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CH2 統計基礎 - Coggle Diagram

- - - - Σ(x-x̄)
        =Σx-Σx̄
        =Σx-nx̄
        =Σx-nΣx/n
        =Σx-Σx
        =0
    - - SSₓ=Σ(x-x̄)²
        =Σ(x²-2xx̄+x̄²)
        =Σx²-2x̄Σx+nx̄²
        =Σx²-2(Σx/n)Σx+n(Σx/n)²
        =Σx²-2(Σx)²/n+n(Σx)²/n²
        =Σx²-2(Σx)²/n+(Σx)²/n
        =Σx²-(Σx)²/n
    - - CP=Σ(x-x̄)(y-ȳ)
        =Σ(xy-x̄y-xȳ+x̄ȳ)
        =Σxy-x̄Σy-ȳΣx+nx̄ȳ
        =Σxy-(Σx/n)Σy-(Σy/n)Σx+n(Σx/n)(Σy/n)
        =Σxy-(ΣxΣy/n)-(ΣxΣy/n)+(ΣxΣy/n)
        =Σxy-(ΣxΣy/n)
    - - Sₓ₊ₐ²
        =Σ[(x+a)-(x̄+a)]²/n
        =Σ(x-x̄)²/n
        =Sₓ²
    - - Sₐₓ²
        =Σ(ax-ax̄)²/n
        =Σ[a(x-x̄)]²/n
        =Σ[a²(x-x̄)²]/n
        =a²Σ(x-x̄)²/n
        =a²Sₓ²
- - - - Cᵪᵧ=Σ(x-x̄)(y-ȳ)/n=CP/n
    - - CP=Σ(x-x̄)(y-ȳ)
    - - rᵪᵧ=Σ(x-x̄)(y-ȳ)/nSᵪSᵧ=Cᵪᵧ/SᵪSᵧ=CP/nSᵪSᵧ
        =CP/√ SSᵪSSᵧ
        =Σzᵪzᵧ/n
  - - - Sᵪ₊ᵧ²
        =Σ[(x+y)-(x̄+ȳ)]²/n
        =Σ[(x-x̄)+(y-ȳ)]²/n
        =Σ[(x-x̄)²+2(x-x̄)(y-ȳ)+(y-ȳ)²]/n
        =Σ(x-x̄)²/n+2Σ(x-x̄)(y-ȳ)/n+Σ(y-ȳ)²/n
        =Sᵪ²+2CP/n+Sᵧ²
        =Sᵪ²+2Cᵪᵧ+Sᵧ²
        =Sᵪ²+2rᵪᵧSᵪSᵧ+Sᵧ²
    - - Sᵪ₋ᵧ²
        =Σ[(x-y)-(x̄-ȳ)]²/n
        =Σ[(x-x̄)-(y-ȳ)]²/n
        =Σ[(x-x̄)²-2(x-x̄)(y-ȳ)+(y-ȳ)²]/n
        =Σ(x-x̄)²/n-2Σ(x-x̄)(y-ȳ)/n+Σ(y-ȳ)²/n
        =Sᵪ²-2CP/n+Sᵧ²
        =Sᵪ²-2Cᵪᵧ+Sᵧ²
        =Sᵪ²-2rᵪᵧSᵪSᵧ+Sᵧ²
- - - - 對稱 =0
      - 負偏 <0
      - 正偏 >0
    - - 高狹 >0
      - 常態 =0
      - 低闊 <0