obun

vertikal

horizontal

P = (20.220182868346363, 6.027874052571414)
O = (46.371920650109736, 41.83494080244431)
N = (34.333819131520244, 60.28766231771623)
M = (23.333484985222952, -14.621600024042404)
L = (5.276332707338717, 31.729879020271582)
K = (-6.346661862333894, 14.155858529536417)
J = (-7.591982709084531, -7.811667083882543)
I = (-23.988707191301256, 4.709822515766263)
H = (-32.0832926951804, -6.273940290943214)
G = (-28.762437103845365, -31.316919490240824)
F = (-45.159161586062105, -14.841275280176616)
E = (-48.06491022848023, -35.271074100656236)
D = (-35.40414828651545, -25.825038086886096)
C = (-20, -20)
Wolke: {C, D, E, F, G, H, I, J, K, L, M, N, O, P}
m_y = mean(y(Wolke))
m_x = mean(x(Wolke))
V_x = Variance(x(Wolke))
c = Covariance(Wolke)
r = PMCC(Wolke)
V_y = Variance(y(Wolke))
s_x: sqrt(V_x)
s_y: sqrt(V_y)
trendlinie_{1-berechnet}(x) = (c / V_x * (x - m_x)) + m_y
trendlinie_1 = FitLineY(Wolke)
trendlinie_{2-berechnet}(x) = (V_y / c * (x - m_x)) + m_y
Mittte: (m_x, m_y)
regressionen_1mal_ regression_2: (Slope[trendlinie_{1-berechnet}] * Slope[trendlinie_{2-berechnet}])
bestimmtheitsmass_{rquadrat}: r^(2)
steigung = 1.14 (slider from -2 to 2, step 0.001)
u(x) = (steigung * (x - m_x)) + m_y
prox: (x(Wolke), u(x(Wolke)))
Vertikal = Sequence(Segment[Element[Wolke, i], Element[prox, i]], i, 1, 14)
Störvarianz_{vertikal}: Sum[Vertikal^(2)] / 14
Scheitel_1: (c / V_x, V_y - c^(2) / V_x)
vertikalstörvarianz(x) = (V_x * (x - x(Scheitel_1))^(2)) + y(Scheitel_1)
D_1: (steigung, Störvarianz_{vertikal})
proy: ((y(Wolke) - m_y) / steigung + m_x, y(Wolke))
Horizontal = Sequence(Segment[Element[Wolke, i], Element[proy, i]], i, 1, 14)
Störvarianz_{horizontal}: Sum[Horizontal^(2)] / 14
D_2: (steigung, Störvarianz_{horizontal})
vertikalsicht = true
horizontalsicht = false
Scheitel_2: (V_y / c, V_x - c^(2) / V_y)
Text1 = LaTeX(Störvarianz_{horizontal}, true, true)
Text2 = LaTeX(Störvarianz_{vertikal}, true, true)
winkelhalbierende: y = x
trendlinie_2 = Mirror(FitLineY[Mirror[Wolke, winkelhalbierende]], winkelhalbierende)
horizontalstörvarianz(x) = (V_y * (1 / x - c / V_y)^(2)) + V_x - c^(2) / V_y
regression_1: c / V_x
regression_2: V_y / c
hh(x) = (V_y * (x - c / V_y)^(2)) + V_x - c^(2) / V_y
DD_2: (1 / steigung, Störvarianz_{horizontal})