What to do with data that are bimodal at two tails of the distribution? I am in a weird position where I prespecified a plan to use linear regression to analyze my data, and stated I would use transformations to address any assumption violations. I'm pretty certain my data are not suitable for linear regression, nor will they be fixed with a transformation. I plan to use a more appropriate analysis, but I'd like to at least entertain the possibility that these data could be transformed OR that they are still acceptable for linear regression. Any ideas for transformations and/or opinions about whether or not it's acceptable to use linear regression with these data?
Edit: I know that survival analysis is more appropriate given that the data are right censored (the response variable is amount of time subjects waited before engaging in a certain behavior, and the experiment was ended if the subject waited 15 minutes). But what I'm asking is whether linear regression can be used on these data (ignoring the censoring issue)/if there is an appropriate transformation? Also, if censoring should not be ignored, why exactly (since it doesn't violate assumptions of linear regression)?
Edit2: Below are some diagnostic plots. 



Thanks!

 A: I would argue that this is not a case of bimodal data, but rather right censoring. You're not interested in how long the experiment goes for (often terminated after 15 minutes), but rather time until action. Unfortunately, you don't also get to observe the time until event for every observation because of early termination. However, on these censored observations, you know that time until event is at least 15 minutes, which is somewhat informative. 
This is well trodden territory in the field of survival analysis. Standard tools include Kaplan-Meier curves (for univariate fits) and Cox-PH (most common) or Accelerated Failure Models (probably an easier model to understand if you are unfamiliar with hazard rates, etc.)
EDIT: It was asked what, specifically, is wrong with using linear regression (without accounting for censoring) in this scenario. The answer is that your estimates will be biased (and in your case, this bias looks to be very serious). As an extreme example, suppose the population mean was greater than 15 (looking at your values, it looks like at least half of the recorded times are censoring 15, which implies that the mean is, in fact, likely to be greater than 15). Since all true response values greater than 15 enter your dataset as 15, you can't possibly estimate a mean of 15 (in fact the expected value of the mean will be much less than 15, even though that's the true mean value). 
A: Ignoring censoring in the data is a bad idea, especially because it's not a small amount of censoring.  It looks like close to half the data is right- censored.  To see why this might be bad, take a true linear regression $y_i=a+bx_i +e_i $ (assume $a,b>0$ for simplicity).  Now suppose we trim all values $y_i $ above $15$ to $15$.  What happens is for the large $y_i >15$ is that the corresponding large $x_i $ no longer sits on the straight line, and sits on a slope of roughly zero (not the "true slope" $b $).  So when you fit the regression model using censored data the estimated slope will be smaller.
Having said all that, your set of predictors looks pretty limited - looks like there are only $3$ distinct combinations from the residual plot - so only $3$ fitted values are possible in any regression model.  You could just run $3$ independent analysis within each group.  Then you're just estimating univariate right censored data.
Hope this helps!
