It should also be noted that I also agreed with much of the criticism in the comments regarding the logarithmic transforms that need to be done on the variables...however, if after taking the ln of each variable, the comparative magnitude of the coefficients remains present, then we can go back to the pre-transformed data and make easier inferences using the coefficients that are present.

So, the dependent variable is gsp/cap, the independent variables are vmt/cap, population density, and education.  The unit of analysis is state, (however we are dropping DE and WY for reasons mentioned earlier.)  (fyi: including them in the analysis weakens the case a bit for VMT, but the education result is still present).

Here's the multivariate regression (using robust standard errors, just because I like overkill) results (using Stata):

gspcap=educ+popden+vmtcap

. regress  gspcap educ popden vmtcap, robust beta plus

Regression with robust standard errors                 Number of obs =      48
                                                       F(  3,    44) =   38.49
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.6664
                                                       Root MSE      =  3555.4

------------------------------------------------------------------------------
             |               Robust
      gspcap |      Coef.   Std. Err.      t    P>|t|                     Beta
-------------+----------------------------------------------------------------
        educ |   659.0628   107.6447     6.12   0.000                 .5328718
     popdens |  -1.443011   7.739639    -0.19   0.853                -.0235832
      vmtcap |   -1.79709   .5305359    -3.39   0.001                -.4813086
       _cons |   38455.69   7496.157     5.13   0.000                        .
-------------+----------------------------------------------------------------

what does this gobbledygook mean?  well, each coefficient is the change in the dependent variable resulting from a one unit change in that independent variable, controlling for the other variables present in the equation.  So, for a one percentage change in percent education of a state, gsp/cap goes up $659.  A one unit change in vmtcap results in a -1.79 unit change in gspcap even after controlling for education.  The effects for education and vmtcap are statistically significant at p<.001 or greater.  (I can explain that more if you all want me to).

The final column out there is what we call a "standardized beta."  It's not the best measure of strength around (trust me, I could explain it, but you don't want me to), but it is an indicator of "standardized explanatory strength."  We cannot directly compare the regression coefficients' magnitudes, but betas can help us do that (caveat: somewhat).  Because the magnitude of the betas are relatively the same, though in different directions (vmt is an inverse relationship, educ a direct relationship), we can say that these two variables have a relatively similar explanatory power.

Now, the question of the logarithmic transforms.  Regression is really robust, but it has some assumptions...one of them is that these variables are normally distributed.  They aren't.  The solution is to attempt to make them more normal by transforming them using some standard...in this case, using natural logs of those variables that are "large," gspcap, vmtcap, and popdens, because it makes them more normal in their distribution.  This is a pretty standard trick.  Here's the results:

. regress  lngspcap educ lnpopden lnvmtcap, robust beta plus

Regression with robust standard errors                 Number of obs =      48
                                                       F(  3,    44) =   36.49
                                                       Prob > F      =  0.0000
                                                       R-squared     =  0.6753
                                                       Root MSE      =  .09517

------------------------------------------------------------------------------
             |               Robust
    lngspcap |      Coef.   Std. Err.      t    P>|t|                     Beta
-------------+----------------------------------------------------------------
        educ |   .0188446   .0030129     6.25   0.000                 .5615207
    lnpopden |  -.0079779   .0159703    -0.50   0.620                -.0678694
    lnvmtcap |  -.4890024    .121637    -4.02   0.000                -.4718397
       _cons |   14.55413   1.181904    12.31   0.000                        .
-------------+----------------------------------------------------------------

no changes, except in the raw coefficients.  The significance levels stay the same, the betas stay relatively similar.  So, we can say with some confidence that the transforms aren't all that necessary.

It should be noted that, because of the transforms we did, we would have to reinterpret (exponentiate them and the dv over e) the coefficients in order to make direct inferences about prediction (such as a rise of 1% in a state's education = $659 in gspcap that I discussed above). However, even if we change them back, we get substantively similiar results.

So, what's the takeaway?  Stuart's right.  States with higher vmts have lower gsp/cap, even after controlling for education and population density.