S statisticsisawesome May 2010 4 0 May 10, 2010 #1 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?

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?

Anonymous1 Nov 2009 517 130 Big Red, NY May 10, 2010 #2 statisticsisawesome said: 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? Click to expand... Well the estimator is dependent on \(\displaystyle x_i:\) \(\displaystyle \hat\beta_1 = \frac{\sum(x_i - \bar x)y_i}{\sum(x_i - \bar x)^2}\) So...

statisticsisawesome said: 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? Click to expand... Well the estimator is dependent on \(\displaystyle x_i:\) \(\displaystyle \hat\beta_1 = \frac{\sum(x_i - \bar x)y_i}{\sum(x_i - \bar x)^2}\) So...

Anonymous1 Nov 2009 517 130 Big Red, NY May 10, 2010 #4 statisticsisawesome said: Is there a way to prove that mathematically? Click to expand... Unless I am mistaken, this is trivially true since: \(\displaystyle y = \beta_0 + \beta_1 x \implies \beta_1 = \frac{y-\beta_0}{x}\) Can you think of a situation in which \(\displaystyle x\) would change and \(\displaystyle \beta_1\) wouldn't?

statisticsisawesome said: Is there a way to prove that mathematically? Click to expand... Unless I am mistaken, this is trivially true since: \(\displaystyle y = \beta_0 + \beta_1 x \implies \beta_1 = \frac{y-\beta_0}{x}\) Can you think of a situation in which \(\displaystyle x\) would change and \(\displaystyle \beta_1\) wouldn't?