V.9:12 (486-487): Fitting a Trendline by Least Squares by Arthur A. Merrill, C.M.T.
Product Description
Fitting A Trendline By Least Squares
by Arthur A. Merrill, C.M.T.
Usually, trendlines are drawn through tops or bottoms. They are also drawn through the center of prices by a lagged moving average or by eye (Figure 1). A straight line through the center of a price channel, if the scale is logarithmic, will give you the percentage growth or decline rate.
If the straight line is drawn by eye, it is subject to debate. This question can be resolved by a mathematically calculated line called "least squares" (Figure 2). The deviations of the points from the line are marked A, B, C, D and E in Figure 2. The line produced by the least squares calculation reduces the sum of the squares of these deviations to a minimum, hence the name "least squares."
The formula for a straight line is:
Y = a + bX
where X is the value of the X (horizontal) axis. When X is zero, Y equals a, which is called the Y intercept (Figure 3). The distance from this level up to the line is bX, which is directly proportional to b, the slope of the line.
Usually, trendlines are drawn through tops or bottoms. They are also drawn through the center of prices by a lagged moving average or by eye (Figure 1). A straight line through the center of a price channel, if the scale is logarithmic, will give you the percentage growth or decline rate.
If the straight line is drawn by eye, it is subject to debate. This question can be resolved by a mathematically calculated line called "least squares" (Figure 2). The deviations of the points from the line are marked A, B, C, D and E in Figure 2. The line produced by the least squares calculation reduces the sum of the squares of these deviations to a minimum, hence the name "least squares."
The formula for a straight line is:
Y = a + bX
where X is the value of the X (horizontal) axis. When X is zero, Y equals a, which is called the Y intercept (Figure 3). The distance from this level up to the line is bX, which is directly proportional to b, the slope of the line.
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