.
, X Y .
X ,, Y , .
, Y X , Y X.
X i - X(i), Y Y(i), 0 < i ≤ n.
X(i) Y(i), Y X. . . .
Statistica 6 Multiple regression ( ).
, Y .
, :
, 0 < i ≤ n
B 1, 0 , e(i)
( X(i), Y(i), 0 < i ≤ n)
( , )
, .
e(i), 0 < i ≤ n . e(i) , . , , . .
, , :
, 0 < i ≤ n,
B 0, B 1, B 2,... k .
Multiple regression ( ).
,
(X1, Y2),... (Xn, Yn):
- 1, B 2, 0 ;
- 1, B 2, 0;
- ;
- .
, Z , Y , , Statistica 6.
, 8.1.
8.1
X Y ; Z
Multiple regression ( ).
X, Y Z.
1. Statistica Multiple regression ( ). Multiple regression ( 8.2).
|
|
8.2
2. ( 8.3).
8.3 Multiple regression
, 8.3. . Variables (), .
, Select dependent and independent variable list ( ) ( 8.4).
8.4
, . , .
X Y, Z. , , Select dependent and independent variable list ( ). . .
.
3. Model Definition ( ) ( 8.5).
8.5 Multiple Regression
, Method (): Standard ().
OK.
, .
4. Multiple Regression Results ( ) . .
: . : , . Multiple Regression Results ( ) , ( 8.6).
.
8.6
.
:
- Dep. Var. ( ). : Z;
- No. of Cases ( , ). 45;
- Multiple R = 0,99 ( );
- R2 ( ), .
, . ,
(
), ;
- Adjusted R2 ( ), : ,
- n , ( 1, );
|
|
- Std. Error of estimate ( ). ;
- Intercept ( ). 0 ;
- Std. Error ( ). 0 ;
- t(df) and p-value ( t- ).
t- .
- F F-;
- df F-;
- .
, , . 0 1. R2 = 0,98. , , 98% Z .
F-
. F- . , , Z X Y , 1 = 0 2 = 0, 1 2 0. F- 1348,89 = 0,0000, , .
.
, Regression summary ( ). spredsheet, ( 8.7).
8.7
. beta ,
beta, .
0 = 5,01.
1 = 0,012 ( X).
2 = 9,33 ( Y).
, 0, 1, 2,
t- . .
, :
5. ( 8.6)
Partial Correlation ( ). 8.8 : rzx-y = 0,93 ( Z X Y) rzy-x = 0,84 ( Z Y X).
t- p = 0,00... , R = 0,99 0,97 0,94 ( 8.11 8.12).
8.8
6. ( 8.6) OK ( 8.9), Scatterplot, Bivariate Correlation. (Z variable)
(X variable) ( 8.10 a). OK.
(Z variable)
(Y variable) ( 8.10 ). OK.
8.9
( 8.11 8.12).
)
)
8.10 ) Z X, ) Z Y
8.11 Z X
8.12 Z Y
7. .
. ( 8.9) Predicted vs. Observed ( ). 8.13. .
|
|
8.13
, .
.
, , .
, , , , .
, (R = 0,99;
F (2, 42) = 1348 < 0,00..) ( ) ( ), :
, , , , .
1 Statistica 6 ( 1).
2 , .
3 .
9
(MS Excel)
: MS Excel.