Standard error for marginal effect in regression?

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SUMMARY

The discussion centers on calculating the standard error for the marginal effect in an Ordinary Least Squares (OLS) regression model that includes both a variable and its squared term. The marginal effect is defined as ME = b1 + 2*b2*x, where x represents the sample average. The variance of the marginal effect is expressed as Var[ME] = Var[b1] + 4x^2 Var[b2] + 4x Cov[b1, b2]. This formula provides a definitive method for obtaining the standard error of the marginal effect.

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  • Understanding of Ordinary Least Squares (OLS) regression
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Statisticians, data analysts, and researchers involved in regression analysis who need to understand the computation of standard errors for marginal effects in OLS models.

annieta
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Hi,

I have a regular OLS regression that includes a variable both by itself and squared (i.e. y=b0+b1*x+b2*x^2). I am interested in the marginal effect of the variable at the mean. I know how to get the point estimate, but does anyone know how to get standard errors for the marginal effect? Many thanks!

Annie
 
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Define ME = b1 + 2*b2*x.

Var[ME] = Var[b1] + 4x^2 Var[b2] + 4x Cov[b1, b2] where x is treated as a constant (for example, x = the sample average).

Can you get to the standard error from here?
 

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