Drawing and interpreting trend lines with café data
Interpreting Real Business Relationships
Use scatter plots to find patterns beyond just time - what else affects café sales?
Sarah realized that looking only at time (month over month) isn't the only useful pattern. She can also look at relationships between two variables: Does advertising spend predict sales? Does temperature predict sales? Does staffing level predict sales?
This Lesson's Focus
Use scatter plots to find and interpret relationships between business variables. This is exactly what Excel's regression tools will automate in upcoming lessons - but understanding the logic first makes you a better analyst.
Business Question
The café manager wants to know: "If I spend more on advertising, will I make more sales?"
Advertising Spend vs. Weekend Sales
Each dot represents one weekend's advertising spend and resulting sales
Interpretation Questions
- What direction does the relationship go? (Positive or Negative?)
- What does the slope tell you? (For each $100 more spent on advertising, about how much more in sales?)
- How consistent is the pattern? (Are dots close to the line or scattered?)
- What would you predict for a weekend with $450 in advertising?
Answers
- Direction: Positive - more advertising → more sales
- Slope: About $2 per $1 spent (each $100 in ads adds ~$200 in sales)
- Consistency: Pretty high - points cluster reasonably close to the line
- Prediction: Approximately $2,000 in sales for $450 advertising
Business Question
"Does weather affect our sales? Should I plan for more inventory on hot days?"
Temperature vs. Weekend Sales
Each dot represents one weekend's high temperature and café sales
Interpretation Questions
- What direction does the relationship go? Is this surprising or expected?
- What does the slope tell you? (For each degree warmer, how much do sales change?)
- What might explain this pattern? (Think like a café owner - what do people want on hot vs. cold days?)
- What would you predict for a 70°F weekend?
Answers
- Direction: Negative - hotter days → lower sales (probably because people stay cool indoors)
- Slope: About -$65 per degree (each degree warmer = $65 less in sales)
- Pattern explanation: On hot days, people may go to air-conditioned malls or avoid the café's outdoor area
- Prediction: Approximately $6,000 in sales for 70°F
Business Question
"How many staff members do I need? Is there a point where adding more staff doesn't help?"
Staff Members vs. Weekend Sales
Each dot represents one weekend's number of staff and café sales
Interpretation Challenge
- What happens to sales as staff increases from 2 to 5? What about 5 to 8?
- What does this suggest about optimal staffing?
- Why might the relationship flatten out at higher staffing levels?
- What other factors might explain this pattern?
Key Insight: Diminishing Returns
The staffing relationship shows diminishing returns. Going from 2→3 staff adds ~$1,300 in sales. Going from 7→8 staff might add only $100. At some point, more staff creates crowding without improving service, or there's simply not enough customers to serve.
This is exactly the kind of insight that makes forecasting valuable - not to get an exact number, but to understand the shape of the relationship and where the optimal point might be.
Team Activity (10 minutes):
Step 1: Choose a scenario (2 minutes)
Each team picks one: advertising, temperature, staffing, or invent your own
Step 2: Make predictions (4 minutes)
For your scenario, predict: (a) direction, (b) approximate slope, (c) confidence level
Step 3: Share with team (4 minutes)
Explain your reasoning - what business knowledge informed your prediction?
Relationships Are Everywhere
Time isn't the only variable that matters. Scatter plots reveal relationships between any two business variables you can measure.
Direction Tells the Story
Positive (both go up) or negative (one goes up, one goes down) - this tells you whether increasing one variable helps or hurts the other.
Slope Quantifies Impact
The slope tells you exactly how much the outcome changes for each unit increase in the input - essential for planning and budgeting.
Fit Shows Certainty
How tightly points cluster around the line shows how reliable your predictions will be. Low fit doesn't mean "bad" - just "less certain."