path analysis (misspecification?)

hi,

I have following data and code;

cov <- 
c
(1.670028
,-1.197685
,-2.931445,-1.197685,1.765646,3.883839,-2.931445,3.883839,12.050816)

cov.matrix <- matrix(cov, 3, 3, dimnames=list(c("y1","x1","x2"),
c("y1","x1","x2")))

path.model <- specify.model()
   x1 -> y1,	x1-y1
   x2 <-> x1,	x2-x1
   x2 <-> x2,	x2-x2
   x1 <-> x1,	x1-x1
   y1 <-> y1,	y1-y1
  x2 -> y1,	x2-y1

  summary(sem(path.model, cov.matrix, N = 422))


and I get following results;



  Model Chisquare =  12.524   Df =  1 Pr(>Chisq) = 0.00040179
  Chisquare (null model) =  812.69   Df =  3
  Goodness-of-fit index =  0.98083
  Adjusted goodness-of-fit index =  0.885
  RMSEA index =  0.16545   90% CI: (0.09231, 0.25264)
  Bentler-Bonnett NFI =  0.98459
  Tucker-Lewis NNFI =  0.9573
  Bentler CFI =  0.98577
  SRMR =  0.027022
  BIC =  6.4789

  Parameter Estimates
       Estimate Std Error z value Pr(>|z|)
x1-y1 -0.67833 0.033967  -19.970 0        y1 <--- x1
x2-x1  3.88384 0.293743   13.222 0        x1 <--> x2
x2-x2 12.05082 0.831569   14.492 0        x2 <--> x2
x1-x1  1.76565 0.121839   14.492 0        x1 <--> x1
y1-y1  0.85761 0.059124   14.505 0        y1 <--> y1

  Iterations =  0


Now I wonder why the chi-square  value is so bad and what Pr(>Chisq) 
tells me.

Can anyone help me on this?


When I allow the path x2 -> y1 I get of course a good fit, but the 
path coefficient of x2 -> y1 is pretty low (-0.084653), so I thought I
can restrict that one to zero.