# Which statistical test to use for comparison of multiple regression coefficients?

#### jorgebm

##### New Member
Hi,

Brief description of my problem: My data consists of physiological data from animal experiments. For each animal I have conducted multiple experiments and the data are best described by linear regression. I wish to compare the regression coefficients (slopes) between my 4 groups.

I've attached an illustration that describes my problem (only 2 groups displayed though). The lines of same color are from experiments conducted on the same animal.

Which statistical test is appropriate for this problem?

Thank you.

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#### Karabiner

##### TS Contributor
So you have simple regressions, not multiple regressions?

With kind regards

Karabiner

#### jorgebm

##### New Member
So you have simple regressions, not multiple regressions?

With kind regards

Karabiner
Hi,

Yes. Simple linear regression Y = ax+b.

#### Karabiner

##### TS Contributor
Your illustration is a bit surprising, though. I cannot believe that each of the 4 or 5 subjects
in a group have exactely the same slope. Am I missing something? What was regressed on
what?

With kind regards

Karabiner

#### jorgebm

##### New Member
Your illustration is a bit surprising, though. I cannot believe that each of the 4 or 5 subjects
in a group have exactely the same slope. Am I missing something? What was regressed on
what?

With kind regards

Karabiner
Hi,

This is just an illustration. Not actual data. I can throw together a speadsheet with actual data and show you, if that helps.

Thanks for helping.

#### Karabiner

##### TS Contributor
Ok then. The easiest way would be to treat each subject's slope (coefficient)
as a dependent variable, and to comapre them between groups using a
"non-parametric" test. Kruskal-Wallis H as omnibus test for all groups,
Mann-Whitney U test for pairwise comparisons between groups.

With kind regards

Karabiner

#### Buckeye

##### Active Member
What is preventing you from using all of the data in a single regression model with indicators for the groups?

#### hlsmith

##### Less is more. Stay pure. Stay poor.
Halt your brakes - this screams repeated measures, right? So multilevel regression would control for observations clustered in animals and would allow you to control for within and between group differences, as well as covariates if desired. Even the graph screams multilevel regression - unless I am missing something.

#### jorgebm

##### New Member
Hi,

So I've attached a tab-delimited text file containing some data. The X values are Ved and the Y values are Ped.

My grouping variables are "Genotype", "Sex" and "Treatment". Only one genotype is listed in the file I added though.

"Animal ID" refers to the experimental unit. For each "Animal ID", a slope must be calculated for each "Experiment number". Then I wish to find the average slope for each "Animal ID". Then I wish to test if the slopes are different between groups.

My experience with Stata is limited, so I would really appreciate if anyone knows how I can do this in Stata.

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