Allgemeine Sinusfunktion
Author: Andreas Jäger
Date: 18 April 2013

Proportionale Regression

Lineare Regression

Hilfslinie

Regressionsanalyse

PRT

LRT

Messpunkte

Steigungsdreieck

SDprop

SDlin

Version Stand
14.10.2024

sss

Version Stand
14.10.2024
Andreas Jäger

Stand

Keine Streuung

Geringe Streuung

Starke Streuung

Nicht-linear

P_1: (04, 03)
P_2: (08, 06)
P_3: (12, 09)
P_4: (16, 12)
P_5: (20, 15)
P_6: (24, 18)
x_m: (x(P_1) + x(P_2) + x(P_3) + x(P_4) + x(P_5) + x(P_6)) / 6
y_m: (y(P_1) + y(P_2) + y(P_3) + y(P_4) + y(P_5) + y(P_6)) / 6
P_0 = (0, 0)
P_m: (x_m, y_m)
a = Ray(P_0, P_m)
b = OrthogonalLine(P_1, xAxis)
c = OrthogonalLine(P_2, xAxis)
d = OrthogonalLine(P_6, xAxis)
e = OrthogonalLine(P_3, xAxis)
f = OrthogonalLine(P_4, xAxis)
g = OrthogonalLine(P_5, xAxis)
P_{10} = Intersect(a, b)
P_{20} = Intersect(a, c)
P_{30} = Intersect(d, a)
P_{40} = Intersect(e, a)
P_{50} = Intersect(f, a)
P_{60} = Intersect(g, a)
n = false
sxy: ((x(P_1) - x_m) * (y(P_1) - y_m)) + ((x(P_2) - x_m) * (y(P_2) - y_m)) + ((x(P_3) - x_m) * (y(P_3) - y_m)) + ((x(P_4) - x_m) * (y(P_4) - y_m)) + ((x(P_5) - x_m) * (y(P_5) - y_m)) + ((x(P_6) - x_m) * (y(P_6) - y_m))
sxx: ((x(P_1) - x_m) * (x(P_1) - x_m)) + ((x(P_2) - x_m) * (x(P_2) - x_m)) + ((x(P_3) - x_m) * (x(P_3) - x_m)) + ((x(P_4) - x_m) * (x(P_4) - x_m)) + ((x(P_5) - x_m) * (x(P_5) - x_m)) + ((x(P_6) - x_m) * (x(P_6) - x_m))
b_R: sxy / sxx
a_R: y_m - (b_R * x_m)
reg(x) = If[x > 0, (b_R * x) + a_R]
A = Intersect(reg, b)
B = Intersect(reg, c)
C = Intersect(reg, d)
D = Intersect(reg, e)
E = Intersect(reg, f)
F = Intersect(reg, g)
o: false
HP_1 = (0.15804826351572748, 0.19430335903973125)
HP_2 = (28.240597925692068, 21.255107820039484)
b_1 = Ray(HP_1, HP_2)
u = true
Text2: "y(x) = " + (LaTeX[y_m / x_m]) + "x"
Text1: "y(x) = " + (LaTeX[b_R]) + "x\ " + (LaTeX[If[a_R > 0, "+", If[a_R ≟ 0, "", "-"]]]) + " \  " + (LaTeX[abs(a_R)]) + ""
v: n
w: o
M1_x = 2.9447512055740623 (slider from 0 to 5000, step 0.1)
M2_x = 18.086866768732342 (slider from 0 to 5000, step 0.1)
M1_y = -0.020671514119846163
M2_y = 0.4881535930904941
M1: (M1_x, M1_y)
M2: (M2_x, M2_y)
c_1 = OrthogonalLine(M1, xAxis)
d_1 = OrthogonalLine(M2, xAxis)
SD_1 = Intersect(reg, c_1)
SD_2 = Intersect(reg, d_1)
SD_3: (x(SD_2), y(SD_1))
Vieleck1, sd_2, sd_1, sd_3 = Polygon(SD_1, SD_3, SD_2)
z: true
G = Intersect(c_1, a)
H = Intersect(d_1, a)
I: (x(H), y(G))
Vieleck2, h, g_1, i = Polygon(G, I, H)
l: false
j: l ≟ true ∧ n ≟ true
k: o ≟ true ∧ l ≟ true
m = false
p = false