Data Detectives Slides
Trend
Detectives
Linear vs. Exponential Regression
GeoGebra Lab Session
The Eyeball Test
Vote: Linear, Exponential, or Random?
Plot A
Plot B
Plot C
Tech Tutorial
Embedded media
Watch For:
- The "Function Bot"
- How to make a List (L1)
- The
FitGrowth command
- What is R-Squared?
"In real life, data usually doesn't fit perfectly on a function."
GeoGebra Command Hub
1
Create Data List
Type all points into one set:
L1 = {(0,10), (1,15), ...}
2
Run Regression
Exponential: FitGrowth(L1)
Linear: FitLine(L1)
The Ultimate Test: R²
R-Squared tells us how "perfect" the fit is. The closer to 1, the better the model!
0 (Awful)
1 (Perfect)
RSquare(L1, f)
Lab: The Challenge
20 Minutes
Scenario A
Population of Bacteria growing in a petri dish over 4 hours.
Data points provided on worksheet.
Scenario B
Water level in a bucket under a dripping faucet over 4 minutes.
Data points provided on worksheet.
Mission: Find which regression (Linear or Exponential) is better for each!
GEOGEBRA.ORG/CALCULATOR
Lab Debrief
?
The "Why" Behind Growth
Why does a population (like bacteria) naturally trend toward Exponential growth instead of Linear?
?
The Constant Drip
Why is the dripping faucet a Linear model? What physical factor keeps it from growing exponentially?
Exit Ticket
In exactly one sentence, explain why we use Regression Analysis instead of just connecting the dots on a scatter plot.
Turn in your slip before leaving the lab.
Population Challenge Worksheet
Trend Tracker
Lab Activity: Population Challenge
Name:
Date:
Video Recon: GeoGebra Skills
Key Commands
Create Point List: L1 = {(x1,y1), ...}
Exp. Regression: FitGrowth(L1)
Lin. Regression: FitLine(L1)
The R-Squared Scale
0 (None) 1 (Perfect)
In your own words, what does an \(R^2\) value of 0.98 tell you about the function you just graphed?
The Population Challenge
Case A: Petri Dish
| Time (hrs) | Bacteria Count |
|---|
| 0 | 100 |
| 1 | 210 |
| 2 | 430 |
| 3 | 890 |
| 4 | 1850 |
Case B: Dripping Faucet
| Time (min) | Water (oz) |
|---|
| 0 | 5.0 |
| 1 | 12.5 |
| 2 | 21.0 |
| 3 | 29.0 |
| 4 | 38.0 |
Analysis Results (from GeoGebra)
| Target Data | FitGrowth \(R^2\) | FitLine \(R^2\) | Winner & Reason |
|---|
| Case A (Bacteria) | | | |
| Case B (Faucet) | | | |
The Big Picture
Look at the Winning Equation for Case A. What is the growth rate/factor? What does this mean in the context of bacteria?
If you were to use the "Dripping Faucet" data to predict how much water would be in the bucket after 100 minutes, which model would you trust more? Why?
Trend Reality Exit Ticket
Function Fit
Lab Exit Ticket // Algebra 1
Detective Name
Date
? The Critical Question
In real-world data science, we rarely "connect the dots" like a puzzle. In exactly one sentence, explain why we use Regression Analysis instead.
Thinking like a mathematician
Cut Here for Student Handouts
