You need to be brought up to date: only oxidized cholesterol is
dangerous.  Lowering your cholesterol raises your risk of cancer and
other "diseases."  Thus, what you really want to do is to make sure you
don't eat oxidized cholesterol and also that you don't eat foods that
act as oxidizing agents once inside your body.  The worst thing for
most people is called lipid peroxidation (fats going rancid), and if
you avoid any major source of unsaturated fatty acids, you prevent this
to a very large degree.  You can also eat berries, dark chocolate, and
other common foods that are high in antioxidants (but do not eat a lot
of beans, whole grains, and leafy greens, which have anti-nutritive
qualities).  You can search this group for montygram and read some of
my older posts, which go into more detail

I don't know about logicol, but studies on some others (Benecol IIRC)
found that they do improve cholesterol levels. But they are a very
expensive means of doing so.

In think that the best results can be achieved by combining several ways to
reduce cholesterol. In the Portfolio diet, developed byt the Toronto
University, they have combined almonds, soy products, soluble fiber, and
cholesterol reducing plant stanol margarines. In studies this Portfolio diet
has been equal with cholesterol lowering statin drugs in reducing
cholesterol.

More about the Portfolio diet:
http://www.portfolioeatingplan.com/

But most likely, drinking lot of squalene in form of olive oil might
perhaps not be a very good idea to combine with such remedies. Even
more if you eat statins. Squalene is a key intermediate in forming
cholesterol, and thus bypassing the step blocked by statins.