Earlier quoted context omitted.
Squares are preferred because that is the same as minimizing Euclidean Distance, which is defined as sqrt((x2-x1)^2).
sqrt((x2-x1)^2) == x2-x1 I think you meant sqrt(x^2+y^2)
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Why does a least squares fit appear to have a bias when applied to simple data?
81–84 of 84 posts
Re: Why does a least squares fit appear to have a bias when applied to simple data?
#82The least squares and pca minimize different loss functions. One is sum of squares of vertical(y) distances, another is is sum of closest distances to the line. That introduces the differences.
"...sum of squared distances to the line" would be a better description. But it also depends entirely on how covariance is estimated
Re: Why does a least squares fit appear to have a bias when applied to simple data?
#83I think the linear least squares is like a shear, whereas the eigenvector is a rotation.
Shear with one component always in the y direction
Re: Why does a least squares fit appear to have a bias when applied to simple data?
#84[dead]