# Interpreting size and direction of fixed effects in a linear mixed effect model

I have some data which, after lots of searching, I concluded would probably benefit from using a linear mixed effects model. I think I have an interesting result here, but I am having a little trouble figuring out how to interpret all of the results. This is what I get from the summary() function in R:

> summary(nonzero.lmer)
Linear mixed model fit by REML
Formula: relative.sents.A ~ relative.sents.B + (1 | id.A) + (1 | abstract)
Data: nonzero
AIC    BIC logLik deviance REMLdev
-698.8 -683.9  354.4   -722.6  -708.8
Random effects:
Groups   Name        Variance   Std.Dev.
id.A     (Intercept) 1.0790e-04 0.0103877
abstract (Intercept) 3.0966e-05 0.0055647
Residual             2.9675e-04 0.0172263
Number of obs: 146, groups: id.A, 97; abstract, 52

Fixed effects:
Estimate Std. Error t value
(Intercept)      0.017260   0.003046   5.667
relative.sents.B 0.428808   0.080050   5.357

Correlation of Fixed Effects:
(Intr)
rltv.snts.B -0.742


My question involves the relationship between the dependent variable ("relative.sents.A") and "relative.sents.B" once the random factors are factored out. I gather that the t-value of 5.357 for relative.sents.B should be significant.

But does this show what the direction of the effect is? I am thinking that because the coefficient for the slope is positive that this means that as relative.sents.B increases, so does my dependent variable. Is this correct?

The book I've been using briefly mentions that the correlation reported here is not a normal correlation, but goes into no details. Normally, I'd look there to figure out the direction and magnitude of the effect. Is that wrong?

If I'm wrong on both counts, then what is a good (hopefully reasonably straightforward) way to discover the direction and size of the effect?