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["Beispiel für die Berechnung einer multivariaten Regression mit Excel"]
[]
["k = Anzahl erhobener Variablen "]
["n = Anzahl Daten pro Variable"]
[]
["Datenmatrix A ="]
["Variable für Konstantenberechnung","Variable 1","Variable 3","Variable 3",null,"n x (k+1)"," = 5 x 4 im Beispiel"," (an erster Stelle bei j x i steht jeweils die Zeilennummerierung, an zweiter Stelle die Spaltennummerierung)"]
[1,5,4,1]
[1,3,3,1]
[1,2,1,0]
[1,1,2,0]
[1,3,2,1]
[]
[]
["Transponierte Matrix A' =",{"$nulls":4},"(k+1) x n"," = 4 x 5 im Beispiel"]
[1,1,1,1,1]
[5,3,2,1,3]
[4,3,1,2,2]
[1,1,0,0,1]
[]
[]
["A*A' =",{"$nulls":4},"(k + 1) x (k + 1)"," = 4 x 4 (im Beispiel)"]
[5,14,12,3]
[14,48,39,11]
[12,39,34,9]
[3,11,9,3]
[]
[]
["Inverse Matrix von A*A' ="]
[1.558823529411764,-0.2647058823529419,-0.4411764705882345,0.735294117647059,null,"(k + 1) x (k + 1)"," = 4 x 4 (im Beispiel)"]
[-0.2647058823529426,0.4411764705882356,-0.26470588235294046,-0.5588235294117666]
[-0.44117647058823367,-0.26470588235294124,0.5588235294117637,-0.26470588235293946]
[0.7352941176470602,-0.5588235294117652,-0.2647058823529417,2.4411764705882373]
[]
[]
["(A*A')-1*A' ="]
[-0.7941176470588246,0.17647058823529393,0.5882352941176457,0.41176470588235303,0.6176470588235283,"(k+1) x n"," = 4 x 5 ( im Beispiel)"]
[0.32352941176470684,-0.2941176470588237,0.3529411764705881,-0.3529411764705879,-0.029411764705883248]
[0.20588235294117563,0.1764705882352945,-0.4117647058823525,0.4117647058823526,-0.38235294117646934]
[-0.6764705882352953,0.7058823529411771,-0.6470588235294118,-0.3529411764705883,0.9705882352941186]
[]
[]
[]
["Vektor y = ",{"$nulls":4},"n x 1 "," = 5 x 1 (im Beispiel)"]
[160]
[140]
[130]
[100]
[110]
[]
[]
["(A*A')-1*A'*y=",{"$nulls":4},"n x 1"," = 5 X 1 (im Beispiel)"]
[83.23529411764659,null,-3.82]
[17.94117647058828,null,15.29]
[3.2352941176471504,null,7.65]
[-22.058823529411754,null,-7.65]
[null,null,-11.47]

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