Why do we want to minimize the square difference from a point to the line instea

Question

Why do we want to minimize the square difference from a point to the line instead of the actual difference when using the least squares method? (answer has more than one option)

(answer has more than one option)

Why do we want to minimize the square difference from a point to the line instead of the actual difference when using the least squares method? It's more accurate to minimize the larger value We could minimize the actual difference as well We want to ensure the value is positive because it is a distance We want to ensure that far away points are weighted more heavily than nearby points

Explanation / Answer

Firstly, the most basic reason for using least squares regression is that we want the error term to be positive. If we do not force the error to become positive and instead use the actual error values, then some error (differences) will be positive and some will be negative. So the overall error might be smaller than it actually is.

Also using the sqaures ensures that points which lie far away from the lines are weighted heavily, which means that it's better to have more points at smaller distances than to have less points at larger distances.

So the correct options are the last two options.

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