Everything else is ready: study the parts, the key terms and the quiz below.
- Part 11Fit one relationship to selected trips
- Part 22Construct the residuals, rather than checking the input shape
- Part 33Build a Q-Q plot point by point
- Part 44Quantify the upper-tail departure
- Part 55Check spread across distance separately
- Part 66Guard against the common wrong diagnostic
- Part 77Reproduce and challenge
Residual Shape and the Q-Q Plot
Diagnose the shape of observed data or model residuals without assuming that every ML feature must be normally distributed.
In this lesson7 parts
- 01Fit one relationship to selected trips
- 02Construct the residuals, rather than checking the input shape
- 03Build a Q-Q plot point by point
- 04Quantify the upper-tail departure
- 05Check spread across distance separately
- 06Guard against the common wrong diagnostic
- 07Reproduce and challenge
Key terms
The words this lesson introduces, each in one line. The module’s glossary collects them all.
- predictor
- Recorded input used to calculate a fitted value; here, trip distance.
- ordinary least squares (narration)
- Chooses the intercept and slope that minimize the summed squared vertical errors.
- intercept
- Fitted duration at distance zero.
- slope
- Change in fitted minutes per additional mile.
- fitted value
- Prediction from the estimated line.
- residual
- Observed outcome minus fitted value.
- normal error shape
- A model assumption about conditional errors around fitted values.
- Q-Q plot
- Paired quantiles from observed data and a reference distribution.
- normal quantile
- Value at a stated cumulative probability in a normal model.
- heavy upper tail
- More or larger high values than the chosen reference predicts.
- positive skew
- A distribution with a longer or heavier right tail.
- residual SD
- Empirical spread of observed minus fitted durations: about 7.71 minutes here.
- heteroscedasticity
- Error spread changes with predictor value.
- constant error spread
- Similar conditional residual variability across predictor values.
Quiz 5 questions
Your first pick on each question is the one that counts, and a right one earns a coin. Getting one wrong here is how the lesson sticks.
Practice
Problems to solve in your own notebook. Each states the problem, not the steps: working out the steps is the exercise. Level A applies the lesson, B combines it with earlier ones, C stretches it.
The self-checking notebook for this lesson is The normal distribution and residual shape.
Common mistakes
What you will see when it goes wrong, why it happens, and the fix.
Where it’s used
Where this lesson’s ideas turn up in real work.