In the full lesson
- Residual (formula)
- What Patterns Reveal (text)
- Checking Conditions (tip)
Open the Regression & Correlation lessons or see what Premium includes.
Module 6 · Regression & Correlation · Topic 7
Residual Analysis
Residual Plots. Plot residuals on the y-axis against x (or ŷ) on the x-axis. A good linear model shows randomly scattered residuals with no pattern. Patterns indicate the model is inadequate.
This is the opening of a Premium lesson. The full lesson, with its 4 sections, reads in the interactive course; the module's first lesson is free.
Key formulas
From the Regression & Correlation formula sheet
- Least-Squares Regression Line:
yhat = a + bx- Line that minimizes the sum of squared residuals. - Pearson Correlation:
r = sum((x_i-xbar)(y_i-ybar)) / sqrt(sum((x_i-xbar)^2)sum((y_i-ybar)^2))- Measures direction and strength of a linear association.
Related glossary terms
- Residual: The observed value minus the predicted value. Example: If y = 12 and yhat = 9, the residual is 3.
Go interactive
Work this topic in StatRise
This module opens on its first lesson free; the rest of it unlocks with Premium. Every calculator and simulation below is free.
Keep reading