The R function you have to use is the
On QuickR you can find a simple and clear tutorial on how to estimate a linear (multiple) regression model generally using the
lm(). As further reference, I suggest you to read the Introducing R tutorial about linear model by G. Rodriguez.
I did not read the paper you cited, but, anyway, you should estimate the model simply by running on the R shell the following command:
results = lm(dependent_variable_name ~ independent_var1_name + ... + independent_var7_name)
and run that by clicking on
CTRL + ENTER.
Of course, replace
dependent_variable_name with the name of the variable you gave previously; the same for the independent variables.
This command does not take into account the problems you should check in order to get reliable estimates, as, for instance, heteroskedasticity, autocorrelation, not normal residuals,... but it would be a too broad topic to deal with here.
You can find a lot of reference and tutorial on the links I posted above, but, you can find help on quant.SE too.
Hope this help.