In a simple linear regression $Y = \beta_0 + \beta_1 X + \epsilon$, if we transform the predictor $X$ to $X^* = aX + b$ ($a > 0$) and the response $Y$ to $Y^* = cY + d$ ($c > 0$), what is the relationship between the new slope $\beta_1^*$ and the original slope $\beta_1$?