Multiple Linear Regression Outperforms Machine Learning for Monthly Temperature Forecasting across the Peruvian Altiplano

Monthly temperature forecasts underpin agricultural planning and frost risk management in the Peruvian Altiplano, yet studies in the region rarely test whether machine learning improves on the standard climatological reference. This study quantifies that improvement at the Puno Principal Climatological Station using 7,279 daily records from 2003 to 2024, and replicates it across eleven independent Altiplano series. Observations were screened, aggregated under the World Meteorological Organization completeness rule, and gaps filled with a calibrated estimator fitted only on training years. Three models were tuned by blocked time-series cross-validation and verified against monthly climatology and persistence. At Puno all three models beat climatology, cutting mean absolute error from 0.597 °C to between 0.415 °C and 0.476 °C, while persistence proved significantly worse than climatology. The neural advantage did not replicate: across 50 random initialisations the perceptron averaged 0.495 °C, and only 4 of 50 beat the deterministic linear model. Linear regression was also the only model whose residuals were normally distributed and serially independent, whereas random forest left a lag-one autocorrelation of 0.427 unexploited. Across 792 test months linear regression was best at 9 of 11 sites, and learning curves extended to 2,475 training months showed the machine learning curves flattening above the linear model without crossing it. Predictive information came almost entirely from combining target-month climatology with recent thermal state; removing humidity, precipitation, and diurnal range changed the error by 0.002 °C. At these sample sizes parsimony and reproducibility therefore favour the linear model, and single-seed reporting of stochastic learners overstates their accuracy.