, . . t-
a:
(n- 2).
:
r:
:
.
. 1 .
:
16.
-
Y = b0 + b1xi1 +... + bjxij +... + bkxik + ei
ei - , , s.
bj , Y, Xj , . . .
:
Y = Xb + e
Y = b0 + b1X1 + b2X2;
.
, m t-:
v = n- m-1. t- .
, , . , Xj Y. bj, Xj. , .
. :
Mbi= SS./n-m-1 * [X T * X] ) ii
SS. = E(y-y )
n
m .
([X T * X] )ii - ii ii ([X T * X] ), y = a+b1x1+ + bpxp + E, i=0,1,2p
Mbo=Ma
0 1 2
0 (0)
1 ()
2 ()
3 ()
SS.\n-m-1
, , , :
|
|
Mb = SS.\ (n-m-1) * E (x x c )
Ma = SS. * Ex \ (n-m-1) * E (x x ) * n
y=a+b1x1++bpxp+ E
Mbi= Gy/Gx * 1-R \ (1 R xi(x)) (n-m-1)
.
R xi (x) = r
, , F-. , F-, .. F:
F= D/D = (R²/1-R²) * (n-m-1/m),
D
R² - ()
n
m x ( )
D .
m , (n-m-1) .
:
1) F
2) F
3) F F, >, P= 1-a (), - .
f-:
, SS =
SS = , n- - , m -
F- .
:
.
df | (MS=SS/df) | F | F, =0,05 | ||
m | SS = ∑(y^-y¯)² | SS/m | MS/ MS | F | |
n-m-1 | SS = ∑(y-y^)² | SS/ n-m-1 | --- | --- | |
n-1 | SS = ∑(y-y¯)² | --- | --- | --- |
19.
- - . , . 1) 1. η yx1*x2x3xn= (G2yx2x3..xm() G2yx1x2x3..xm())/G2yx2x3..xm() - x1 . 2) ryx1*x2x3..xm= (1-(1 R2yx1*x2x3..xm)/(1- R2yx2x3..xm)) 1 : - , . 2 :
|
|
ryx1*x2= (ryx1 - ryx2* rx1x2)/ ((1- ryx22)* (1- rx1x22))
ryx2*x1= (ryx2 - ryx1* rx1x2)/ ((1- ryx12)* (1- rx1x22))
-1 1. - - . 0, . .
20. F-
- , . - , . .
Fxj =((R2 yx1x2...xm R2 yx1x2xj-1,j+1xm)/(1- R2 yx1x2...xm))*((n-m-1)/1)
F (,1, n-m-1) Fxj F xj ..
y=a+b1x1+b2+b3x3+e, F- 1, F- 2, . . , ,, F- 3, .. 3 x12. F- 2 1 F- 3, F-, , . t- F-. F- . y=a+b1x1+b2+b3x3+e 1,2,,b3 .
:
lnE^2=a+bln*xi+,
xi - ,
- ( . . )
- b (, t >t ),
,
.
|E| = +bxi^k +
,b , .
k , k : -2;-1;-0,5;0,5;1;2.
b, (.. x y)
, . t>t -> -> (xi).
->
.
(E).
.. .
, , .. , .
,. , , + + ,- .
(x1 x2), - :
E2=a+b11x1+b21x2+b12x12+b22x22+c12x1x2+δ
- . , F- . F>F =>. => - => -. .
- , - - . -, . - t- . T T>T => - , , T<T, =>- . .. T=2,45, T (x2)= - 4, , x2 .(.. t- !)
|
|
-.
() .
:
- - , . .
- - (n1,n2,n3). , n1 n3 - -(n1=n3). n2 . =n1 n3 (!), n1 n3.
- 1 3 - - .. , . - . .. . - 2 - (x1,x2), - -.
- . 2- - ( SS1 SS3)
- .- F-, . . (. SS1 /SS3)
- F df1=df2=n1-m-1. F>=F, - , . - 1.
: - x2( - )
Y x1 x2
121 56 28
80 114 36
56 124 42
75 98 46
88 102 50
45 17 54
110 116 54
63 28 56
113 50 63
160 115 88
203 118 105
237 154 106
- 3 :n1=n3=n3=4
- n1 n3 : y=a +b1x1+b2x2 +E
y = 193 0,64x1 1,25x2 + E
y = -17,8 + 0,49x1 + 1,57x2 + E
SS(1): = 57,1
SS(3)= 503,3
F=503,3/57,1= 8,8
df1 = df2 = 4 -2-1 = 1, F=161,4 => F<F, 2 , => E -
30 (, , , )
, , .
( )
M :
∑y= n*a + b*∑x + c* ∑x^2
∑y*x= a*∑x + b*∑x^2 + c*∑x^3
∑y*x^2 = a*∑x^2 + b*∑x^3 + c* ∑x^4
a, b :
a= ∆a/∆; b=∆b/∆; c=∆c/∆
31 .
= f (x)* x / f (x) . :
( ):
Y=a + bx +cx^2 + E
Y = b+2c,
= ((b + 2*c*x) *x)/ (a+b*x+c*x^2)
x x . - , . ( . = b*x c./ y .)
: = -b/ (a*x + b)
: = x * ln b
:
F (x) = a*b*x^(b-1) = b
35 (, )
, , . , ().
|
|
y=a+b/x +E
y=a+bx+E
x()=1/x
y+(-)t()*m()
y=ax^bE
lny=lna+blnx+lnE
Y=A+BX+E
Y(), =5 y(), =^y=^5
Y .min=3 y .min= ^3
Y.max=7 y .min=^7