Regression Lab Teacher Guide Regression Lab
Teacher Facilitation Guide
11th Grade Statistics
Unit: Bivariate Data
Instructional Objective
Students will master the technical competency of performing regressions using GeoGebra. By the end of the lesson, students will be able to import raw datasets, generate linear and exponential models, and use \(R^2\) values to determine the strength of a fit.
Pacing Guide (50 Minutes)
05 min
Warm-up: The Vocab Vault
Quick review of Scatter Plots, Correlation, and Regression definitions.
15 min
Guided Tech Tutorial
Video: "Approximating Functions for Data". Focus on L1 lists and the FitGrowth command.
20 min
Independent Practice: Market Crashers
Students analyze raw stock price data to find the best mathematical model.
05 min
Closure: Troubleshooting
Debrief common errors (rounding, command choice).
05 min
Homework Launch
Assigning the "Data Detective" web search.
Materials
Student Laptops/Chromebooks
Access to GeoGebra.org
Video Tutorial Guide
Raw Data Files Worksheet
Projector + YouTube Access
Critical Teaching Moments
Timestamp 3:38 — Command Confusion
GeoGebra suggests FitExp first. Stop the video here. Explain that FitExp uses base \(e\) (Euler's number), while FitGrowth provides the standard \(y = a \cdot b^x\) format they are accustomed to in high school algebra.
Timestamp 5:47 — The \(R^2\) Reality Check
The video shows \(R^2\) logic. Emphasize that \(R^2 = 1\) isn't just "good," it means the model is perfect. In real statistics, a "good" \(R^2\) depends on the field (e.g., 0.9 in physics is expected, but 0.7 in sociology might be groundbreaking).
The "Messy Data" Shift
Remind students that regression is an approximation . If they get a result that looks "ugly," that's normal. Technology allows us to handle the messiness that hand-calculation cannot.
Independent Practice Tip
Students often forget to create the L1 list . If their FitLine(L1) command throws an error, it's usually because the list wasn't defined first.
Common Pitfalls
01
Rounding Too Early: Students often round \(a\) and \(b\) values to one decimal place, which drastically changes the trajectory of exponential curves. Encourage them to use at least 4 decimal places.
02
Linear Bias: Students often assume a linear fit is best because it's simpler. Use the \(R^2\) comparison to "prove" the best model objectively.
03
Data Entry Errors: One mistyped coordinate can ruin a regression. Teach students to look at their scatter plot visually to spot "outliers" that might just be typos.
Video Tutorial Guide REGRESSION TUTORIAL
Name: ___________________________
Date: ___________________________
Video Title
Approximating Functions for Data — Justin
1
Warm-up: The Vocab Vault
Define Regression:
In real life, why doesn't data always fit perfectly on a function?
2
Guided Tech Lab (Follow Along)
2:26
Setting up the Window & Data
Go to geogebra.org/calculator. Enter the coordinates from Example 1 into a single list called L1.
List Command: L1 = {(x1,y1), (x2,y2)...}
3:21
The Command Choice
When typing "Fit", what command should you use for standard exponential growth? (Highlight one)
FitExp(L1) FitGrowth(L1)
Why? ________________________________________________________________________
5:47
The Truth Detector: R-Squared (\(R^2\))
Record the results for the first dataset:
Exponential Fit \(R^2\)
Linear Fit \(R^2\)
The closer \(R^2\) is to 1, the ________________ the fit.
3
Pause & Practice
6:43 PAUSE POINT
Follow the video prompt. Enter the second dataset, run both models, and record the winner below.
EXPONENTIAL MODEL
Equation:
\(R^2\) Value:
LINEAR MODEL
Equation:
\(R^2\) Value:
Winning Model:
Exp
Linear
Regression Lab Practice Market Crashers
REGRESSION LAB // DATASET ID: NASDAQ_08X
Technical Proficiency
11th Grade Stats
The Scenario
You are a junior analyst at Apex Growth Funds. You've been handed a raw data export of "Luna-Tech" (LNTH) stock prices from its first 12 days on the market.
Mission Objective
Perform a regression analysis to determine if the stock is growing Linearly or Exponentially . Recommend a model for future predictions.
raw_export_lnth.csv
Day (x) Price USD (y) Notes 1 $12.50 IPO Start 2 $15.20 3 $19.80 4 $23.10 5 $28.90 6 $36.40 8 $55.20 Missing Day 7 10 $84.70 12 $129.50 Market Close
Step-by-Step Analysis
01
Enter Data into GeoGebra
Create the list L1 using the points above. Watch out for the skipped days (Day 7, 9, 11)!
L1 List Confirmed
02
Linear Model Test
Command: FitLine(L1)
Equation (f)
Correlation Coefficient
Command: RSquare(L1, f)
\(R^2\) Value
03
Exponential Model Test
Command: FitGrowth(L1)
Equation (g)
Correlation Coefficient
Command: RSquare(L1, g)
\(R^2\) Value
Final Recommendations
1. Which model "fits" the reality of the stock market data better? Justify using your \(R^2\) values.
2. Growth Factor: Using your winning model, what is the daily growth rate? (%)
3. Prediction: Based on your model, what will the stock price be on Day 20?
Regression Lab Answer Key Answer Key
Regression Lab: Master Technical Guide
I. Video Tutorial Guide
Vocab & Warm-up
Regression: Using technology to create a function that approximates data as perfectly as possible.
Why doesn't data fit perfectly? Real-world factors (measurement error, environmental noise, human behavior) mean data is "approximately" exponential or linear, not perfectly so.
Tutorial Data Checkpoints
Command Choice (3:21)
FitGrowth(L1)
Why? FitExp uses base \(e\), while FitGrowth provides the \(a \cdot b^x\) format used in standard growth/decay problems.
Truth Detector (5:47)
Exponential fit \(R^2\): ~0.9954
Linear fit \(R^2\): ~0.9091
Conclusion: Exponential is much better.
Pause & Practice (6:43) — Dataset 2
Exponential Model:
\(R^2 \approx 0.957\)
Linear Model:
\(R^2 \approx 0.982\)
Winning Model: Linear
Equation: \(y = 9.85x + 57.27\)
II. Market Crashers Lab Practice
CALCULATED RESULTS (L1 Data)
Linear Model (f)
\(f(x) = 10.14x - 14.89\)
\(R^2 \approx 0.9084\)
Exponential Model (g)
\(g(x) = 10.32 \cdot (1.2371)^x\)
\(R^2 \approx 0.9997\)
Justification:
The exponential model is an almost perfect fit (\(R^2 = 0.9997\)) compared to the linear model (\(R^2 = 0.9084\)). The stock price is clearly accelerating rather than growing at a constant rate.
Growth Rate:
~23.7%
(From the base 1.2371)
Day 20 Prediction:
$752.48
(Substitute x=20 into g(x))
Homework Keys
Homework is open-ended. Success criteria:
Dataset includes at least 8 data points.
Correct use of FitGrowth or FitLine.
Correct interpretation of the \(R^2\) value for the chosen model.
