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Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決
Yahoo!奇摩知識+ - 分類問答 - 科學常識 - 已解決 
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數學(統計學)Bi計算問題需要解答?
Nov 12th 2013, 17:07

Cov(Ri,Rm) 用 sample covariance (S_{i,m}) 樣本共變異數去估量。
Var(Rm) 用 sample variance (S_m²) 樣本變異數去估量。

先計出
μi = (6%+7%+5%+8%+9%+7%)/6 = 7%
μm = (4%+6%+5%+6%+7%+6%)/6 = 5.6667%

估量Cov(Ri,Rm) = S_{i,m} = [(6%)(4%)+(7%)(6%)+(5%)(5%)+(8%)(6%)+(9%)(7%)+(7%)(6%) - 6*(7%)*(5.6667%)]/(6-1) = 0.00012 ≈ 0.0001

估量Var(Rm) = S_m² = [(4%)²+(6%)²+(5%)²+(6%)²+(7%)²+(6%)² - 6*(5.6667%)²]/(6-1) = 0.000106667 ≈ 0.000107

Beta = Cov(Ri,Rm)/Var(Rm) ≈ S_{i,m} / S_m² = 0.0001/0.000107 = 0.934579439 ≈ 0.93

但我實話實說,以上的計算雖然可以解答你的發問,但這個計法有很過份的捨入誤差,如果你用較準確的數,你應得出
Beta = 0.00012/0.000106667 = 1.125

用Excel 可用:
=COVARIANCE.S(A1:F1,A2:F2) = 0.00012
=VAR.S(A2:F2) = 0.000106667

或直接用
=SLOPE(A1:F1,A2:F2) = 1.125

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