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Linear Modelinghard
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If two variables X1X_1X1​ and X2X_2X2​ are perfectly uncorrelated (Corr(X1,X2)=0Corr(X_1, X_2) = 0Corr(X1​,X2​)=0), what happens to the estimate of β1\beta_1β1​ when adding X2X_2X2​ to a simple regression Y=β0+β1X1+ϵY = \beta_0 + \beta_1 X_1 + \epsilonY=β0​+β1​X1​+ϵ?