Thank you so much Anonymonk, now I am getting somewhere. The fragment of code I am now using, culled from a larger script goes like this ...

    # OK, now lets use linear regression to fit
    my $reg = Statistics::Regression->new( $data->{Name}, [ "Const", "
+Theta1", "Theta2" ] );

    # Add data points
    for ( @{$data->{values}} ) {
            # some time conversion goes on here to make times into Epo
+ch ...
            my $epoch = mktime($s, $m, $h, $D, $M-1, $Y);
            my $x = $_->[2];
            print "\$reg->include ( $epoch, [1, $x, ". $x**2 ." ] )\n"
+;
            $reg->include ( $epoch, [1, $x, $x**2 ] );
    }
    print "Results are ...\n";
    $reg->print();
[download]

Here is some output, now mostly it is working, but then on one set of data it chokes...

# This is printed by the lines above, this one works fine...

$reg->include ( 1491858157, [1, 95.24, 9070.6576 ] )
$reg->include ( 1491944593, [1, 95.24, 9070.6576 ] )
$reg->include ( 1492030986, [1, 95.22, 9066.8484 ] )
$reg->include ( 1492117236, [1, 95.23, 9068.7529 ] )
$reg->include ( 1492203637, [1, 95.23, 9068.7529 ] )
$reg->include ( 1492290038, [1, 95.23, 9068.7529 ] )
$reg->include ( 1492376435, [1, 95.23, 9068.7529 ] )
$reg->include ( 1492462840, [1, 95.23, 9068.7529 ] )
$reg->include ( 1492549241, [1, 95.23, 9068.7529 ] )
$reg->include ( 1492621259, [1, 95.24, 9070.6576 ] )
Results are ...
****************************************************************
Regression '3116.dpepicqt.SYSAUX'
****************************************************************
Name                   Theta          StdErr     T-stat
[0='const']     -22405806112434.5120    16790271247707.7460       -1.3
+3
[1='Theta1']    470587750270.0963       352619498612.0823          1.3
+3
[2='Theta2']    -2470766737.1275        1851377334.2664   -1.33

R^2= 0.206, N= 10, K= 3
****************************************************************

# This one chokes ...

$reg->include ( 1491858157, [1, 93.6, 8760.96 ] )
$reg->include ( 1491944593, [1, 93.6, 8760.96 ] )
$reg->include ( 1492030986, [1, 93.6, 8760.96 ] )
$reg->include ( 1492117236, [1, 93.6, 8760.96 ] )
$reg->include ( 1492203637, [1, 93.6, 8760.96 ] )
$reg->include ( 1492290038, [1, 93.6, 8760.96 ] )
$reg->include ( 1492376435, [1, 93.6, 8760.96 ] )
$reg->include ( 1492462840, [1, 93.6, 8760.96 ] )
$reg->include ( 1492549241, [1, 93.6, 8760.96 ] )
$reg->include ( 1492621259, [1, 93.64, 8768.4496 ] )
Results are ...
****************************************************************
Regression '3116.dpepicqt.SYSTEM'
****************************************************************
Report.pl::Statistics::Regression:standarderrors: I cannot compute the
+ theta-covariance matrix for variable 3 0
 at C:/Perl64/site/lib/Statistics/Regression.pm line 619.
        Statistics::Regression::standarderrors(Statistics::Regression=
+HASH(0x44dfe90)) called at C:/Perl64/site/lib/Statistics/Regression.p
+m line 430
        Statistics::Regression::print(Statistics::Regression=HASH(0x44
+dfe90)) called at Report.pl line 125
        main::predict(HASH(0x4340ec8), 10) called at Report.pl line 85
[download]

I am guessing I may not have enough variation in that data for it to find an optimum, but if anyone can see I am barking up the wrong tree, please do shout

Cheers,
R.

Update

I have now tried it with a cubic term, and it failed on an earlier data set. Then I tried it with just the Constant and an X terms, no square or higher, and it ran the complete set. So now I can get a best fit line. Next step is to see if I can feed it some guess values for the theta vector.