Not sure how you can be sure that 1400 nonlinear regressions all converged, but assuming you are, the following table and script should point you in the right direction. The formula in the :Formula column is b0 + b1*x where the parameters b0 and b1 are 1 and 2 respectively.
Script:
nlin = Nonlinear(
Y( :y ),
X( :Formula ),
Unthreaded( 1 ),
Newton,
Finish,
By( :ID )
);
rnlin1 = Report( nlin[1] );
parms = rnlin1["Nonlinear Fit ID=1"]["Solution"][Table Box( 2 )]
<< make combined data table;
parms << Transpose(
columns( :Estimate ),
By( :ID ),
Label( :Parameter ),
Output Table( "Parameters by ID" )
);
/*
parms << Split(
Split By( :Parameter ),
Split( :Estimate, :ApproxStdErr ),
Group( :ID )
)
*/
Demo Data Table:
ID x y Formula
1 1 14.007192425 3
1 2 17.212873694 5
1 3 19.206116204 7
1 4 22.698900479 9
1 5 26.547313123 11
1 6 27.964537384 13
1 7 32.187880488 15
1 8 34.471305291 17
1 9 37.982516136 19
1 10 39.725363966 21
2 1 18.727600524 3
2 2 20.500227504 5
2 3 18.715068521 7
2 4 22.667963466 9
2 5 25.505984818 11
2 6 25.947839552 13
2 7 27.933068812 15
2 8 31.390339224 17
2 9 32.390010591 19
2 10 34.514002505 21