Hello, when a variable enters an estimation model in a quadratic term as well, there are two coefficients estimated. One for the linear and one for the quadratic one.
My question is: To find out whether the effect of the independent variable is signifcantly different from zero, is it enough to check if both coefficients are significant on a certain sign. level or do I have to test a joint hypotheses?

I produced an example:

Code:

. reg senroll_L young_0 senroll_0 war c.urban##c.urban

      Source |       SS           df       MS      Number of obs   =        99
-------------+----------------------------------   F(5, 93)        =     72.61
       Model |  60270.7708         5  12054.1542   Prob > F        =    0.0000
    Residual |  15439.6573        93  166.017821   R-squared       =    0.7961
-------------+----------------------------------   Adj R-squared   =    0.7851
       Total |  75710.4281        98  772.555389   Root MSE        =    12.885

---------------------------------------------------------------------------------
      senroll_L |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
----------------+----------------------------------------------------------------
        young_0 |  -.2650453   .0984708    -2.69   0.008    -.4605889   -.0695018
      senroll_0 |   .4667379   .0752275     6.20   0.000     .3173509    .6161249
            war |  -.9163032   4.187421    -0.22   0.827    -9.231691    7.399085
          urban |   .4259049   .2661305     1.60   0.113    -.1025775    .9543874
                |
c.urban#c.urban |  -.0024026   .0023005    -1.04   0.299    -.0069709    .0021657
                |
          _cons |   53.62803   11.36246     4.72   0.000     31.06443    76.19164
---------------------------------------------------------------------------------

. test c.urban#c.urban urban

 ( 1)  c.urban#c.urban = 0
 ( 2)  urban = 0

       F(  2,    93) =    2.65
            Prob > F =    0.0757
Here the p-values of urban c.urban#c.urban and of the test are different. Which should one interpret? Has urban a significant effect (say on a 10% sign. level)?

Thank you!!