I was constructing a multiple regression model and was inspired by two papers the two papers didn't test stationarity although when I tried to test stationarity and took the difference all the variables were insignificant and R squared was too low 0.22 , but when I tried without taking difference of stationarity the variables were significant and R squared was 0.78
Paul F Velleman
If by "stationarity" you mean constant variance of the errors, then no, you shouldn't test it; it is an *assumption*. However, it is always a good idea to examine your residuals for curvature and heteroskedasticity. Finding either (or both) suggests you may need to re-express your response variable. But you don't need a hypothesis test for that
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