# What are the standard hypothesis tests in any type of regression?

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 $\beta_0= \beta_1$?

• Indeed, softwares return the $p$-value for $H_0:\{\theta=0\}$ for each parameter $\theta$ of the model. Commented Jan 18, 2013 at 20:00
• @StéphaneLaurent: Is there a way to test for example $H_0: \theta_1+\theta_2 = 2$? Commented Jan 18, 2013 at 20:02
• Is this homework? Commented Jan 18, 2013 at 20:14
• @proton For a Gaussian linear regression model it is easy to test about any linear combination of the parameters. Commented Jan 18, 2013 at 20:16
• @StéphaneLaurent: How about for other types of regression. Commented Jan 18, 2013 at 20:21

You can create a contrast matrix $L$ and a vector of parameters $\beta$. Then test any kind of linear combination of the parameters using the null hypothesis, $H_0:L\beta=d$. You can use a Wald test or a Likelihood Ratio Test (LRT) for testing your $H_0$.
• What if you want to test $H_0: \frac{\beta_0}{\beta_1} = 1$ vs $H_a: \frac{\beta_0}{\beta1} \neq 1$? Commented Jan 21, 2013 at 14:56
• It is all the same as $H_0:\beta_0-\beta_1=0$, isn't it? More over you could also test $H_0:\frac{\beta_0}{d\beta_1}=1$ by constructing a contrast matrix $L$ such that $H_0:\beta_0-d\beta_1=0$. Commented Jan 21, 2013 at 18:36