In general, what the the standard hypothesis tests in all types of regression? We get some coefficients and then test the hypotheses that these coefficients are significant (i.e not equal to $0$)? For example, in logistic regression the p-value indicates that the regression coefficients are significant or not? Likewise with linear regression?
Question: Suppose coefficients $\beta_0$ and $\beta_1$ are significant in linear regression. Can we deduce anything about the significance of $\beta_0+\beta_1$? What about $\beta_0= \beta_1$?