Math 3 Quiz
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MODELING & APPLICATIONS
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A meteorologist is comparing two models for predicting daily temperature (T) in degrees Fahrenheit based on the day of the year (d), where January 1st = day 1. Model X: T=68+22sin⁡(2π(d−81)365)T = 68 + 22\sin\left(\frac{2\pi(d-81)}{365}\right) Model Y: T=45+0.08d−0.0001d2T = 45 + 0.08d - 0.0001d^2 Model X is based on sinusoidal temperature variation, while Model Y assumes temperatures increase through summer then decrease. Both models were tested on one year of data.
If Model X has RMSE = 8.2°F and Model Y has RMSE = 12.1°F, but Model Y predicts that December 31st will be warmer than January 1st, which evaluation is most appropriate?
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