Unformatted text preview: m is to ﬁnd a line
which is in some sense ‘close’ to all the points, even though it may go through none of them. The
way we measure ‘closeness’ in this case is to ﬁnd the total squared error between the data points
1
and the line. Consider our three data points and the line y = 2 x + 1 . For each of our data points,
2
we ﬁnd the vertical distance between each data point and the line. To accomplish this, we need to
ﬁnd a point on the line directly above or below each data point  in other words, point on the line
with the same xcoordinate as our data point. For example, to ﬁnd the point on the line directly
1
below (1, 2), we plug x = 1 into y = 1 x + 2 and we get the point (1, 1). Similarly, we get (3, 1) to
2
5
correspond to (3, 2) and 4, 2 for (4, 3). 4 3 2 1 1 2 3 4 We ﬁnd the total squared error E by taking the sum of the squares of the diﬀerences of the y coordinates of each data point and its corresponding point on the line. For the data and line above
2
9
E = (2 − 1)2 + (1 − 2)2 + 3 − 5 = 4...
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 Fall '13
 Wong
 Algebra, Trigonometry, Cartesian Coordinate System, The Land, The Waves, René Descartes, Euclidean geometry

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