Hi, folks. Please note that the example I gave below is specifically a
shift from 0% to 10% on the assumed pop75 scale. Because the quadratic
curve is non-linear (by definition), a 10% increase in pop75 will
translate into different amounts of change in the dependent variable,
depending on the *levels* of pop75. For example, the shift from 10% to
20% in pop75 would be associated with a
[2*20 + 3*(20^2)] - [2*10 + 3*(10^2)] = 1240 - 320 = 920
unit change in the dependent variable. This is very different from the
320 unit change associated with a change from 0 to 10%. Sorry for any
confusion this (incomplete) example may have caused. This example should
now be easier to reconcile with Alison's note, as well.
Cheers,
Ryan
Hi, Lucy. For illustration, let's assume the
coefficient on pop75 is 2
and on pop75^2 is 3, and assume that pop75 is measured in percentage
points. Then, a 10%-point increase in pop75 would be associated with a
2*10 + 3*(10^2) = 320 unit increase in our dependent variable.
Make sense?
Ryan
------------------------------------------
Ryan T. Moore ~ Government & Social Policy
Ph.D. Candidate ~ Harvard University
Homepage:
http://www.people.fas.harvard.edu/~rtmoore/
Gov1000:
http://www.courses.fas.harvard.edu/~gov1000/
On Sat, 4 Dec 2004, Lucy Clare Barnes wrote:
Hi guys,
How can we interpret the coefficients/significance of the results of
models in which you have both eg x1 and x1^2 (as in lecture slide 390).
With simple numerical models it makes sense, but how should we best
interpret if we think that we need to include, say, both population over
75 and population over 75 squared?
thanks
Lucy
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