Visualizing Multidimensional Data: Scatter Plots, Color Encodings & Log Scales

One Scatter Plot, Four Insights: Color, Size & Log Scales You just learned plt.plot(x, y) — two variables, one line. Your boss now asks: "Show me spend vs revenue, but also which campaigns were most profitable and which reached the most customers — in one chart for the deck." That is 4 variables and you have a 2D screen. This article shows how color, size, and log scales turn a plain scatter into a 4-dimensional story — using a 5-row campaign table you can picture immediately.

1. The Data: 5 Campaigns, 4 Numbers Each Same e-commerce context as the rest of the course — each row is a marketing campaign:

Campaign Spend ($) Revenue ($) Profit Margin (%) Customers Reached Summer Sale 10,000 42,000 18 8,200 Influencer Push 35,000 95,000 31 3,100 Email Blast 2,000 18,000 42 12,400 TV Spot 120,000 210,000 12 1,800 Referral Bonus 8,000 38,000 35 6,500 Plotting only x=spend, y=revenue hides that Email Blast (tiny spend, 42% margin, 12K customers) was the most efficient and TV Spot (huge spend, 12% margin) was wasteful. Let's encode the other two columns visually.

2. 4 Dimensions on a 2D Screen — How Each Channel Maps Visual Channel Data Column Parameter What the Viewer Sees Horizontal position Spend x= Left = cheap, Right = expensive Vertical position Revenue y= Bottom = low revenue, Top = high Color Profit Margin c= + cmap='viridis' Dark purple = thin margin, Yellow = fat margin (colorbar tells the scale) Dot size Customers Reached s= Small dot = niche, Big bubble = mass reach

3. The Code — Read It as "One Line Per Dimension" import matplotlib.pyplot as plt

plt.figure(figsize=(10, 6))

# x and y → spend vs revenue # c + cmap → profit margin as color # s → customers as bubble size # alpha → transparency so overlapping bubbles stay readable scatter = plt.scatter( x=df['marketing_spend'], y=df['revenue'], c=df['profit_margin'], # 3rd dimension: color cmap='viridis', # yellow = high margin, purple = low margin s=df['customer_count'] / 10, # 4th dimension: bubble size (divide to fit screen) alpha=0.65, # see-through so overlaps don't hide edgecolors='w', linewidth=0.5 )

cbar = plt.colorbar(scatter) cbar.set_label('Profit Margin (%)', fontsize=11)

plt.xlabel('Marketing Spend ($)', fontsize=12) plt.ylabel('Revenue Generated ($)', fontsize=12) plt.title('Campaign Performance: