Results 1 to 4 of 4

Math Help - Effect on beta one

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    4

    Effect on beta one

    In linear regression, If the value of the x-variable changes, how do I provide a proof that the value of beta one will be affected?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    Quote Originally Posted by statisticsisawesome View Post
    In linear regression, If the value of the x-variable changes, how do I provide a proof that the value of beta one will be affected?
    Well the estimator is dependent on x_i:

    \hat\beta_1 = \frac{\sum(x_i - \bar x)y_i}{\sum(x_i - \bar x)^2}

    So...
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    May 2010
    Posts
    4
    Is there a way to prove that mathematically?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member Anonymous1's Avatar
    Joined
    Nov 2009
    From
    Big Red, NY
    Posts
    517
    Thanks
    1
    Quote Originally Posted by statisticsisawesome View Post
    Is there a way to prove that mathematically?
    Unless I am mistaken, this is trivially true since:

    y = \beta_0 + \beta_1 x \implies \beta_1 = \frac{y-\beta_0}{x}

    Can you think of a situation in which x would change and \beta_1 wouldn't?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Effect on beta one by changing x variables
    Posted in the Advanced Statistics Forum
    Replies: 10
    Last Post: May 17th 2011, 10:31 AM
  2. Effect of singuar
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: October 29th 2010, 06:41 AM
  3. Effect of beat
    Posted in the Differential Equations Forum
    Replies: 0
    Last Post: December 23rd 2009, 08:56 AM
  4. y'' + by' + 4y = 0; what effect does changing b have?
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: March 26th 2009, 10:12 PM
  5. derive cos(alpha+beta) sin(alpha+beta)?
    Posted in the Trigonometry Forum
    Replies: 3
    Last Post: December 7th 2008, 04:27 PM

Search Tags


/mathhelpforum @mathhelpforum