# Finding standard error of price elasticity

I have a regression that is of the following form:

$$\text{salespc} = \beta_1 + \beta_2 \text{realprice} + \beta_3 \text{realincpc} + e_i$$

My output from R is as follows:

           Coef     S.E.   t     Pr(>|t|)
Intercept 253.5044 9.2183 27.50 <0.0001
realprice -18.4374 2.6315 -7.01 <0.0001
realincpc  -0.0035 0.0004 -8.45 <0.0001


I'm supposed to find price elasticity of demand and its standard error. I think that the elasticity is $$\beta_2 \frac{\text{realprice}}{\text{salespc}}$$ at given values of $\text{realprice}$ and $\text{realincpc}$. But I'm not sure how to find the SE. I know this isn't an econ forum but I thought it may be my best shot. Thanks.

I'm supposed to do a similar question with

$$\log(\text{salespc}) = \gamma_1 + \gamma_2 \log(\text{realprice}) + \gamma_3 \log(\text{realincpc}) + e_i$$

but I think once I get the first part I can do the second.

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The first question is tough: one tends to think of parametric bootstrapping or the delta method. Are these the sorts of calculations that would be expected of you? The second, in comparison, is almost trivial, so consider addressing it first. –  whuber Nov 3 '11 at 5:09
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