Added interaction term, standard errors inflated I am running a simple regression of an index of cardiovascular health (Heart Rate Variability) on Age and Gender (as a dummy variable), n=430. I first ran: $$HRV \sim \beta_0 + \beta_1Age +\beta_2Gender$$
To obtain the following results (s.e. in brackets):

$\beta_0 = 7.47 (0.2) $
$\beta_1 = -0.04 (0.004) $
$\beta_2 = -0.23 (0.09) $
Residual Standard Error = $0.776$

I then wanted to check if Gender was had an effect of the age decline of HRV, so ran: $$HRV \sim \beta_0 + \beta_1Age +\beta_2Gender +\beta_3(Gender*Age) $$
But I wasn't too sure about the results:

$\beta_0 = 7.53 (0.36) $
$\beta_1 = -0.04 (0.008) $
$\beta_2 = -0.296 (0.43) $
$\beta_3 = 0.0016 (0.0097) $
Residual Standard Error = $0.777$

Could you please explain why my standard errors have inflated so drastically in the second model, in particular on the Gender coefficient? Many thanks in advance.
Edit: I have added a plot illustrating the residuals of the first model (Res1) against the residuals of a regression of Gender*Age on Age and Gender (Res2), as per @whuber 's suggestion:
 A: This is a good illustration of the problems of collinearity in your data.  Your values of gender and of gender*age are going to be strongly correlated (especially if you have a limited range of ages for whichever gender you have coded as one in the gender dummy).  All the values of the interaction term are 0 for one gender value - and equal to the value of age for the other gender value.  That means that, for your stats package, those two variables look very similar, and it becomes mathematically difficult to allocate the impact on your dependent variable to one or the other variable.   That "difficulty" becomes manifested in your results by having a large standard error for the estimated slope coefficeints.
Any basic textbook on regression will talk about multicollinearity and its impact on regression results in much more mathematical detail.  In your case, I would probably simply say that adding an interaction term doesn't seem to help much, and would revert to the estimates that do not include the interaction.
