Grade 8 · Data and regression
Recycling records: Separate trend from causal claims
Recycling records investigation: separate trend from causal claims. Change the quantities, follow the motion, and explain the result using the displayed mathematical relationship.
Predict what will happen, press Play, then pause and explain what changed. Every control also works without playback.
Watch the relationship
PausedHD animation studio
From experiment to screen.
Present a crisp Canvas scene, save a full-HD image, or capture your model as a silent video.
Understand what you are seeing
The idea behind the motion.
A scatter plot separates a trend from the deviations around it. These five constructed points have residuals whose sum and linear trend both vanish, so y=ax+b is their exact least-squares line. Correlation measures linear association and cannot, by itself, establish cause. This investigation begins with trend slope = -1; trend intercept = 1; residual scale = 0.5. Treat the named setting as a constructed classroom model, then explain which relationships would still hold if its numbers changed.
A relationship to keep
yᵢ = axᵢ+b+c·eᵢ; e=(1,−2,0,2,−1), x=(1,2,3,4,5)
Read the symbols alongside the explanation. A diagram shows the relationship; the assumptions tell you when it applies.
- STEP 1
Represent the given quantities
Read each plotted input-output pair; the five inputs are fixed at one through five.
- STEP 2
Follow the changing model
Playback reveals points and their vertical residual segments. The reference line is fitted to the complete five-point set.
- STEP 3
Check and explain the relationship
Change the residual scale and compare the scatter with the same fitted slope. A zero slope can coexist with variation.
Your turn to explain
Make a prediction. Test your reasoning.
Recycling records: For the five-point residual pattern in this investigation, what are the least-squares slope and mean output?
Use the values specified in the question. Reset restores the initial values for this investigation.
Compare your explanation
Slope -1; mean output -2. The residuals sum to zero and have zero covariance with the five inputs.
Work through a full lesson
Connect the animation to a worked example and practice questions.