(b) Refer to part (a). Compute the probability that: next week Amaze will occur on Monday and Thursday and will not occur on Tuesday and Wednesday. (Note: You are being asked to calculate to the fourth decimal place)

4. 建立多元迴歸模式(multiple regression model)分析資料需要評估共線性(collinearity)的問題。假設建立的線性迴歸模式為： $Yi = \beta0 + \beta1 X{1i} + \beta2 X{2i} + \varepsiloni$，$\beta0$、$\beta1$、$\beta2$ 分別是截距項與解釋變數($X1, X2$)的係數，$\varepsiloni$ 是隨機誤差項，$i = 1, 2, \dots, n$，$n$ 為樣本大小，$\varepsiloni$ 滿足基本假設。就此模式而言，請問：(1)共線性問題指的是什麼？(10%) (2)藉由變異數膨脹因子(variance inflation factor, VIF)評估這個問題該如何進行(符號可自訂)? (10%) (3)假設 $X1$ 的 VIF 值為 4，這個數值的意義為何？(5%) 對 $\beta1$ 的估計檢定有何影響？(5%)

(b) Refer to part (a). Compute the probability that: next week Amaze will occur on Monday and Thursday and will not occur on Tuesday and Wednesday.

(Note: You are being asked to calculate to the fourth decimal place)

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