Please anyone help due monday

May 2016
26
0
sydney
Hey guys, Im doing a mathematics degree and have this stats subject and honestly have no clue whatsoever on how to do anything in this class. I have looked over all my lectures and pracs and we have an assessment and the content is not related to anything.

If anyone could help me in anyway, by answering or even just guiding as to where I could find some sort of help to help me figure out the question or even just how to start it I will be very grateful.

Q)

Consider the simple linear regression model of y on x,y = β0 + β1x + ε where ε ∼ N(0, σ2)

Define z = x − x¯, i.e., x centered around the mean.

(a) Show that the regression of y on z has intercept equal to y¯.

(b) Show that the slope from the regression of y on z is the same as that fromthe regression of y on x.
 

romsek

MHF Helper
Nov 2013
6,836
3,079
California
Hey guys, Im doing a mathematics degree and have this stats subject and honestly have no clue whatsoever on how to do anything in this class. I have looked over all my lectures and pracs and we have an assessment and the content is not related to anything.

If anyone could help me in anyway, by answering or even just guiding as to where I could find some sort of help to help me figure out the question or even just how to start it I will be very grateful.

Q)

Consider the simple linear regression model of y on x,y = β0 + β1x + ε where ε ∼ N(0, σ2)

Define z = x − x¯, i.e., x centered around the mean.

(a) Show that the regression of y on z has intercept equal to y¯.

(b) Show that the slope from the regression of y on z is the same as that fromthe regression of y on x.
a) plug $x=z+\bar{x}$ into your regression for $y$ and solve for the intercept

b) same thing but solve for the slope
 
May 2016
26
0
sydney
Thanks so much for helping, could u just elaborate abit more i am so bad at this subject
 

romsek

MHF Helper
Nov 2013
6,836
3,079
California
Thanks so much for helping, could u just elaborate abit more i am so bad at this subject
you're studying for a mathematics degree but can't do a bit of algebra?
 
May 2016
26
0
sydney
Lol its only stats i get lost, so y = β0 + β1(z+x¯ ) + ε , then which parts the intercept is it β0 ? and the slope is β1 ? Or is it just when x=0 the y int.
 
Last edited:

romsek

MHF Helper
Nov 2013
6,836
3,079
California
Lol its only stats i get lost, so y = β0 + β1(z+x¯ ) + ε , then which parts the intercept is it β0 ? and the slope is β1 ? Or is it just when x=0 the y int.
dude...

$y=\beta_0 + \beta_1 x + \epsilon$

$\bar{y} = \beta_0 + \beta_1 \bar{x} + \bar{\epsilon} = \beta_0 + \beta_1 \bar{x}$

$z=x-\bar{x}$

$x = z+\bar{x}$

plug into equation for $y$

$y=\beta_0 + \beta_1 (z+\bar{x}) + \epsilon$

$y = \beta_1 z + (\beta_0 + \beta_1 \bar{x}) + \epsilon = m z + b + \epsilon$

This is the regression of $y$ on $z$

$m = \beta_1$ is the slope

$b = \beta_0 + \beta_1 \bar{x}$ is the intercept

note that $b=\bar{y}$ as calculated up at the top.

Similarly $m=\beta_1$ which is the same slope of the original regression of $y$ on $x$
 
Last edited:
May 2016
26
0
sydney
LOOL you are a legend man thanks alot saved my life.