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Slope
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1.
Linear Regression

Investor/RT Tour
( more on Technical
Indicators )
Linear Regression Slope
The Formula
. . . 
. . .more
on Formulas 
Slope =
Change in Price / Bar
Normalized Slope = % Change in Price / Bar
See Also...
...Linear Regression
...Linear Regression
Forecast / Bands
...Linear Regression
Acceleration


The
Presentation . . . 
. . . more
on Charts 
Above is a Daily Candlestick Chart of an Microsoft
Corp (MSFT). The histogram in the lower window pane represents
the normalized slope using the preferences specified below. A
13period linear regression line with 2standard deviation channels
is drawn overlaying the candles in the upper pane. 

The
Preferences . . . 
. . . more
on Preferences 


Price  Price
data to be used in computation.

MA Type
 Type of presmoothing to be applied prior to regression.

MA Period  Presmoothing
period to be used prior to regression.

Regression Period
 Number of bars to be used in computing the regression
line. If the period is N, then the resulting slope will be
the slope of the regression line involving the current bar and
the previous N1 bars.

x 100 / Price
(Normalize)  Option to normalize the resulting
slope value. More details on normalization can be found in
the description below.

Histogram Color  Colors
of the resulting histogram in chart.


The
Description . . . 
The Linear Regression Slope indicator provides the slope at each bar of theoretical regression lines which
involve that bar and the previous N1 bars (N being the regression
period).
First, the data, based on the price
selected, is smoothed using the moving average period and type
(specify a period of 1 if no presmoothing is desired). The resulting data is then used to form regression lines
ending at each bar, using the regression period specified. The
slope of each bars regression line is the recorded as the linear
regression slope value for that bar. For instance, assume a MA
period of 1 and a Regression Period of 13. The raw closing price would be
used and no smoothing performed since the MA period is 1. For each bar, we would
then use the price data for that bar and the previous 12 bars (13 total) to form a regression line. The slope of that
regression line is then recorded as the indicator value for that
bar. The same calculation is done for each bar and then
plotted in the chart. The slope can then be optionally
normalized. Normalization is discussed in further detail
below.
The raw slope essentially gives us the change in price per bar of
the regression (best fit) line. If the slope is 1, then the
regression line is rising at a rate of $1 per bar. Similarly,
a slope of 0.25 would indicator that the line that best fits the
last N bars of data is falling at the rate of $0.25 per bar.
If the "x 100 / Price (Normalize)" options is checked,
then the resulting value will be divided by 100, and then multiplied
by the price of that bar. This normalizes the data for the
sake of comparison among instruments that trade in different price
ranges. If you are interested in using this study to compare
slopes between instruments, it's important that this normalizing
option be used. The difference between the normalized slope
and the raw slope is similar to the difference between percent
change (normalized), and change(unnormalized). If you're
comparing two instruments, one that's trading at 200 and another
that's trading at 10, then it's not fair to compare the change in
price, although the normalized value of percent change does give us
a fair basis of comparison.
The normalized slope value essentially gives us the percent
change is price per bar of the regression (best fit) line. If
the normalized slope is 0.10, then the regression line is rising at
a rate of 0.10% per bar. Similarly, a normalized slope of
0.25 would indicator that the line that best fits the last N bars
of data is falling at the rate o 0.25% per bar.
The resulting slope is drawn as a histogram that oscillates about
0. A reference line is drawn at the 0 level. A slope
that is rising (greater than previous value of slope) is drawn in
the up color, while a slope that is falling (lower than previous
value of slope) is drawn in the down (dn) color.

Keyboard
Adjustment . . . 
The periods involved in the
LRS indicator
can be adjusted directly from they keyboard without opening up the
preference window. First, select the indicator, then use the
up and down arrow keys to adjust the regression period up or down by
1. To adjust the MA period, hold down the shiftkey while
hitting the up and down arrows. For more information on technical
indicator adjustment, click here.

RTL
Token . . . LRS ( more
) 
The RTL Token for Linear
Regression Slope is LRS. If the normalize value is required,
then check the "x 100 / Price (Normalize)" checkbox.
This option is recommended for doing comparisons among indicators
that don't trade in the same range. See above for more
details. If the normalize checkbox is unchecked, then the
result will be the raw slope value (change / bar) of the regression
lines. If it is checked, the result will be the normalized
slope, or % change / bar, of the regression lines.

User
Strategies . . . 


Linn Software  Chad Payne 
02/25/02 
I have added a Linear
Regression Oscillator to I/RT. This oscillator represents the number
of standard deviations of current price from the linear regression
line. A value of 2 means that price is currently 2 standard
deviations above the linear regression line (using the regression
period specified...ending on that bar). A value of 1.5 means price
is currently 1 1/2 standard deviations below the regression line.
This options has been added as a "Linear Regression
Oscillator" checkbox to the LRF indicator. When drawn,
reference lines are automatically drawn at 2, 1, 0, 1, and 2
standard deviations....
This, along with normalized linear regression slope, provide two
informative and comparative pieces of data regarding regression
analysis....
Normalized slope gives a good indication of direction of the trend (a positive value indicates an uptrend, while a negative values indicates a downtrend)... It also tells how steep, or powerful, the trend is, based on it's value from 0.
The Linear Regression Oscillator tells how far the current price has
deviated from the regression trendline, in units of standard
deviations. How far the price has deviated from the general trend
established by the regression analysis (using period specified)....
A powerful aspect of these indicators is that it is logical to compare both these values across instruments that don't necessarily trade in the same range. Their resulting values are based on the same scale regardless of whether they trade in a $1020 range, or a $200400 range. An oscillator value of +2 standard deviations is just as significant for a stock that's trading at $10 as it is for on that's trading at $350. A normalized slope of 0.25 (% change per bar) is just as significant for a $5 stock as it is for a $1500 index.
In version 5.4.4, both these values will be available in RTL... The oscillator will be built into LRF, while the normalized option will be built into LRS.
I would love to hear any ideas on how these two can be used together to find trading opportunities.....
When a stock is trading at 2 standard deviations above it's regression trendline, do you consider it oversold? What if the trendlines slope is strongly positive?
Or what if the trendlines slope is strongly negative....but the current price has broken to 2 standard deviations above the regression line? Buying opportunity?
Would love to hear some of your ideas.... How would we use these two tokens together....
Please send any comments to support@linnsoft.com
. I'll post any relative comments here.


