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


"Brablo" <gestureofrespect@xxxxxxxxx> wrote in message
news:1171836504.421599.33040@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
I was regressing the book value of the company to the market cap of
the company for 500 different companies. The "arithematic
average" (AA) was found by summing the market caps of all 500
companies. This value represents the "P" in the numerator of the P/B
ratio. The book values of all the companies were summed up, and this
is the "B" of the P/B ratio. The average P/B ratio using this
straight-forwards approach is 2.85.

However, when I attempt to regress the market cap to the book value
without using a constant, I get something totally different! The
equation for market cap as a function of Book Value (BV) is:

Market Cap (BV) = 2.502215 * BV

The regression statistics are below, and it has an R^2 of 0.76. This
implies that the average BV using this method is 2.502!

Why do these 2 different methods yield different results for the BV of
a company?

2.502215472
0.053283967
0.755752231

2.85E+00


Without seeing your data is rather difficult to check what you have done?

The difference seems to be as you have said - that in one you have allowed a
constant, whereas in the other the intercept is zero.

A difference in slope of 2.5 and 2.85 doesn't seem very great.

It might be that there is a cluster of points in one area and in another
area, which make very unlikely that there is an intercept of zero, yet in
one you have put this constraint.

Nick


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