Hypothesis test

I need to test the difference between two coefficients (I have two different regressions), how I did:

car<- mtcars


first<- lm(formula =  vs ~ gear + carb,
                 data = car)

second<- lm(formula =  vs ~ gear + disp,
           data = car)


coef_diff <- coef(first)["gear"] - coef(second)["gear"]
t.test(coef(first)["gear"], coef(second)["gear"],choice= "two.side",var.equal= TRUE)

The message I receveid:

Error in t.test.default(coef(first)["gear"], coef(second)["gear"], choice = "two.side",  : 
number insufficient of observations 

You could use the linearHypothesis function from the car package, which can test whether two coefficients in the same model are equal.

third <- lm(formula =  vs ~ gear + carb + disp, data = car)

car::linearHypothesis(third, "carb = disp")

Linear hypothesis test

Hypothesis:
carb - disp = 0

Model 1: restricted model
Model 2: vs ~ gear + carb + disp

  Res.Df    RSS Df Sum of Sq      F  Pr(>F)  
1     29 3.4685                              
2     28 3.1136  1   0.35489 3.1914 0.08486 .