# Thread: hypothesis testing comparing 2 multiple regression models

1. ## hypothesis testing comparing 2 multiple regression models

Hi guys, I beg u to help me with this:

Currently I have 2 models
y1 = a1*x1 + b1*z1 + c1
y2 = a2*x2 + b2*z2 + c2

y1 is taken from 18 data samples.
y2 is taken from 72 data samples.

I want to perform null hypthesis as a1 = a2, b1=b2, c1=c2.
My goal is to show that first model is different than second model.

Do u know some links or books that can be useful to me?
or maybe u can help me to figure out what I should do.....
Thanks so much.... I'm so desperate with this...

//////////////////////////////////////////////////////////////

I couldn't find any relevant examples for this problem
Usually... the example is only
y1 = a1*x1 + c1
y2 = a2*x2 + c2
with null hypothesis, a1 = a2, c1 = c2.

And it's not sufficient for my case....

or the other pupolar example is
y = a*x1 + b*x2 + c*x3 + d*x4
with null hypothesis, a = b.

And it's not sufficient for my case....

//////////////////////////////////////////////////////////////

I used R statistical package to provide the model.
But after that I'm lost.....

2. Originally Posted by neosonic
Hi guys, I beg u to help me with this:

Currently I have 2 models
y1 = a1*x1 + b1*z1 + c1
y2 = a2*x2 + b2*z2 + c2

y1 is taken from 18 data samples.
y2 is taken from 72 data samples.

I want to perform null hypthesis as a1 = a2, b1=b2, c1=c2.
My goal is to show that first model is different than second model.

Do u know some links or books that can be useful to me?
or maybe u can help me to figure out what I should do.....
Thanks so much.... I'm so desperate with this...

//////////////////////////////////////////////////////////////

I couldn't find any relevant examples for this problem
Usually... the example is only
y1 = a1*x1 + c1
y2 = a2*x2 + c2
with null hypothesis, a1 = a2, c1 = c2.

And it's not sufficient for my case....

or the other pupolar example is
y = a*x1 + b*x2 + c*x3 + d*x4
with null hypothesis, a = b.

And it's not sufficient for my case....

//////////////////////////////////////////////////////////////

I used R statistical package to provide the model.
But after that I'm lost.....

When faced with a stats problem that I don't know much about
I usually consider using some form of Monte-Carlo method to
investigate the distribution of the parameters of interest.

For instance your models are in reality of the form:

y=ax+by+c+r

where r is a noise term usually (if things are going right) zero mean
normal with sd s say, which you can estimate from the residuals.
(note if the residuals show noticeable departures from independence and
normality you are in trouble and need to reconsider the models)

Now assume some value of a, b and c (the same for both samples) and
generate 100 (or a 1000 or whatever) replicates of the estimates of
(a1-a2, b1-b2, c1-c2), and compute an estimate of the covariance matrix
of this vector for the 100 replicates.

The vector (a1-a2, b1-b2, c1-c2) that you observe should be more
or less multivariate normal, and we now have an estimate of its
covariance matrix, so we can test it (you will have to look up test for
the this).

This sort of analysis is of an exploratory nature and will give a rough
indication if the models are significantly different.

For a more theoretical (academically respectable) approach you will need to
look at a reference on regression models, or general linear models (GLM).
There should be a vast literature on testing such models, which I am not
familiar with.

RonL

3. Originally Posted by neosonic
Hi guys, I beg u to help me with this:

Currently I have 2 models
y1 = a1*x1 + b1*z1 + c1
y2 = a2*x2 + b2*z2 + c2

y1 is taken from 18 data samples.
y2 is taken from 72 data samples.

I want to perform null hypthesis as a1 = a2, b1=b2, c1=c2.
My goal is to show that first model is different than second model.

Do u know some links or books that can be useful to me?
or maybe u can help me to figure out what I should do.....
Thanks so much.... I'm so desperate with this...

//////////////////////////////////////////////////////////////

I couldn't find any relevant examples for this problem
Usually... the example is only
y1 = a1*x1 + c1
y2 = a2*x2 + c2
with null hypothesis, a1 = a2, c1 = c2.

And it's not sufficient for my case....

or the other pupolar example is
y = a*x1 + b*x2 + c*x3 + d*x4
with null hypothesis, a = b.

And it's not sufficient for my case....

//////////////////////////////////////////////////////////////

I used R statistical package to provide the model.
But after that I'm lost.....

The test you're looking for is a Chow Test. The test statistic is

where RSS1 is the sum of squared residuals from the first regression, RSS2 is from the second regression and RSS is from the pooled regression.

4. ## Thanks, by the way, how do we get RSS?

Originally Posted by JakeD
The test you're looking for is a Chow Test. The test statistic is

where RSS1 is the sum of squared residuals from the first regression, RSS2 is from the second regression and RSS is from the pooled regression.
Wow, thanks guys... I appreciated much...
This is my 100% project testing... thx so much.

Yup, chow test is very acceptable in this case
By the way... how do we get RSS?

Thanks Bro, God bless

5. Originally Posted by neosonic
By the way... how do we get RSS?
It's from the pooled regression, which has all the observations in it.

6. ## Thanks Bro:)

Thanks Bro, it's the final step of my calculation
Just need to confirm, k in this case is 3 rite? (k in chow test formula applied to my model).

Thanks, God bless

7. Originally Posted by neosonic
Just need to confirm, k in this case is 3 rite? (k in chow test formula applied to my model).

Thanks, God bless
Yes and you're welcome!