The residuals, unlike the errors, "do not all have the same variance:" the variance decreases as the corresponding "x"-value gets farther from the average "x"-value. This is not a feature of the data itself, but of the regression better fitting values at the ends of the domain. It is also reflected in the influence functions of various data points on the regression coefficients: endpoints have more influence. This can also be seen because the residuals at endpoints depend greatly on the slope of a fitted line, while the residuals at the middle are relatively insensitive to the slope. The fact that "the variances of the residuals differ," even though "the variances of the true errors are all equal" to each other, is the "principal reason" for the need for studentization.