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📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Question:** A statistician is comparing two models for predicting rainfall. Model X has a mean squared error (MSE) of 0.04, and Model Y has an MSE of 0.01. If the total sum of squared errors (SSE) is proportional to the MSE and the number of data points is 100, what is the ratio of SSE for Model X to SSE for Model Y?

📌 Since MSE is defined as $ \text{SSE} / n $, where $ n $ is the number of data points, and $ n = 100 $ is constant, we can write:

📌 SSE for Model X = $ 0.04 \times 100 = 4 $

📌 SSE for Model Y = $ 0.01 \times 100 = 1 $

📌 \text{Ratio of SSE for X to Y} = \frac{4}{1} = 4

📌 Question:** A marine specialist is monitoring coral growth in two restoration zones. Zone Alpha shows a growth rate of $ 5\% $ per month, and Zone Beta shows a growth rate of $ 3\% $ per month. If Zone Alpha starts with 200 coral colonies and Zone Beta starts with 300 colonies, after how many months will the number of coral colonies be equal in both zones?

📌 Let $ t $ be the number of months after which both zones have the same number of coral colonies.

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