If a simple linear regression model $Y = \beta_0 + \beta_1 X + \epsilon$ is fitted, and we transform the predictor $X$ to $X^* = aX + b$ ($a > 0$) and the response $Y$ to $Y^* = cY + d$ ($c > 0$), how does the new slope $\beta_1^*$ of the model $Y^* = \beta_0^* + \beta_1^* X^* + \epsilon^*$ relate to the original slope $\beta_1$?