HP50G : TRN vs TRAN

[Gil]

Say X is the following Matrix:

[[ 1 6.35676254625 ]
[ 1 6.35675231425 ]
[ 1 6.3567482106 ]
[ 1 6.3567338557 ]],

without dots (.) after the ones.

Try a):
X TRAN X *

You get
[[ 4 25.4269969268 ]
[ 25.4269969268 161.633043179 ]]
(no dot after the 4).

Now try b):
X TRN X

You get apparently the same result:
[[ 4. 25.4269969268 ]
[ 25.4269969268 161.633043179 ]]
(but with a dot after the 4 => approximate mode).

Now try a2) :
X TRAN X * INV
YOU get
[[ 321639766412. -50598152402.8 ]
[ -50761421319.8 7985437126.68 ]]


Now try b2) :
X TRN X * INV
YOU get
[[ 322677625975. -50761421319.8 ]
[ -50761421319.8 7985437126.68 ]] }

The result are quite different.

Above all for the final result if I work for a regression, where
Beta = [(X'X)^(-1)X']Y,
where Y= [[ 20.0039363988 ]
[ 20.0039203398 ]
[ 20.0039138995 ]
[ 20.0039080362 ]].

I am somewhat puzzled in the choice
between TRN and TRAN when calculating
for the beta values.