up Next · Lesson 28

Categorical Visuals

Bar charts, count plots, and stacked visuals — how to show categorical data in ways that make patterns immediately obvious to anyone in the room.