Zerlegung  von e         (4),(7)   [17]       η + ε  = ß (ξ+δ)   ;    η - ßξ  = 0

                                                                     [18]            e   =  ε  - ß δ

                                                                  [19]          y    =  ßx  + ε - ßδ

                                                                  [20]     y - ε   =  ß ( x -  δ ) 

         Synthese  zu  e                           [21]        {[ (η = ßξ | + ε) |:ß ] + δ } |*ß

                                                                     [22]    η + ε  = ß (ξ+δ) + ε – ßδ ,     y  =  ßx  + ε – ßδ 

Die Erweiterung der CAUCHY-SCHWARZ`en Ungleichung

[23]        σ_ηξ    =   σ_yx     ≠  σ_y σ_x ,           µ(yx = ηξ + ηδ +ξε + εδ)   = σ_ηξ  ;       y = η+ε ,  x = ξ+δ

[24]        σ_ηξ    =  signσ_ηξ  σ_ησ_ξ       SCHWARZ 

[25]        σ_yx   =  σ_ηξ   ^  σ_ηξ  =  signσ_ηξ  σ_ησ_ξ    -->    σ_yx  =  signσ_xy  σ_ησ_ξ 

[26]                                                                               σxy²  =   σ²_ξσ²_η              

Wahre Varianzen           [27]      σ²_η  =  ßσ_yx     =  ( signσ_xyσ_η/σ_ξ)  signσ_xy σ_ησ_ξ   = σ²_η 

                                           [28]      σ²_ξ  =  σ_yx/ß   =  signσ_xy σ_ησ_ξ /(signσ_xy  σ_η/σ_ξ)  = σ²_ξ

 Varianzen der Fehler    [29]        ε  =  y – η   -->  σ²_ε  = σ²_y - σ²_η  = σ²_y - ßσ_yx        (25)    

                                            [30]        δ  =   x – ξ    -->    σ²_δ = σ²_x  -  σ²_ξ  = σ²_x - (1/ß) σ_yx  (25) 

ß-Identifikation ableitungsfrei

[30]              ß  =  (σ²_y  -  σ²_ε) / σ_yx ,      ß  ≥  ß_e ,  (6), (27)      

[31]              ß  =   σ_yx  / ( σ²_x  - σ²_δ  ) ,   ß  ≥  ß_e ,  (6), (28)

[31a]            ß  =    σ_yx / σ²_ξ = sign σ_yx  σ_ησ_ξ /σ²_ξ     

ß-Identifikation methodisch paradox

[32]     0  =   ∂σ²_ε / ∂ß  ≠ 0   -->      ß  =   σ_yx  / ( σ²_x  - σ²_δ  ),                ß = ßε ≥ ß,  (6)

[33]     0  =   ∂σ²_δ / ∂ß  ≠ 0    -->    ß  =  (σ²_y  -  σ²_ε) / σ_yx ,                 ß = ß_δ ≤ ß,    (6)