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Mike

Posted: Wed Apr 02, 2008 2:17 pm

Guest

Hi,

Similar to the case proposed by
http://groups.google.com/group/sci.stat.math/browse_thread/thread/04f2f87c22564319?hl=en#
Suppose y is yield of wheat per acre and one x is irrigation in

Quote:

gallons per acre and another is fertilizer in pounds per acre. Then
the regression coefficients tell you the effect of using water versus
fertilizer. But if you want to compare "sensitivity," you have to take
a stand on how much would be a big change in water versus a big change
in fertilizer.
-Dick Startz- Hide quoted text -
So if I want to know sensitivity of yield of wheat per acre Y to

irrigation in gallons per acre X, how to determine "a big change in
water " and a reasonable change?
Is it one standard deviation of X? two stdev of X?

Thank you in advance.
Mike

Guest

Posted: Wed Apr 02, 2008 7:26 pm

On Wed, 2 Apr 2008 17:17:27 -0700 (PDT), Mike <SulfateIon@gmail.com>
wrote:

Quote:

Hi,

Similar to the case proposed by
http://groups.google.com/group/sci.stat.math/browse_thread/thread/04f2f87c22564319?hl=en#
Suppose y is yield of wheat per acre and one x is irrigation in
gallons per acre and another is fertilizer in pounds per acre. Then
the regression coefficients tell you the effect of using water versus
fertilizer. But if you want to compare "sensitivity," you have to take
a stand on how much would be a big change in water versus a big change
in fertilizer.
-Dick Startz- Hide quoted text -
So if I want to know sensitivity of yield of wheat per acre Y to
irrigation in gallons per acre X, how to determine "a big change in
water " and a reasonable change?
Is it one standard deviation of X? two stdev of X?

Thank you in advance.
Mike

Mike:

You ask a good question, but it's not necessarily one answerable by
statistics. It probably belongs in the problem domain. In this
contrived example, how much does water costs the farmer? How much does
fertilizer cost?

Sometimes people do use a standard deviation of X. If all the X
variables are normally distributed, a change of one standard deviation
moves all of them across an equal part of their respective probability
distributions. Sometimes that's an interesting comparison. Mind you,
there's no particular reason for an X variable to be normally
distributed.

-Dick Startz

Phil Sherrod

Posted: Thu Apr 03, 2008 8:42 am

Guest

On 2-Apr-2008, Mike <SulfateIon@gmail.com> wrote:

Quote:

So if I want to know sensitivity of yield of wheat per acre Y to
irrigation in gallons per acre X, how to determine "a big change in
water " and a reasonable change?
Is it one standard deviation of X? two stdev of X?

The first question is what you mean by "sensitivity". My understanding of that
term in statistics is the ratio of the change in the dependent variable for a
given change in an independent variable -- that is, (delta y)/(delta x). I
would find it the same way you compute a partial derivative: hold all of the
other variables constant and compute the derivative of the dependent variable
relative to the independent variable you're evaluating. In the case of a
multivariate linear regression, select the base values for the other
independent variables and compute the dependent variable using a starting value
of the independent variable being evaluated. Then add a small delta value to
the single independent variable and compute (delta Y)/(delta X). Note that the
sensitivity will depend on the values you chose for the other independent
variables -- just as it does when you compute a numerical partial derivative in
calculus.

--
Phil Sherrod
(PhilSherrod 'at' comcast.net)
http://www.dtreg.com (Decision trees, Neural networks, SVM and Genetic
modeling)
http://www.nlreg.com (Nonlinear Regression)

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