Desmos Tricks
Residual Plots
Visually check if a linear model is appropriate.
📉 Residual Logic
Random means Good. Pattern means Bad.
Random Scatter = Good Model.
Pattern (U-shape) = Bad Model (Wrong type).
📝 SAT Problem
Fit a Linear Regression to the data below. Is the linear model appropriate?
| x | y |
|---|---|
| 1 | 8 |
| 2 | 4 |
| 3 | 2 |
| 4 | 4 |
| 5 | 8 |
(A) Yes, random residuals
(B) Yes, \(R^2 = 1\)
(C) No, U-shaped residuals
(D) No, r is negative
Step 1: Enter Data & Run Linear
Type the table. Run y1 ~ mx1 + b.
Step 2: Plot Residuals
Click the plot button next to e1 in the regression box.
Step 3: Check Patterns
The dots form a U-shape (High-Low-High).
A pattern means the linear model found the wrong shape. It is not appropriate.
✅ Final Answer: (C)