R() = [R(X,Y)]^2
:-)
58 Yˆ Y. R2.
R2:
,
, .
.
Yˆ Y:
59 . . R2.
, ( ):
, , .. TSS = ESS + RSS
RSS =
TSS=
ESS =
TSS- Total Sum of Squares -
ESS - Explained Sum of Squares - -
RSS - Residual Sum of Squares -
TSS= RSS+ ESS
=
:
RSS ESS, . .
R2, . .
Ho: R2= 0 vs H1: R2 0
R2 ()
f(R2 ) = F ( )
(**) F= ((ESS/SS) *1/k) / ((RSS/TSS) * 1/N-k) = ((1/k-1) * R2)) /((1/N-k) * (1- R2) )
k- ()
N
Ho: F ~ F (k-1; N-k)
( )
F (k,m) = (1/k * χ² (k)) / (1/m * χ² (m))
χ² (k) = ∑z², Z ~ N (0,1) z
F (**), , R2
R2 =1, ,
R2,
t-, .
:
0: B0=0
H1: B1 0.
F- t-
t < t, H , .. , b rxy x, t > t o
. .
TSS, RSS, ESS.
TSS (Total) = RSS () + ESS ( )
TSS = ∑(yi y)2
ESS = ∑(y y)2
RSS = ∑(yi y)2
reg dem_2000 cli gini_ye
. -
|
|
Source | SS df MS Number of obs = 25
-------------+------------------------------ F(2, 22) = 13.86
Model | 6.88491132 2 3.44245566 Prob > F = 0.0001
Residual | 5.46595999 22.248452727 R-squared = 0.5574
-------------+------------------------------ Adj R-squared = 0.5172
Total | 12.3508713 24.514619638 Root MSE =.49845
------------------------------------------------------------------------------
dem_2000 | Coef. Std. Err. t P>|t| [95% Conf. Interval]
-------------+----------------------------------------------------------------
cli |.3920828.0807622 4.85 0.000.2245922.5595733
gini_ye |.0022019.0182327 0.12 0.905 -.0356105.0400143
_cons | -.7912347.7457838 -1.06 0.300 -2.337896.7554263
------------------------------------------------------------------------------
:
dem_2000 = - 0,79 + 0,39*cli + 0,002*gini_ye + εi
65,66
67. ?
, .
68. ?
. , .
, . . , ,
69. 1 :
- '. ' , .
- . , 0,8