Long-term vibration monitoring of hydroelectric dams requires separating structural change from repeatable environmental and operational effects. This paper evaluates how air temperature, headpond level, and generating load affect tracked frequency and damping estimates from four modal families of the Mactaquac Intake Structure. Multiple linear regression models are assessed using two structured studies: first, predictor and polynomial complexity are evaluated without temperature lag; second, the same combined model hierarchy is re-evaluated with optimized temperature lag. Candidate models are ordered using a total-complexity score based on the number of non-intercept regression terms, and performance is assessed using out-of-sample prediction skill and improvement over the best lower-complexity model. The results show whether improved normalization is obtained primarily by increasing polynomial flexibility or by representing the delayed thermal response. The study provides a practical model-selection framework that favours physically interpretable lagged thermal predictors and operational load terms before high-order polynomial complexity.