Standard error for marginal effect in regression?

In summary, the standard error for marginal effect in regression is a measure of the uncertainty or variability in the estimated marginal effect of an independent variable on a dependent variable. It is calculated using a formula that takes into account sample size, standard deviation, and covariance. This measure is important in regression analysis as it provides information about the precision and reliability of the estimated effect. It cannot determine the significance of a variable on its own, but is used in conjunction with other factors. Standard error for marginal effect can be interpreted in terms of confidence intervals, indicating the likely range of the true effect with a certain level of confidence.
  • #1
annieta
1
0
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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  • #2
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?
 

Related to Standard error for marginal effect in regression?

1. What is the definition of standard error for marginal effect in regression?

The standard error for marginal effect in regression is a measure of the uncertainty or variability in the estimated marginal effect of an independent variable on a dependent variable in a regression model. It indicates how much the estimated marginal effect may vary if the same model is applied to different samples.

2. How is standard error for marginal effect calculated?

The standard error for marginal effect is calculated using the standard error formula, which takes into account the sample size, the standard deviation of the dependent variable, and the covariance between the independent and dependent variables.

3. Why is standard error for marginal effect important in regression analysis?

The standard error for marginal effect is important because it provides information about the precision and reliability of the estimated marginal effect. A smaller standard error indicates a more precise estimate, while a larger standard error indicates a less reliable estimate.

4. Can standard error for marginal effect be used to determine the significance of a variable in a regression model?

No, the standard error for marginal effect alone cannot determine the significance of a variable in a regression model. It is used in conjunction with the estimated coefficient and its corresponding p-value to determine the significance of a variable.

5. How can standard error for marginal effect be interpreted?

Standard error for marginal effect is often interpreted in terms of confidence intervals. It represents the range in which the true marginal effect is likely to fall with a certain level of confidence. For example, a 95% confidence interval would indicate that we are 95% confident that the true marginal effect lies within the calculated range.

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