Texas HS Mathematical Models Question of the Day

Ask, "Do regions have good or bad yields?" Label each field as good/bad using a threshold and run logistic regression. Ignore weather and soil differences; report classification accuracy only.

Ask, "Which region has the highest average yield?" Collect one recent year of yields and compute region means. Rank regions and declare the top mean as best; no modeling or checks.

Ask, "Are yields rising over time?" Use statewide annual yields for 3 years to fit a straight line vs. year. Report slope; ignore regions and weather.

Ask, "How do rainfall, growing degree-days, soil type, irrigation, and region predict county-level yield?" Collect 5 years of county yields, seasonal rainfall, growing degree-days, soil class, irrigation indicator, fertilizer rates, and region. Fit multiple regression with region fixed effects and interactions (e.g., rainfall×region). Validate via residual diagnostics, $R^2$, outlier influence, and holdout testing; report confidence intervals and effect sizes. Conclude which factors explain regional differences and estimate expected yield by region under typical weather.