When should one use multiple regression with dummy coding vs. ANCOVA? I recently analyzed an experiment that manipulated 2 categorical variables and one continuous variable using ANCOVA.  However, a reviewer suggested that multiple regression with the categorical variable coded as dummy variables is a more appropriate test for experiments with both categorical and continuous variables.
When is it appropriate to use ANCOVA vs. multiple regression with dummy variables and what factors should I consider in selecting between the two tests?
Thank you.
 A: ttnphns is correct.  
However, given your additional comments I would suggest that the reviewer wanted the change merely for interpretation.  If you want to stick with ANOVA style results just call it ANOVA.  ANCOVA and ANOVA are the same, as ttnphns pointed out.  The difference is that with ANCOVA you don't treat the covariates as predictors and you definitely appear to want to do just that.
What the reviewer was getting at was that, while you can perform an ANOVA on continuous predictors, it's typical that one perform a regression.  One feature of this is that you get estimates of the effects of the continuous variable and you can even look at interactions between it and the categorical (which aren't included in an ANCOVA but could be in an ANOVA).
You may need some help with interpretation of regression results because funny things happen on the way to interactions if you're going to use the beta values to determine the significance of your effects.
A: These two are the same thing. For example, in SPSS the procedure where I specify ANCOVA is called GLM (general linear model); it askes to input "factors" (categorical predictors) and "covariates" (continuous predictors). If I recode the "factors" into dummy variables (omitting one redundant category from each factor) and input all those together with the covariates as "independent variables" in REGRESSION procedure (linear regression), I will obtain the same results as with GLM (taken that the dependent variable is the same, of course).
P.S. The results will be identical if the models are identical. If regression contains only main effects then ANCOVA should be specified without factor by factor interactions, of course.
A: ANCOVA is a form of regression but not identical to other multiple regression techniques. SPSS is not robust enough software to trust in anything outside of some psychology research. Within econometrics, biology, chemistry, physics, and finance SPSS is not accurate or useful in general. Even within psychology, SPSS preset regression corrections are often problematic.
Within education research here are examples of misuses of multiple regression and ANCOVA; they are similar but it is 100% wrong to say they are the same or almost identical.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5701329/
A: Multiple linear regression appears to me more appropriate than ANCOVA in this situation, as the journal reviewer recommends.
Try running both a multiple regression and an ANCOVA, and comparing the results.  They probably will not be identical.
ANCOVA and multiple linear regression are similar, but regression is more appropriate when the emphasis is on the dependent outcome variable, while ANCOVA is more appropriate when the emphasis is on comparing the groups from one of the independent variables.  In the experiment described above, the emphasis seems clearly to be on the outcome variable.
Finally, unless you are really certain that you way of doing things is better than the Reviewer's, and can explain why, then you should probably just concede to the Reviewer's expertise, so you can get your paper published.
