Regression Battle Slides Algebra 2: Unit 5
REGRESSION
BATTLE
When data gets messy, the math gets real.
The Battleground
MODEL A
Linear Fit
MODEL B
Exponential Fit
Which is "better"? How do we PROVE it?
Intelligence Briefing
Embedded media
Watch For
R-Squared (R²)
Scale Range
0.0 to 1.0
Conclusion
1.0 = Perfect Fit
GeoGebra Arsenal
01 L1 = {(x1, y1), ...}
02 f(x) = FitLine(L1)
03 g(x) = FitGrowth(L1)
04 RSquare(L1, f)
WARNING: Use FitGrowth, not FitExp.
Regression Battle
1
Grab a Data Intel Card with your partner.
2
Input data and run both models in GeoGebra.
3
Calculate R² values for both functions.
The Defense
"The numbers don't lie, but they do tell a story."
Defend your choice on the Battle Log using specific R² evidence.
25:00 ON THE CLOCK
The Debrief
The Vision Test
Can R² be high even if the graph looks "wrong"?
The Outlier Bomb
What happens to R² if we add one "crazy" data point? Why?
IS R² THE FINAL SAY?
Data Intel Cards Data Intel Cards
Cut along the dotted lines. Assign one card per pair.
Intel: Sector A
Exp. Decay
The Cold Case: Coffee Cooling
Target: Track the temperature of a hot latte left on a desk over 30 minutes.
Time (min) Temp (°F) 0 185.0 5 168.2 10 153.1 15 139.5 20 127.2 25 116.3 30 106.8
CMD: FITGROWTH(L1) VS FITLINE(L1)
Intel: Sector B
Biometrics
The Vitruvian Man: Growth Check
Target: Relationship between height and arm span in teenagers.
Height (in) Arm Span (in) 60 60.5 62 61.0 64 64.5 66 65.8 68 68.2 70 71.1 72 72.4
CMD: RSQUARE(L1, F) VS RSQUARE(L1, G)
Intel: Sector C
Biological
The Petri Dish: Colony Count
Target: Population of E. coli in a controlled petri dish over 6 hours.
Hour (x) Pop. (count) 0 100 1 160 2 256 3 410 4 655 5 1048 6 1677
DANGER: DO NOT USE FITEXP
Intel: Sector D
Economics
The Career Ladder: Paycheck
Target: Starting annual salary based on years of experience in IT.
Years (x) Salary ($k) 1 45.0 3 52.2 5 61.5 7 70.8 9 81.1 12 96.5 15 115.0
AMBIGUOUS DATA DETECTED - CALCULATE BOTH
End of Intelligence Brief - Distribute Securely
Regression Battle Log Battle Log
Operation: Regression Justification
Agents:
Date:
Mission Objective
Analyze the assigned data sector. Prove which regression model is superior using R² evidence.
Sector
A B C D
I. Intelligence Gathering
Input your data into a single list in GeoGebra. Record your list name (e.g., L1) and a quick sketch of the scatter plot below.
Visual Scan
List ID:
Data Range:
Initial visual guess: Does it look more like a line or a curve?
II. Model Comparison
Linear Fit
Equation [f(x)]
R-Squared Value
Exponential Fit
Equation [g(x)]
R-Squared Value
III. The Final Defense
In the space below, mathematically justify which model is the "winner." You must explicitly reference both R² values and explain what they mean in the context of this data.
IV. Strategic Reflection
Scenario: A data set has an R² of 0.98 for Linear and 0.97 for Exponential. Is the Linear model automatically the best choice? Why or why not?
Verified for Accuracy - Data Command Headquarters
Regression Battle Teacher Guide Battle Brief
Instructional Facilitation Guide
Lesson Topic
Justifying Regression Models
Timeline
Hook 5 min
Briefing (Video) 10 min
Battle Activity 25 min
Debrief 5 min
Objectives
Students will use R² values to mathematically justify why a linear or exponential model is a better fit for real-world data.
Gear Needed
Devices with GeoGebra Graphing Calculator, Data Intel Cards, Battle Logs, Rubrics.
01 Operational Guidance
The Hook: Visual Intuition vs. Math
Display the two graphs. Most students will guess the exponential curve is better because it "looks" closer. Ask: "In science or business, is 'looks close' enough to invest millions of dollars? How do we quantify 'closeness'?"
The Battle: Technical Support
Monitor pairs for common GeoGebra roadblocks:
Ensure students wrap points in curly braces: L1 = {(1,2), (3,4)}.
Remind them that RSquare requires two inputs: the list and the function name.
Watch for students using FitExp. They must use FitGrowth for standard \(y = ab^x\) forms.
02 Intelligence Key (Answer Key)
Sector Linear R² Exp. R² Superior Model Key Justification A (Coffee) ~0.978 ~0.999 Exponential Cooling follows Newton's Law of Cooling (Exponential). B (Bio) ~0.991 ~0.985 Linear Height vs Arm Span is nearly 1:1 (Linear relationship). C (Bacteria) ~0.880 ~0.999 Exponential Population doubles/increases by a factor (Exponential). D (Salary) ~0.988 ~0.998 Exponential Salary grows by percentages over time, creating a curve.
03 Post-Battle Debrief
Discussion Starters
"If the R² is 0.99 but the residual plot shows a pattern, is it still the best model?"
"Why might a business choose a simpler linear model even if exponential is slightly higher R²?"
Extension: Outliers
Regression Scorecard Rubric Regression Scorecard
Battle Assessment Rubric
Total Score
/ 16
Criteria 1 - Novice 2 - Apprentice 3 - Specialist 4 - Master Technical Execution
GeoGebra use & Equation recording
| Unable to generate regression equations; significant command errors. | Generated equations but recorded them incorrectly or with missing variables. | Accurately generated and recorded both model equations in proper notation. | Equations are perfect; used correct function notation [f(x) and g(x)] correctly. |
|
R² Calculation
Accuracy of R-Squared values
| R² values are missing or significantly incorrect. | Found R² for only one model or values are swapped/rounded poorly. | Accurately calculated R² values for both models. | Calculated R² values to appropriate precision for both models. |
|
The Defense
Mathematical justification
| Choice of model is purely visual with no math support. | Choice mentions R² but lacks a comparison or clear explanation. | Justified choice by explicitly comparing both R² values. | Masterful defense; explains the R² scale and why "closer to 1" is decisive. |
|
Strategic Thinking
Contextual interpretation
| Reflection is incomplete or doesn't address the scenario. | Reflection is vague (e.g., "Math is hard"). | Reflection identifies that R² isn't the only factor (visual check matters). | Nuanced reflection; mentions real-world factors vs. pure statistical fit. |
Commander's Comments (Teacher Feedback)
Promoted?
Final Rank Achievement
Novice
Apprentice
Specialist
Master
