# [R] Multivariate multiple linear regression question

Virendra Mishra virendra.mishra at gmail.com
Sat Feb 20 18:53:52 CET 2016

```Hi R-users,

I have a fairly simple question to ask but I havent yet got an answer to
the question. I will describe my experiment, analysis and what have I done
and what is the question in the following paragraphs and I would appreciate
if anyone could point me to use right statistical tools to answer my
question.

Experiment:
I have 2 groups and both groups undergo 2 set of evaluations, one with MRI
scanner and the other in the lab to test for their behavior. Both these
evaluations are known to have statistically significant relationship with
age and gender.

Statistical question of interest:
Whether there is:
1) statistically significant difference between the 2 groups on each
evaluation ?
2) Whether there is any relationship between and within the 2 groups
between each evaluation

Model:

I model the problem as following:
MRI_measure = Intercept + Slope1 * Age + Slope 2 * Gender + Slope3 * Group
[Age is continuous and gender , Group are factors/categorical]

Lab_measure = Intercept + Slope1 * Age + Slope 2 * Gender + Slope3 * Group
[Age is continuous and gender , Group are factors/categorical]

In order to obtain the solution in R:
MRI_model<-lm(cbind(MRI_measure, Lab_measure) ~ age+gender+group,
data=data)

Result of R:
manova(MRI_model) suggests that yes indeed all the slopes are significantly
different than 0 suggesting a relationship between my measures.

Question:
1) In order to test whether the difference in the MRI_measure is
statistically significant different between the 2 groups, I use
MRI_model\$fitted.values for each dependent measure and do a statistical
test (either t-test or Wilcox) and claim that the difference is
significant.
In the paper I write, multivariate multiple linear regression was performed
for the groups while controlling for age and gender. The regressed out
MRI_measure was statistically compared to see if the difference is
different.

I am assuming that the predicted/fitted.values in model are the regressed
out variables. Can I show this and use this result? Is this right

If no, what is the correct way to statistically compare whether my 2 groups
differ in their MRI measure and lab measure when controlled for age and
gender. Any R library, literature, possibly a script will be greatly
appreciated.

2) I also want to see if there is any relationship between MRI_measure and
Lab_measure within the group after they are controlled for age and gender.
What is the correct way to do this in R?

Further, I also want to see if there is any significantly different
association between the 2 groups for my set of dependent variables. I am
thinking this can be done: I first find the correlation between 2 dependent
variable in each group and test if this correlation is statistically
different between the 2 groups? Is this logic right? And if it is, how do I
compare the correlation? If not, what is the right way to do this? Any R
library, literature, possibly a script will be greatly appreciated.