Module 5 Multiple linear regression and model diagnostics
Module overview: multiple regression with several NOAA predictors; interpreting coefficients with “holding others fixed” language; diagnostics, multicollinearity awareness, residuals; joint hypothesis testing with \(F\)-tests; richer forecasting discussions.
5.1 Data source
Use the NOAA Integrated Surface Database (ISD) for multivariate station records.
- Core variables: temperature, dew point, wind, pressure, visibility, precipitation indicators (subset to what you teach)
- Portal: NOAA Integrated Surface Database
5.2 Statistics topics
- Multiple linear regression with several predictors
- Partial effects (marginal interpretation holding others fixed)
- Multicollinearity concepts and basic diagnostics
- Joint tests with \(F\)-tests; residual-based model checks
5.3 Suggested workflow
- Download ISD data for a chosen station and period.
- Build a multivariable analysis table (cleaned and coded as needed).
- Fit a model with at least three predictors.
- Interpret key coefficients with careful wording on conditioning variables.
- Report a joint \(F\)-test (or nested model comparison as taught) with residual checks.