
Most simple regression models assume that the X variable is fixed by the experimenter and has no error associated with it, only the Y variable has random error, so all residual errors are vertical deviation from the trend line. As a result, the line is tilted to be ‘flatter’ than the main axis of the data.
In reality, the X variable often has just as much error/uncertainty as the Y variable, and the residuals should be perpendicular to the trend line.
One regression that allows for that is Major Axis Regression.
Another is to just take the main axis from PCA.















We moved to a neighbourhood with few cars and a nice park, but there were almost never kids in the park… until they built a new set of play equipment. The influx of kids checking it out created a critical mass that lasted.
For some reason, seeing all the other kids there made some parents feel safer letting their kids play there unsupervised, even after dark.