I now know that a multiple regression is not a multivariate analysis, although I have seen millions of incorrect references that mistakenly call it multivariate. The hint is the number of the DVs which determines being multivariate or else. And a sophisticated regression model is still univariate since it has only one DV.

Another myth is the wrong explanation given here about the univariate analysis, being confused by descriptive analysis.

And an interesting point is that a sophisticated multiple regression is univariate while a chi-square or a correlation coefficient are bivariate!

Another interesting point is that a repeated-measures ANOVA is multivariate since a DV is repeated for some times and we have actually more than one DV.

I would add more detailed discussions here, but I have available this one:

"victorxstc 20.8.2013: I received a SPSS result from a student. Apparently her staistician has done rmANOVA. There is a section which reads "Multivariate Tests" under which these tests appear: Pillai' trace, Wilks Lambda, Hoteling's trace, Roy's largest root... besides the term "multivariate tests" there is a "b" indicator which refers to the table legend "b". This table legend reads: "Design: Intercept + X + X2 + X1 * X2"... In this analysis, there is only one DV (which is the increase in temperature of tooth). There are definitely no two or more DVs. However, the line reads "multivariate analysis". So I don't understand... Maybe since it is repeated-measures, there have been somehow two DVs and this is why it is multivariate. I don't know but interesting

...

Spunky: @victor: repeated-measures ANOVA can either be analysed the usual, univariate way or as a MANOVA. the multiple DVs come from the fact that you took repeated measurments on the same subjects over time (hence multiple DVs because of the repeated measurements). that's an interesting question, actually."