# Thread: Effect on beta one

1. ## 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?

2. Originally Posted by statisticsisawesome
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...

3. Is there a way to prove that mathematically?

4. Originally Posted by statisticsisawesome
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?