# Mixed model_Identifying the random effect in a analysis

I am working on a project which we have two groups of people; normal vs obese. I have a data set like the following sample:

Subject  group  time  Cholesterol
1        normal  1     12
1        normal  2     14
1        normal  3     15
2        normal  1     16
2        normal  2     18
2        normal  3     19
3        obese   1     15
3        obese   2     19
3        obese   3     19


I think the model is like the mixed model. But I was wondering which variable is the fixed effect and which one random effect? I would like

1. To find any difference between normal and obese at each time point.
2. To comapre Cholesterol at each time point with Time=$1$ inside of each group to see whether there is a difference or not.

Any advice would be highly appreciated. I want to use R, I am not sure whether this function is a right one for this analysis:

lm <- lme(Cholesterol~time*group, (1|Subject), data=Data)


Is it the right function to use? Should I include time*group in the model or just time+group would be enough? Also how I can compare each time with the baseline within each group?