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HAMS Technologies
www.hams.co.in
director@hams.co.in
priyank@hams.co.in
vivek@hams.co.in
HAMS Technologies
There is a very special property of all linear regression model that
if the summation of all the independent variable is constant then
dependent variable grow fastest only if
Ratio of independent variable is equal to ratio of exponential respective
model coefficient.
or we can
Ratio of model is same as ration of logarithmic respective independent
variable value
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HAMS Technologies
Mathematically ..
Given a regression model
y  1 x1   2 x2   3 x3 ...... n xn
also given,
x1  x2  x3 ......xn  K  cons
Then y grow faster only if
x1 / x2  e1 / e 2
or say
1 /  2  log( x1 ) / log( x2 )
1
2
3
4
n
R  A M1 M 2 M3 M 4 M n
HAMS Technologies
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Lets prove this…
Given Regression model is
y  1 x1   2 x2   3 x3 ...... n xn
now consider
y  log( R), x1  log(M 1 ), x2  log(M 2 )......xn  log(M n )
Then original regress model will be
log( R)  1 log(M 1 )   2 log(M 2 )......   n log(M n )
 log( R)  log(M 11 M 2 2 M 3 3 M 4 4  M n n )
 R  M 11 M 2 2 M 3 3 M 4 4  M n n
now Normalize this equation w.r.t M
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M n n
M 1 1
M 2 2

 R  (
) .(
)  (
) *  M i i
 Mi  Mi
 Mi
1. This factor will
remain constant for
given problem
2. So the growth of R will be directly
proportional to this factor, For further derivation
consider the number of independent drivers are
two , n=2. We can use same approach for large n
 R  (
M1
M2
)1 .(
) 2
M1  M 2
M1  M 2
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HAMS Technologies
1  0.9,  2  0.1
M1
M2
R(
) 1 * (
) 2
M1  M 2
M1  M 2
x  M1 / M 2
R
R(
1
1 1
) 1 * (
x
1
x 1
) 2  f ( x )
1
1
R
(
) 1 * (
) 2  0
x
x 1
1 1
x
1 (
1   2  0.5
1  0.1,  2  0.9
x
1
1
1
1
x 1 1
x 1
)
*(
)2 * (
) 2  (
) * 2 (
) 2 1 * ( 1) * (
)2  0
1 x
1 x
1 x
1 x
1 x
1 x
1 /  2  x  M 1 / M 2
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HAMS Technologies
So,
1 /  2  x  M 1 / M 2  log( x1 ) / log( x2 )
Ratio of model is same as ratio of logarithmic respective independent
variable value
or
x1 / x2  e1 / e 2
Ratio of independent variable is equal to ratio of exponential respective
model coefficient.
hence proved ..
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HAMS Technologies
Thank you
Kindly drop us a mail at below mention address for any
suggestion and clarification. We like to hear from you
HAMS Technologies
www.hams.co.in
director@hams.co.in
priyank@hams.co.in
vivek@hams.co.in
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HAMS Technologies