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Linear Modelinghard
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In a simple linear regression model Y=β0+β1X+ϵY = \beta_0 + \beta_1 X + \epsilonY=β0​+β1​X+ϵ, if we transform the predictor XXX to X∗=aX+bX^* = aX + bX∗=aX+b (a>0a > 0a>0) and the response YYY to Y∗=cY+dY^* = cY + dY∗=cY+d (c>0c > 0c>0), how does the new slope β1∗\beta_1^*β1∗​ of the model Y∗=β0∗+β1∗X∗+ϵ∗Y^* = \beta_0^* + \beta_1^* X^* + \epsilon^*Y∗=β0∗​+β1∗​X∗+ϵ∗ relate to the original slope β1\beta_1β1​?