regresie muiltilineara
Post on 28-Feb-2018
215 Views
Preview:
TRANSCRIPT
-
7/25/2019 Regresie Muiltilineara
1/6
Regresie multilineara y(x1,x2,x3,x4) = Fm[(Va)T*Vx] = a + bx1 + cx2 + dx3 + hx4
In spatiul cu 5 dimensiuni : Fm este o functie de variabila vectoriala cu valori reale, astfel :
Fm a b c d h x1 x2 x3 x4 a b x1 c x2 d x3 h x4
x1t 1.11 1.25 1.49 1.61 1.82 2.05 2.27 2.44 2.61 2.89( ) Unde s-au notat cu : xit , i = 1,2,3,4 vectorii transpusi ai valorilormasurate.
x2t 1.25 1.39 1.85 1.93 2.35 2.72 3.08 3.74 3.93 4.26 ( )
x3t 2.36 2.64 2.87 2.99 3.65 4.44 4.86 5.69 5.88 6.33( )
a b x1 c x2 d x3 h x4 a b c d h( )
1
x1
x2
x3
x4
= VaT
Vx( )=
x4t 1.51 1.96 2.31 2.45 2.84 3.14 3.59 4.75 5.02 5.66 ( )
Yt 14.2 15.5 18.4 20.4 22.3 22.9 26.7 35.2 44.4 53.9( )
x1t T
0
0
1
2
3
4
5
6
7
8
9
1.11
1.25
1.49
1.61
1.82
2.05
2.27
2.44
2.61
2.89
x2tT
0
0
1
2
3
4
5
67
8
9
1.25
1.39
1.85
1.93
2.35
2.72
3.083.74
3.93
4.26
x3tT
0
0
1
2
3
4
5
67
8
9
2.36
2.64
2.87
2.99
3.65
4.44
4.865.69
5.88
6.33
x4tT
0
0
1
2
3
4
5
67
8
9
1.51
1.96
2.31
2.45
2.84
3.14
3.594.75
5.02
5.66
Se defineste vectorul: U 1 1 1 1 1 1 1 1 1 1( )
-
7/25/2019 Regresie Muiltilineara
2/6
Necunoscute : a, b, c, d, h
S a b c d h( )0
n
i
Fi yi 2
=
n 5 Fi yi diferenta pentru fiecare punct=
Fm xt
T
1 YtT
1 Fm xtT
2 YtT
2. . .
with :a
Sd
d0=
bS
d
d0=
cS
d
d0=
dS
d
d0=
hS
d
d0= a, b, c, d, h
S a b c d h( )
0
9
j
Fm xitT
.j Yt T
j
2
=
|
|
|
|
|
|
|
|
|
|
|
|
|
|
aS
d
d0=
Sistem de 5 ecuatii cu 5 necunoscute :
Derivatele partiale ale Sumei patratelordistantelor de la valorile masurate la
planul in cinci dimensiuni Fm(Va,Vx),
Unde :
Vx = (xt1 xt2 xt3 xt4)
Va = (a b c d h) = Vectorul necunoscut ce
trebuie determinat
bS
d
d0=
cS
d
d0= 2( )
dS
d
d0=
hS
d
d0=
S a b c d h( )
0
9
i
a b x1tT
i c x2t
T
i
d x3tT
i
h x4tT
i
YtT i 2
U 0 1 2 3 4 5 6 7 8 9
0 1 1 1 1 1 1 1 1 1 1
-
7/25/2019 Regresie Muiltilineara
3/6
aS
d
d2
0
9
i
a b x1tT
i c x2t
T
i
d x3tT
i
h x4tT
i
YtT
i
= 0=
0
9
i
YtT
i
U YtT
= v0 U Yt T
bS
d
d2
0
9
i
a b x1tT
i c x2t
T
i
d x3tT
i
h x4tT
i
YtT
i
x1tT
i
= 0=
0
9
i
YtT
ix1t
T
i
Yt x1tT
= v1 Yt x1tT
cS
d
d2
0
9
i
a b x1tT
i c x2t
T
i
d x3tT
i
h x4tT
i
YtT
i
x2tT
i
= 0=
0
9
i
YtT
ix2t
T
i
Yt x2tT
=
v2 Yt x2tT
dS
d
d2
0
9
i
a b x1tT
i c x2t
T
i
d x3tT
i
h x4tT
i
YtT
i
x3tT
i
= 0=
0
9
i
YtT
ix3t
T
i
Yt x3tT
= v3 Yt x3tT
hS
d
d2
0
9
i
a b x1tT
i c x2t
T
i
d x3tT
i
h x4tT
i
YtT
i
x4tT
i
= 0=
0
9
i
YtT
ix4t
T
i
Yt x4tT
= v4 Yt x4tT
0
9
i
1
10
0
9
i
x1tT
i
U xtT
=
0
9
i
x2tT
i
U x2tT
=
-
7/25/2019 Regresie Muiltilineara
4/6
Definesc :Elementele matricei M[5 x 5]
M1 10 M2 U x1tT
M3 U x2tT
M4 U x3tT
M5 U x4tT
M2 U x1t
T N1 x
1tx
1t
T
N2 x1t x2tT
N3 x1t x3tT
N4 x1t x4tT
M3 U x2tT
N2 x1tx2tT
P1 x2t x2tT
P2 x3tx2tT
P3 x4t x2tT
M4 U x3tT
P2 x2t x3tT
Q1 x3t x3tT
Q2 x4t x3tT
N3 x1t x3t
T
Q2 x3t x4tT
R1 x4t x4tT
M5 U x4tT
N4 x1t x4tT
P3 x2t x4tT
M
M1
M2
M3
M4
M5
M2
N1
N2
N3
N4
M3
N2
P1
P2
P3
M4
N3
P2
Q1
Q2
M5
N4
P3
Q2
R1
M
10
19.54
26.5
41.71
33.23
19.54
41.392
57.528
89.311
72.317
26.5
57.528
80.629
124.678
101.491
41.71
89.311
124.678
193.391
156.821
33.23
72.317
101.491
156.821
128.072
V1
v0
v1
v2
v3
v4
V1
273.9
601.08
845.39
1.304 103
1.071 103
Determinantul Matricei M este notat : |M| M 0.192 M1
10.205
15.201
15.671
3.796
1.834
15.201
30.073
22.887
1.39
3.399
15.671
22.887
36.151
9.657
7.966
3.796
1.39
9.657
5.647
0.939
1.834
3.399
7.966
0.939
3.727
-
7/25/2019 Regresie Muiltilineara
5/6
Fm a b c d h x1 x2 x3 x4 a b x1 c x2 d x3 h x4
M1
V1
6.594
13.995
19.901
2.283
20.733
a 6.594 b 13.995 c 19.901 d 2.283 h 20.733
Rezulta Fs :
Fs x1tx2t x3t x4t 6.594 13.995x1t 19.901 x2t 2.283 x3t 20.733 x4t
Fs x1tT
x2tT
x3tT
x4tT
Reprezinta valorile functiei calculate in punctele initiale masurate
Fs x1tT
x2tT
x3tT
x4tT
YtT
Reprezinta valorile erorilor, ca diferenta dintre valorile calculate si cele masurate
Fs x1tT
x2tT
x3tT
x4tT
0
0
1
2
3
4
5
6
7
8
9
9.983
17.847
18.783
21.499
22.658
22.93
27.216
38.616
42.378
51.971
Yt( )T
0
0
1
2
3
4
5
6
7
8
9
14.2
15.5
18.4
20.4
22.3
22.9
26.7
35.2
44.4
53.9
Fs x1tT
x2tT
x3tT
x4tT
Yt( )T
0
0
1
2
3
4
5
6
7
8
9
-4.217
2.347
0.383
1.099
0.358
0.03
0.516
3.416
-2.022
-1.929
-
7/25/2019 Regresie Muiltilineara
6/6
Calculul si graficul erorilor : epsilon = |Fs[(Vx)T] - (Yt)T|
0 0.9 1.8 2.7 3.6 4.5 5.4 6.3 7.2 8.1 9
5
10
15
20
25
5
10
15
20
25
Fs x1tT
x2tT x3t
T x4tT i Yt
T i
i i
m
0
9
i
Fs x1tT
x2tT
x3tT
x4tT
i YtT
i
10
m 1.632
p0
9
i
Fs x1tT
x2tT
x3tT
x4tT
i YtT
i
2
10 9
p 2.165 103
p 0.68 1.472 103
1 m 1 1.633
2 m 2 1.63
1.630 1.633
Fm1 x y a b c( ) a bx
cy
Fm3 x y a b c d( )a
xb ln x( )
c
y d ln y( )
Fm2 x y a b c( ) a xb cy Fm4 x y a b c( ) a sin x( )
b cos y( )c
Fm02 x y z a b c d( ) a xb
yc
zd
Fm5 x y a b c( ) a sin x( )b
sin y( )c
Fm03 x y z u a b c d e( ) a xb
yc
zd
ue
Fm6x y a b c d( ) a b x c y d x y
top related