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Linear Modelinghard
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Given a dataset of size nnn, if the variance of the OLS slope estimator β^1\hat{\beta}_1β^​1​ is Var(β^1)=σ2∑(Xi−Xˉ)2Var(\hat{\beta}_1) = \frac{\sigma^2}{\sum (X_i - \bar{X})^2}Var(β^​1​)=∑(Xi​−Xˉ)2σ2​, what is the effect of increasing the dispersion of XXX values, ∑(Xi−Xˉ)2\sum (X_i - \bar{X})^2∑(Xi​−Xˉ)2, while keeping σ2\sigma^2σ2 constant?