# Inclusion of standard error in regression equation

\begin{alignat}{14} P = 11&.32 &+ 0&.71 \,\text{PASN} &+ 1&.54 \,\text{DIS} &- 1&.02 \,\text{DIS}^2 &+ 3&.44 \,\text{FUEL} &+ 1&.36 \,\text{FIRST} &+ 1&.12 \,\text{BIS} \\[-25px] (5&.16) & (0&.11) & (1&.91) & (0&.41) & (1&.17) & (0&.91) & (0&.52) \end{alignat} \\[25px] R^2 = 0.56; ~~ \text{RSS} = 211.22; ~~ \text{RR}\left(1,\text{d.f.}\right) = 9.48; ~~ W\left(1\right) = 17.11

I often see that standard errors are displayed under the regression equation but I don't really understand the purpose of it. Are those the standard errors of the estimated slope coefficient? And how does the inclusion of this information help with the statistical analyses? Thanks

$$\begin{eqnarray*} \hat{\beta_{j}} & \pm & t_{\alpha/2,n-p}\times (Standard\,Error) \end{eqnarray*}$$
Where $$\hat\beta_j$$ is the $$j$$-th parameter estimate, $$n$$ is the number of observations, $$p$$ is the number of parameters to be estimated in the regression model, and $$t_{\alpha/2,n-p}$$ is the $$\alpha/2$$ quantile of a Student's $$t$$-distribution with $$n-p$$ degrees of freedom.