Re: "Regression" average VS the "Arithematic" Average

[ Top posting corrected ]

"Brablo" <gestureofrespect@xxxxxxxxx> wrote in message
news:1171894627.132992.255930@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

On Feb 19, 4:55 am, "The Last Danish Pastry" <cli...@xxxxxxxxx>
wrote:
"Brablo" <gestureofresp...@xxxxxxxxx> wrote in message

news:1171855401.344234.270730@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Here is the data (all ~487 or so points of the S&P 500).

You totally misunderstood what I'm saying. I did *NOT* set up
one
experiment with a constant. Let me re-clarify what I did.

1. In my first experiment, I simply took the arithematic average
of
the P/B ratio of all 487 points. P/B is simply the market cap of
the
stock divided by the book value of the company. So to find the
average (market capped weighted, essentially), summed up the
entire
market cap of the S&P 500. I also summed up the entire book
value
of
these 487 companies. Now i have 2 very, very large numbers.
When I
divide the first of these numbers (total Market Cap which exceeds
$12T) by the second, I get 2.85.

2. In my second experiment, I decided to regress the market cap
(MC)
to the BV without including a constant. It was found that the
slope
relating the BV to the MC (the P/B ratio) was 2.50. This value
is
quite different from the first answer of 2.85.

It would probably be simpler if we reduced the number of companies,
and the sizes of the numbers involved.

Consider just two companies, C1 and C2.

C1: MC= 3, BV=1
C2: MC=21, BV=2

Your first experiment would give, I think, a result of 8
= (3+21)/(1+2) = 24/3

Your second experiment would give, I think, a result of 9
= (3x1 + 21x2)/(1x1 + 2x2) = 45/5

# Are my 8 and 9 correct?

# Do you understand why the two numbers are different?

Danish Pastry,

Very good point. I understand the formulation of the slope and my
method to calculate the mean. Qualitatively, what does taking the
slope explain? This seems to be a weighted average of some sort.

You have not directly answered my two questions, but I shall try to
answer yours.

In the first experiment you compute the slope of the line which joins
the origin to the centroid of the points.

In the second experiment you compute the best-fit line (in the
least-squares sense) which passes through the origin.

--
Clive Tooth
http://www.shutterstock.com/cat.mhtml?gallery_id=61771




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