Numerical Example of the Metric
Effect for a Polynomial
To help demonstrate the metric effect of a polynomial the
previous example is utilized. The following represents the
relationship of between age and attitudes toward military intervention.
X1 represents age and
X2 represents age squared.
The general
model estimated is:
Y= 58.3 + -4.1( X1) + .7 (X2
)
The metric effect of age (X1
) on salary (Y) at different values of age:
Age Group 1: -4.1 + 2(.7)(1)= -2.7
Age Group 2: -4.1 + 2(.7)(2)= -1.3
Age Group 3: -4.1 + 2(.7)(3)= 0.1
Age Group 4: -4.1 + 2(.7)(4)= 1.5
Age Group 5: -4.1 + 2(.7)(5)= 2.9
The results provided above represent the estimate of the conditional
effect of age on attitudes toward military intervention at specified
values of age.
The predicted values of the response variable can also be obtained as
follows:
Age Group 1: 58.3 + -4.1(1) + .7(1)(1) = 54.9
Age Group 2: 58.3 + -4.1(2) + .7(2)(2) = 52.9
Age Group 3: 58.3 + -4.1(3) + .7(3)(3) = 52.3
Age Group 4: 58.3 + -4.1(4) + .7(4)(4) = 53.1
Age Group 5: 58.3 + -4.1(5) + .7(5)(5) = 55.3
The predicted value of the response variable indicate that the evaluation
of military intervention becomes decreasingly negative to the inflection
point at which evaluations become increasingly positive.
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Revised: August 17, 1999.