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

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

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Yes. The estimated standard error gives the analyst (or reader) an idea of how precise the parameter estimate (estimated coefficient/slope) is: the larger the standard error, the less precise the estimate. To help you see this, recall that the standard errors are directly tied to confidence intervals of parameter estimates in simple multiple regression by the following:

\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.

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