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?
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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 $\displaystyle x_i:$ $\displaystyle \hat\beta_1 = \frac{\sum(x_i - \bar x)y_i}{\sum(x_i - \bar x)^2}$ So...
Is there a way to prove that mathematically?
Originally Posted by statisticsisawesome Is there a way to prove that mathematically? 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?
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