ANOVA and multiple regression are two “flavors” of the general linear model (historically, they developed separately before being integrated in the same general framework and are still taught differently depending on the discipline but this is really all the same). Specifically, the analysis you carried out could also be described as an ANCOVA. Because of the links between multiple regression, ANOVA and GLM, it can be performed in SPSS using three different procedures:
/METHOD ENTER Factor Covariate.
UNIANOVA ResponseTime BY Factor WITH Covariate.
GLM ResponseTime BY Factor WITH Covariate.
The difference lies in the way the information is presented in the graphical user interface, some default settings and other options of each procedure and some details of the output and its interpretation but all three basically fit similar models and present equivalent tests for the main effects of each variable. Also, using one for the other does not free you from any assumption.
That said, there are a few puzzling things in your question. First, I only see a single outcome (response time) and therefore do not understand your instructor's advice to use a multivariate model (are you sure she didn't say “multiple regression”?).
Second, the binary nature of the outcome is surprising, response times are usually more or less continuous. Did you dichotomize this variable? Also, if it is really dichotomous, then none of this (GLM, ANOVA, ordinary regression) might in fact be the best way to analyze these data. Instead, you should probably look at generalized (not general) linear models or logistic regression.
I just realized that your main question seems to be about the interaction between covariate and factor (sorry for not focusing on that first). In SPSS, such a model can indeed be fitted with the
GLM procedure. You will find more on this in ANCOVA and its disturbing assumptions and How to specify ANCOVA interactions in SPSS? (in particular see this link from @JeromyAnglim's answer).
In your case the syntax would probably be something like
GLM ResponseTime BY Factor WITH Covariate
/DESIGN Factor Covariate Factor*Covariate.
You can also fit the same model with
UNIANOVA or through the graphical interface (by clicking the “model” button in the “General linear model/Univariate” dialog box and defining a custom model). The resulting syntax would be:
UNIANOVA ResponseTime BY Factor WITH Covariate
/DESIGN Factor Covariate Covariate*Factor.
(In both cases, the key element is the
Covariate*Factor part of the
/DESIGN statement, this adds an interaction to the model.)