Work through the list without notes. If you cannot do a statement, follow its link, then come back. Guide = study guide; Practice = practice questions.
Understanding
- I can explain a residual as the vertical distance from a point to the regression line, and say that it has the units of the response variable. (Guide: “How wrong was the prediction?”)
- I can explain what a positive, negative and zero residual mean about the model’s prediction. (Guide: “What the sign tells you”; Practice Q2, Q7)
- I can describe a residual plot and say that it may use x or ŷ on the horizontal axis. (Guide: “Residual plots”)
- I can explain why random scatter in a residual plot supports a linear model and curvature does not. (Guide: “Residual plots”; Practice Q3)
Skills
- I can calculate a residual as observed − predicted, after finding ŷ from the model. (Guide: Worked example 1; Practice Q1, Q4)
- I can find an observed value from a predicted value and a residual, keeping the sign. (Guide: Worked example 2; Practice Q5)
- I can find which point a model predicted best or worst, using the residual closest to or furthest from 0. (Guide: Worked example 1; Practice Q4)
- I can describe the pattern in a residual plot (random, U-shape or arch). (Guide: Worked example 3; Practice Q6)
Reasoning
- I can interpret a residual in context, with units, saying whether the model underpredicted or overpredicted. (Practice Q4, Q5)
- I can explain why a value of r close to −1 or 1 does not by itself show that a linear model is appropriate. (Guide: Worked example 3; Practice Q6)
- I can use the sign of the residuals at the edge of the data to say whether an extrapolation is likely to be too high or too low. (Practice Q6)
- I can explain why one zero residual, or a random residual plot, does not mean every prediction is accurate. (Practice Q5, Q7)
All ticked? Move on to Topic 5.5: Least-Squares Regression, or return to the course roadmap.