Three IVs, one DV. What test to use? I've gotten myself into a pickle with my experimental design. I'm looking at how the temperature at which an organism dies is affected by:
- the population it came from (e.g. Pop1, Pop2, Pop3)
- the temperature at which I kept them (Pop1 was split into three different incubation temperatures, etc.)
- the weight of organisms
I believe that gives me 2 categorical and 1 ratio predictor variables, but I don't know what stats test to use, because I've never dealt with so many IVs at once. My statistics knowledge isn't great so I'd appreciate any help.
 A: You will want to use some form of regression model. Note that a regression model is different than a test. Under the null hypothesis significance testing (NHST) paradigm, the tests that you perform based on a model correspond directly to your hypotheses. So in order to tell you which tests to perform you will need to specify some set of null hypotheses.
The model you will fit may look something like this:
$$ Y_{ijk} = \beta_0 + \beta_{1_j}*Pop_{ij} + \beta_{2_k}*Temp_{ik} + \beta_{3_jk}*Pop_{ij}*Temp_{ij} + \beta_4*Weight_{ijk} + \epsilon_{ijk} $$
Where:


*

*$Y_{ijk}$ is the response of the $i^th$ experiment unit in the $j^{th}$ population exposed to the $k^th$ temperature 

*$\beta_0$ is the overall mean 

*$\beta_{1_ij}$ is the difference in mean due to $Pop_{ij}$, the populations (e.g. 1,2 or 3) . In terms of fitting the model, $Pop_{ij}$ is an indicator variable that is 1 if the experimental unit belongs to the $j^{th}$ population and 0 otherwise.  

*$\beta_{2_ik}$ is the difference in mean due to $Temp_{ij}$, the temperature treatment.

*$\beta_{3_ijk}$ is the difference in mean due to the interaction of population and temperature.

*$\beta_{4_ijk}$ is the difference in the mean response due to weight and $Weight_{ijk}$ is continuous.

*$\epsilon_{ijk}$ is unexplained error, typically distributed as $N(0, \sigma^2)$


In this model you would be fitting a different mean response to each combined population treatment, but each treatment would have the same slope due to weight. You can visualize this as 9 parallel lines running through your data that describe the mean for each treatment with weight on the x-axis and the response on the y-axis. An alternative model might be that there is a different trend (a different slope) with weight for each treatment in which case you would add additional interaction terms.
Now maybe one of your questions is whether there is evidence for that the slope with weight really is different for at least one of these treatments. To test that you would fit the fullest possible model (one with all the relevant interaction of population and temperature and weight) and compare it to the somewhat simpler model above. You could do that with a likelihood ratio test, or with F-tests by partitioning the variance in an ANOVA table. Or maybe one of your questions is whether there is evidence that mean response for different populations responds different to different temperatures. This is equivalent to testing whether at least one of the $\beta_3$ terms from the above model is statistically different than zero. Again you could fit the simpler model and compare it to the fuller model with a likelihood ratio test, or with the ANOVA table. Or maybe your question is whether population 1 is different than population 2 under temperature treatment 1. That is one of several pairwise differences you could test for. Once again you would use your regression model, but this time you would be testing something called a contrast. You'd be using the t-distribution instead of the F-distribution. If you are interested in testing for more than one pairwise difference, then you should consider controlling for multiple comparisons.
In short, there are lots of formal hypotheses you could have given your experimental design. For each hypotheses, there is a corresponding statistical test. The form that test takes depends on the hypotheses. All of these tests rely on one or more regression models fit to your data. 
EDIT: As @NickNichiporuk points out, linear regression and tests of linear regression model rely on certain assumptions (such as the distribution of the error). You should check these assumptions prior to performing any formal hypothesis test and caveat as necessary for any violations or potential violations.
A: Multiple regression allows you to predict values of a continuous dependent variable (response variable) from 2 or more independent variables (predictors) of any type (i.e. categorical or continuous). More specifically, multiple regression estimates how changes in one predictor relate to changes in the response variable, while automatically controlling for all other predictors in the model.
If you plan to use multiple regression, check your data to make sure it meets certain assumptions. Here is a link to a wikiuniversity site that outlines and explains each of the assumptions.
