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# Wald Statistic for testing a derivative

I am writing a paper in which I need to do a Wald Test (or get Wald Statistics) in two similar regressions.
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(1)
Y = Intercept + η1 X1 + η2 X2 + φ1 X1 * Z1 + φ2 X2 * Z1
+ ϕ1 lagGO + ϕ2 lagSize + + ϕ3 IdioSyncVar + ϕ4 RegDummy + ϕ5 Z1
Here Z1 is a continuous variable. μ = (β ÷ α) = (η2 + φ2 Z1) ÷ (η1 + φ1 Z1), α = δ Y ÷ δ X1 =η1 + φ1 Z1, β = δ Y ÷ δ X2 =η2 + φ2 Z1, μ = β ÷ α , and
(δ μ ÷ δ Z1) = { φ2 * η1 - φ1* η2 } ÷ (η1 + φ1 Z1)2.
After I get the coefficients using Proc Surveyreg, how do I get Wald Statistic for this derivative (δ μ ÷ δ Z1) in SAS (I want to test whether the derivative is positive)?
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(2)
Y = Intercept + η1 X1 + η2 X2 + θ1 X1 * W1 + θ2 X2 *W1
+ ϕ1 lagGO + ϕ2 lagSize + ϕ3 IdioSyncVar + ϕ4 RegDummy + ϕ5 W1
Here W1 is a binary variable, μ = (β ÷ α) = (η2 + θ2 W1) ÷ (η1 + θ1 W1), α = δ Y ÷ δ X1 =η1 + θ1 Z1, β = δ Y ÷ δ X2 =η2 + θ2 Z1, μ = β ÷ α , and
μ(W1=1) = (η2 + θ2) ÷ (η1 + θ1), μ(W1=0) = η2 ÷ η1.

After I get the coefficients using Proc Surveyreg, how do I get Wald Statistic in SAS in order to test whether μ(W1=0) is significantly higher than μ(W1=1).
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Thank you,
jais. Message was edited by: jais
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