R Help: F-Statistic regression test holding one variable constant

I am trying to run a number of F tests on a regression to test whether or not elasticity coefficients are statistically different from 0. The regression I am using is shown below, and I am trying to test dem-elasticity of gdp.

reg7=lm(log(gdp)~log.dem+educ+log.dem_educ+age+popscaled+d1970+d1975+
        d1980+d1985+d1990+d1995+d2000)

Where:

log.dem represents a log of a variable "dem"
log.dem_educ represents an interaction regressor, a product of log(dem) and a continuous variable "educ"
educ represents the average years of education completed by residents

The elasticity of dem is given by the sum of the coefficient of log.dem, and the coefficient log.dem_educ multiplied by educ.

Elasticity = coeff(log.dem) + coeff(log.dem_educ)*educ

I want to test the statistical significance of the elasticity of dem for different values of educ (educ=1, educ=2, ..., educ=10), but am unsure how to accomplish this with R. For the case of educ=1, I can just run an F-test using the code shown below since elasticity is just the sum of coeff(log.dem) + coeff(log.dem_educ)*1. However, I am unsure of how to adapt this to test elasticity coefficients for values of educ greater than 1.

linearHypothesis(reg7,c("log.dem + log.dem_educ = 0"),vcov = vcovHC(reg7, "HC1"))

Any suggestions would be greatly appreciated!

Solution

I wonder if c("log.dem = 0","log.dem_educ = 0") are really the hypotheses you want to test for the significance of the marginal effect of log.dem when educ is 1. Do you mean instead "log.dem + log.dem_educ = 0"?

In a similar manner, for different levels of educ you would run

linearHypothesis(reg7, "log.dem + 2 * log.dem_educ = 0", vcov = vcovHC(reg7, "HC1"))
linearHypothesis(reg7, "log.dem + 3 * log.dem_educ = 0", vcov = vcovHC(reg7, "HC1"))
linearHypothesis(reg7, "log.dem + 4 * log.dem_educ = 0", vcov = vcovHC(reg7, "HC1"))

and so on.