# Thread: Change regression model ($x^*_i = x_i -10$)

1. ## Change regression model ($x^*_i = x_i -10$)

Hi there.
I'm solving an exercise on multiple linear regression. Near the end I will be asked for the same data as the previous model, it is the maximum likelihood estimates.

The previous model:
I have the matrix and the matrix and the model is:

Now I have:

To transform the model can I decrease the Matrix data for 10?

The same thing can I make it also for the matrix ?
I have many doubts.
Publishing the text so it is more understandable.

Consider the regression model linear:

with independent and identically distributed random variables and x_i, i = 1, ..., 0 constant fix.

The only data I have are these:

https://s32.postimg.org/o20r1i5et/Immagine.png

I have to rewrite the whole thing ... I tried so:

Now I have to calculate the inverse? I'm following proper solution?

Excuse me , but does not write well in English
Thanks.

2. ## Re: Change regression model ($x^*_i = x_i -10$)

Are you just trying to find the estimates of the parameters for the model using the transformed data? I would just figure out what the new parameters are in terms of the old parameters and then use the invariance property of MLEs to get the estimates.

3. ## Re: Change regression model ($x^*_i = x_i -10$)

The question is:
Consider , for the same data , the model

with , independent random variables and identical cally distributed N ( 0 , σ2 ) . It is the maximum likelihood estimates γ0 , γ1 , γ2.

4. ## Re: Change regression model ($x^*_i = x_i -10$)

Originally Posted by Dason
and then use the invariance property of MLEs to get the estimates.

In this case the estimate remains the same?

ecc..
I do not have a real transformation of the initial parameters , but only a "data processing " . What I did is right ?

5. ## Re: Change regression model ($x^*_i = x_i -10$)

Consider just a simple linear regression and the transformation you had. Our original model would be

With our model is

Replace with our definition of to get

Expand and rearrange and we have

Now since we already know

we can now say that

and

So using this (since we're assuming we know the values for [math]\beta_0[math] and we can solve for the new coefficients. It's the process with your problem but since you have a quadratic the equations take a little bit more work.

6. ## Re: Change regression model ($x^*_i = x_i -10$)

Wow!

Thank you so much.
I try now to do the exercise right!

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