Name, Sometimes Called:
Linear Regression Slope
Brief Description:
The slope of a linear regression trend line, fitted
using the method of least squares, is the Linear Regression Slope.
The slope shows how prices have changed per unit of time.
Definitions, Formulas:
The Linear Regression Slope is the slope of a linear
regression trend line, plotted using the least
squares fit method. The slope shows how prices have changed
per unit of time.
The formula for any straight line is
y = a + bx
where
x = the current time period
n = the total number of time periods. We use n
= 14. Each summation is over the entire 14 periods.
The Linear Regression Slope is the quantity b in the
formulas above.
Positive Development Calculation:
The Linear Regression Slope and the R-squared TAI
are used together to compute a single positive development. Both
of the following conditions must hold:
(1) The linear regression slope must cross above zero
and
(2) r squared (r2) must equal
or exceed 0.27. For more on r2,
see the R-squared technical analysis
indicator.
Similarly, the Linear Regression Slope and the R-squared TAI are
used to determine when a development is no longer positive. If either
of the following conditions holds, then a development is no longer
positive:
(1) The linear regression slope crosses below zero
or
(2) r squared (r2) is less
than 0.27. For more on r2, see
the R-squared technical analysis indicator.
To reduce the potential of false positives produced by the traditional
specifications, we require that the 3-day price slope also trend
upward before a development is considered to be a positive development.
If this TAI is still positive tomorrow, it will no longer be new,
but will be a cumulative positive development (CPD).
If this TAI was a new positive development (NPD)
yesterday, and is still positive today, then it becomes a cumulative
positive development (CPD).
History:
Tushar Chande, known for developing the Chande
Momentum Oscillator, recommends using the Linear Regression
Slope with r-squared; we do so
here. The slope gives the trend’s direction and degree of tilt,
while r2 gives the trend’s strength.
There are many ways to use the linear regression outputs of r-squared
and Slope in trading systems. For more detailed coverage, see the
book The New Technical Trader by Tushar S. Chande and Stanley Kroll
(John Wiley & Sons, Inc., 1994).
The chart below shows the Linear Regression Slope indicator in
use with r-squared. During the period shown there were several new
positive developments, but we’ve highlighted only two. First, locate
the green-A. It indicates a point where the linear regression slope
(LRS) crossed over the zero point. This is, by itself, positive.
If you trace down you will see that r-squared was still under 0.27.
Both indicators have to be positive before there is a new positive
development (NPD). The vertical green bar shows where r-squared
crossed over 0.27 and LRS was still positive.
A few days later r-squared dipped below 0.27 and came back up
over it. This is a whipsaw. Had you exited your position and gotten
back in when r-squared crossed back over 0.27 you’d still be in
positive territory but with an increase in your commission expenses.
The red vertical line indicates where these two TAI no longer
indicate a positive development (NLPD). Or does it? Find the red-B.
Just a little before the day that LRS crossed under zero you can
see that r-squared dropped below 0.27 again. Remember, for this
technical analysis indicator BOTH have to be positive. That vertical
red line should be a bit earlier.
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