A valid mathematical regression assumes that most standardized residuals would ideally fall within ±2 standard deviations due to the empirical rule, and the sum of the residuals is typically zero because they are mean-centered. They should also roughly follow a normal distribution. However, stating that 'all of the standardized residuals will be within ±3 Standard Deviations' is incorrect because a small number of residuals could still fall outside this range due to natural variation and outliers.