Confidence interval and interaction terms

[Aktar]

Hello,

I would like to compute the confidence interval for an interaction term.

I have the following model:

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y_{t}=\beta_{1}x_{1}+\beta_{2}x_{2}+\beta_{3}(x_{1}+x_{2})

The total effect of

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x_{1}

is

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\beta_{1}+\beta_{2}x_{2}

I am just wondering what is the formula for computing the confidence interval of this total effect.

Thank you very much

[startz]

standard error = sqrt(var(beta1) + x^2*var(beta2) + 2*x*cov(beta1,beta2))