What test should be used to compare several regression lines? I want to determine if there are significant differences between movement and temperature of three groups. I have four regression lines and I want to know if there are significant differences in the slopes. What test do you use to do this? I had read about the ANCOVA, but recently someone suggested I not use it.
 A: I think what you want is a multiple regression model.  One issue here is that due to tradition there are a number of different models / analyses that are essentially the same, but go by different names and sometimes require you to use your software differently.  This makes it more confusing than it should be.  For example, traditionally the term 'ANCOVA' was used for what is (in essence) a multiple regression model with a categorical covariate (a factor), and a continuous covariate, but not an interaction between them (hence the 'parallel slopes' assumption).  To make this potentially more confusing, you should realize that people don't always use the terms that way anymore.  The thing is, in order to test if the slopes are different, you need an interaction term.  Using the terminology from multiple regression (which I find more intuitively transparent), including the group factor only allows you to test if the intercepts differ.  Thus, you should fit a multiple regression model where your response variable (${\rm movement}$?) is regressed onto ${\rm group}$, ${\rm temperature}$, and the ${\rm group}\times {\rm temperature}$ interaction.  Again, the last term will tell you if the slope of the relationship between ${\rm movement}$ and ${\rm temperature}$ varies by ${\rm group}$.  
A: It sounds like you want two regressions:
1) Movement ~ group
2) Temperature ~ group
But it's a little hard to tell. You might need multivariate regression if movement and temperature are related and you want to account for both in one model - this gets complex. 
You might have other variables; you might violate the assumptions of the OLS model. But this is a place to start.
