(c) What is the multicollinearity problem?

5. (12分) In a random sample of 400 industrial accidents, it was found that 231 were due at least partially to unsafe working conditions. Please construct a 99% confidence interval for the corresponding true proportion. (Refer to the attached Tables if necessary)

6. (10分) Let the variables X₁, X₂ and X₃ have variances σ₁² = 1.0, σ₂² = 3.0 and σ₃² = 5.0. Let these variables be independent and Y = 13 - 2X₁ + 3X₂ - 10X₃. Find the variance of Y.

(a) How much the degree of freedom will be when applying a sample of size n to estimate  the model?

(b) What are 「R²」and 「adjusted R²」? And what is the difference between them?

(d) What is the heteroscedasticity problem?

(a) Show that if x ＜ α/(1 - β), then x ＜ E(Y) ＜

(b) Show that if x ＞ α/(1 - β), then x ＞ E(Y) ＞, and conclude that E[Y] is always  between x and α/(1 - β).

第一題: English to Chinese - 英文翻譯中文Preparations for loading cargo (verifying the loading capacity of voyage,studying the cargo information, making out the cargo plan, initial checking the stability, trim and stresses).proper stowage and securing of cargo (ensure a solid stow and effective securing of cargo units, keep air passage in advance, and that for convenient cargo inspection).Check the stability, trim, stresses for the cargo loading condition of the voyage.According to the inspection of cargoes and records of findings at regular intervals and to the measures taken, take further actions to avoid any damages to the ship or cargoes.Identify any damage to the ship or cargoes after discharging and determine possible causes.Correctly fill the "cargo papers" and "mate's remark".

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第三題: Chinese to English -中文翻譯英文致高雄ABC代理行敬啟者:提要:添加淡水之請求請安排添加250淡水到本輪,本輪現在拋錨在高雄港第二錨區。本人同意每噸淡水美金1.50元及美金150元作為拖船及水駁船的服務費。請確認在2023年7月21下午前完成添加淡水之作業。謝謝你的合作海龍輪船長