Mixed effect linear regression model output interpretation

I just fitted the following linear mixed effects model:

Linear mixed model fit by maximum likelihood  ['lmerMod']
Formula: price ~ variable + (1 | product)
Data: podzbior

AIC       BIC    logLik  deviance  df.resid
130840.14 130868.85 -65416.07 130832.14      9674

Scaled residuals:
Min      1Q  Median      3Q     Max
-6.2824 -0.3099 -0.0547  0.2201 12.4291

Random effects:
Groups           Name     Variance Std.Dev.
product         (Intercept) 427375   653.7
Residual                     25930   161.0
Number of obs: 9678, groups: product, 1222

Fixed effects:
Estimate Std. Error  t value
(Intercept)     9.362e+02  1.899e+01    49.29
variable      -7.521e-04  1.171e-04    -6.42

Correlation of Fixed Effects:
(Intr)
variable    -0.050


That was output from summary(lmerModel), after the run of lmer I got this warning:

Warning:
In checkScaleX(X, ctrl = control) :
Some predictor variables are on very different scales: consider rescaling


Q1 Predictor variable is numeric from 0 to something like 100k, how It should be scaled?

Random effects with confidence intervals chart for this model looks like this, is it OK?:

I am pretty sure residuals are not OK. What should I do in this case?

How can I go deeper with this model diagnostic, besides checking p-values?

• This QQ-plot strongly suggests you have a heavy-tailed distribution. The "most vanilla" rescaling would be to first try to make your data zero-meaned and having std.deviation of 1; this is not a final solution just a first step. Try it and see if your model behaves better. Commented Aug 14, 2014 at 21:40
• Well, I have used scale() to make predictor variable with mean equal 0 and sd equal 0 - qqplot still looks the same, any other ideas for rescalling? Commented Aug 15, 2014 at 10:19
• OK, so something more informed might be helpful. What is variable? Is is reasonable to take the sqrt of it? To log it? To do something like I(variable/1e6) maybe? Try to think easily interpretable transformations before doing something heavy-handed like a Box-Cox. Commented Aug 15, 2014 at 21:50
• Box-Cox gave me lambda close to 0 so this mean log transformation, still nothing close to normality in qqplots of residuals Commented Aug 19, 2014 at 20:56
• Try then robust regression methods. In particular the functionality offered by the packages lqmm and robustlmm might can handy... Commented Aug 24, 2014 at 4:55