Interpreting standard error for dummy variables in linear regression models Is there any way to interpret the standard error of dummy variables created to represent a categorical variable in a linear regresion model? I saw a great mathematical explanation here, but I am still having trouble with the "real-life" interpretation, if any.
As an example, let's say that this is the result of a case study:
> summary(results)$coefficients

Coefficients:
             Estimate Std. Error t value Pr(>|t|)    
(Intercept)  31.35750    2.32037  13.514 1.55e-14 ***
sexwoman     -0.53100    1.77624  -0.299   0.7670 

Representing the average sallary of employees of a company (in thousands) based on their sex. How would we interpret this standard error?
 A: The underlying math is that the intercept ($\beta_0$) indicates the average salary of men, in \$1000; the parameter $\beta_1$ indicates the difference between the average woman's and average man's salary.  So we could say something like "on average, women make \$530 less than men (with a standard error of \$1,776)". The $\pm 2 \mbox{SE}$ confidence intervals on the difference range from women's salaries being \$2,306 less to \$1,246 more than men's.
$\pm 2 \textrm{SE}$ is a commonly used shortcut; it is a little wider than the Normal-based 95% confidence interval ($\pm 1.96 \textrm{SE}$) and is a good approximation when your residual degrees of freedom (number of observations minus the number of model parameters) is moderate. In particular, the SE multiplier (which is can be computed in R via qt(0.975, df) for a given df) is:

*

*1.96 (actually 1.9599) as df $\to \infty$

*2.008 for df = 50

*2.086 for df = 20

*2.228 for df = 10

*2.571 for df = 5.

and so on. The SE multiplier that I back-calculated from your comments is approximately 2.6, so my guess is that you had approximately 5 residual df (the residual df are displayed in the summary() output, but you haven't shown us ...)
Interpreting dummy variables associated with factors can get considerably more complicated when different contrasts, and interactions among predictors, are present, but your case is simple.
