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 24. Volume Breakdown
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   9. TLB Oscillator
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   3. Regression Slope
   2. Regression Bands
   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 

Linear Regression Slope

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 13-period linear regression line with 2-standard deviation channels is drawn overlaying the candles in the upper pane. 

 
The Preferences . . . 

. . . more on Preferences 

Linear Regression Slope Preferences

  • Price - Price data to be used in computation.

  • MA Type - Type of pre-smoothing to be applied prior to regression.

  • MA Period - Pre-smoothing 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 N-1 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 N-1 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 pre-smoothing 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 shift-key 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 $10-20 range, or a $200-400 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.