If and how to use one-tailed testing in multiple regression I have one-sided hypotheses that I want to test with multiple regressions. Does anyone know how to perform a one-sided hypothesis testing? I heard of different positions regarding this matter ("not possible to test one-tailed with regression" and "for one-sided hypotheses just cut the p-value in half"). Or maybe I need another command in with my statistics program (I use R)!? 
I didn't think this to be a difficult question but couldn't find a consistent and satsfying solution. 
Thank you in advance for any helping comments.
 A: It only requires minimal manual computations to perform one-sided hypothesis testes concerning the regression coefficients $\beta_{i}$.
Two possible one-sided hypotheses are:
\begin{align}
\mathrm{H}_{0}&:\beta_i \geq 0 \\ \tag{1}
\mathrm{H}_{1}&: \beta_i < 0 
\end{align}
or 
\begin{align}
\mathrm{H}_{0}&:\beta_i \leq 0 \\ \tag{2}
\mathrm{H}_{1}&: \beta_i > 0
\end{align}
The $p$-values provided by R are for the two-sided hypotheses and are calculated as $2P(T_{d}\leq -|t|)$ where $T$ is the test statistic (i.e. the regression coefficient divided by its standard error) and $d$ are the residual degrees of freedom.
The corresponding one-sided $p$-values are $P(T_d\leq t)$ and $P(T_d\geq t)$, for the first $(1)$ and second $(2)$ one-sided hypotheses, respectively.
Here is how to calculate the one-sided $p$-values in R:
mod <- lm(Infant.Mortality~., data = swiss)
res <- summary(mod)

# For the two-sided hypotheses

2*pt(-abs(coef(res)[, 3]), mod$df)

(Intercept)   Fertility Agriculture Examination   Education    Catholic 
0.118504431 0.007335715 0.678267621 0.702498865 0.476305225 0.996338704 

# For H1: beta < 0

pt(coef(res)[, 3], mod$df, lower = TRUE)

(Intercept)   Fertility Agriculture Examination   Education    Catholic 
  0.9407478   0.9963321   0.3391338   0.6487506   0.7618474   0.5018306

# For H1: beta > 0

pt(coef(res)[, 3], mod$df, lower = FALSE)

(Intercept)   Fertility Agriculture Examination   Education    Catholic 
0.059252216 0.003667858 0.660866190 0.351249433 0.238152613 0.498169352

mod$df extracts the residual degrees of freedom and coef(res)[, 3] extracts the test statistics.
A: I'm not a statistician, so take my answer with a grain of salt but here goes. p-values reported in in linear regression will be obtained using F-test, commonly used for evaluating least-square fitting problems like linear regression). F-test doesn't have two tail version because the distribution of F-value is one-tailed (because F=t^2) to begin with. Read a more detailed answer here
