In a regression study, the original model is $\hat{y} = \beta_0 + \beta_1 x$ with residuals $e_i = y_i - \hat{y}_i$. If we create a new response variable $y'_i = y_i + 15$ for all observations and fit a new regression model $\hat{y}' = \beta'_0 + \beta'_1 x$ with residuals $e'_i$, how do the new residuals $e'_i$ compare to the original residuals $e_i$?