Comparing raw data and covariance matrix as inputs

Hi,

I am comparing the models using raw data versus summary statistics as inputs. First, let us consider a simple regression model (see the attached example). The model fit should be perfect with df=0. With the raw data as inputs, the chi-square statistic is 2.103206e-11, which is quite reasonable.

When the summary statistics (covariance matrix and means) are used as the inputs, the chi-square statistic is -0.01006717, which is relatively big.

I wonder why the discrepancy is so significant. Are there any ways to increase the accuracy when the summary statistics are used? I really appreciate any help.

Mike