ANOVA with metric dependant variables? I often see multiple or simple linear regression coupled with ANOVA.
From my understanding, ANOVA is to test if there is a mean difference within a group, the values have then to be categorical or be like dummy variable 0-1 no? I fail to understand the ANOVA with metric dependant variable, and what if you have multiple dependant variables ?
Let`s say I have three metric variable:


*

*Response is user

*DV: time

*DV: temperature


The linear Regression Model would be:
lm(user~time+temperature)
The ANOVA Model would be the same
aov(user~time+temperature)
 A: An ANOVA is actually a kind of model comparison and the GLM framework is the one you should have in mind to understand the concept in all its generality, both for metric/continuous variables and for categoric variables (i.e. when you compare groups). 
An ANOVA answers the question: if I add a given term to my model (time, temperature in your example, but also a categorical variable) does this term explains a significant portion of variance in the data? If yes ANOVA is significant. 
When you do an ANOVA you compute an F value which is always something like:
$$
F = \frac{\textrm{explained variance}}{\textrm{unexplained variance}}
$$
For a categorical term I guess you have heard of the expression:
$$
F = \frac{\textrm{variance between groups}}{\textrm{variance within groups}}
$$
But in practice what you are computing (and this will be valid both for a categorical variable like group/treatment and a continuous variable like temperature) is a ratio of residual sums of squares $RSS(\textrm{X})$ where X indicates the set of variables in the model. For example computing an ANOVA for the term temperature (temp) in your model would look like this:
$$
F = \frac{\frac{RSS(\textrm{time})-RSS{(\textrm{time, temp}})}{2-1}}{\frac{RSS{(\textrm{time, temp}})}{n-2}}
$$
where $n$ is the number of observations. 
