Line Minimizing
What is the minimum distance from the origin to the line y=4x+7?
You have to minimize the distance but I do not know how
The minimum distance will be the line from the origin that is perpendicular to y = 4x + 7.
If it is perpendicular, and passing through the origin, we know that the slope of this intersecting line with be - 1/4.
So the equation of the intersecting line will be y = -1/4x.
Solve for the point of intersection:
-1/4x = 4x+ 7
so x = -28/17.
This means that y = 7/17.
So the coordinate of intersection is (-28/17, 7/17).
Use the pythagorus theorem to solve for the length from the origin to this point.
Proof (Part 1) Minimizing Squared Error to Regression Line
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