Interpretation when Linear Combination of Coefficients in linear regression is not significant I have a linear regression (OLS) and was told that I could use Linear Combination of Coefficients (lincom with Stata) to analyze the influence of those variables. Unfortunately, my stat skills are not very good and I searched the web without finding a proper explanation of what this actually does. 
I found that running
lincom var1-var2

tests if both variables are equal. I, however, have not found out what it tests when I run
lincom var1+va2.

With the person telling me I should run the latter without providing me with an explanation what it does and after hours of searching without finding an easy solution, it would be great if someone could help me out. 
If I run a regression with my data, var1 is significant while var2 is not. When I run lincom, this is the result I get. 
. lincom var1 + var2   

 ( 1)  var1 + var2 = 0

------------------------------------------------------------------------------
ln_varA |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
         (1) |   4.187462   3.686233     1.14   0.259    -3.141757    11.51668
------------------------------------------------------------------------------

My questions:


*

*What do I test for with this?

*How is the interpretation when it is significant / not significant. 

 A: *

*You are testing the null hypothesis that the sum of the two coefficients (not variables) is zero, or that the two effects cancel out (they are equal in size & opposite in direction, or maybe both just zero). The alternative hypothesis here is that the sum is not zero (a two-sided alternative).

*You can look at the p-value or the confidence interval or even the t-statistic to decide on significance. In your case, the p-value of 0.259 is large and the 95% CI includes zero and the t-statistic is 1.14, so you cannot reject the null that the sum is zero at conventional levels. This means the data is consistent with the null of the sum being zero. The significance of the sum (or difference) will depend on the standard errors of the two coefficients and the coefficients themselves, which you can see in the regression output, but also on their covariance, which is not shown by default. In other words, the individual significance of the coefficients is not sufficient to tell you about the significance of the sum. 


Here are 3 equivalent ways to test such composite linear nulls more generally (i.e., not just for zero). Here will will test that the combined effect of an additional 1000 lbs of weight and of foreign origin is 10K dollars of additional car price (this should make sense: heavier cars cost more to make and to transport):
sysuse auto, clear
replace weight = weight/1000
reg price mpg weight foreign
display _b[foreign]+_b[weight] - 10000
lincom foreign + weight - 10000
margins, expression(_b[foreign] + _b[weight] - 10000)
test _b[foreign] + _b[weight] = 10000

Personally, I find the last the most intuitive, though all have the same p-value here. The CIs will vary slightly, depending on whether Stata does a t-test or a z-test. We can easily reject the null that the combined effect of weight and origin is $10K, in favor of the alternative hypothesis that it is not.
