. . .more on Formulas 

Regression Band = Reg(SmoothPrice , X) + Slope * Y
where
   Z = MA Period
   X = Regression Period
   Y = Forecast Period (optional - can be 0)
   Slope = Slope of regression line

Upper Band = Regression Band + StdDev(SmoothPrice, X) * N
where
   N = Standard Deviation(s)
   X = Regression Period

Lower Band = Regression Band - StdDev(SmoothPrice, X) * N
where
   N = Standard Deviation(s)
   X = Regression Period

Linear Regression Oscillator
     = (Price - Regression Band) / StdDev(SmoothPrice, X)
where
   X = Regression Period

See Also...
   ...Linear Regression
   ...Linear Regression Slope
   ...Linear Regression Acceleration

. . . more on Charts 

Above is a Daily Candlestick Chart of an Intel Corporation (INTC).  The Linear Regression Forecast (LRF) is drawn in black, with an upper 2 standard deviation band drawn in blue, and a lower band drawn in red.

. . . more on Preferences 

• Price - Price data to be used in computation.

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

• MA Period - Smoothing period to be used prior to regression.

• Regression Period - Number of bars to be used in computing the regression line.

• Forecast Period - The middle regression band can optionally be forecast into the future by a user specified number of bars.  If the forecast period is 0, no forecasting will occur.  If the forecast period is greater than 0, then the linear regression line (computed using the regression line) is projected forward to determine the regression value for that bar.

• Regression Band - Middle band, determined by computing a regression line using current bar and previous X-1 bars (X being regression period), and projecting that line forward by Y bars (Y being forecast period), and then taking the endpoint of the line as the value.

• Upper Band - Standard deviation band drawn above the regression line.  Uses the number of standard deviations specified below.  The standard deviation is computed over the regression period specified.

• Lower Band - Standard deviation band below above the regression line.  Uses the number of standard deviations specified below.  The standard deviation is computed over the regression period specified.

• Standard Deviation(s) - How many standard deviations from the middle regression band that the upper and lower bands will be drawn.

• Linear Regression Oscillator - The Linear Regression Oscillator represents the number of standard deviations of current price from the linear regression line.  A more complete explanation can be found in the description below.

The name of this indicator is somewhat misleading, as forecasting is optional, and only a small part of what this indicator can do.  In its most basic form, with no smoothing (ma period of 1) and no forecasting (forecast period of 0), LRF simply gives the ending point of linear regression lines that ending at each bar, and using the regression period provide.  This option alone provides a nice moving average substitute, and is actually identical to the Least Square moving average type available in Investor/RT (add both to your chart and see).

A smoothing (MA) period, caused the data to be pre-smoothed, prior to performing any regression analysis or forecasting.  A forecast period takes the linear regression line ending at each point, and projects it forward X number of bars, X being the forecast period.  This projected value is then used as the LRF value for that bar.

The bands that are drawn use a standard deviation that changes over time.  The standard deviations are computed just as they are for the Linear Regression study.  The standard deviation multiplier specified in the preferences is multiplied by the standard deviation value to determine how far the bands will be drawn from the base line.

The Linear Regression 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.  It is recommended that the Linear Regression Oscillator be drawn in a separate window pane from price data.  The Linear Regression Oscillator tells how far the current price has deviated from the regression trendline, in units of standard deviations, or how far the price has deviated from the general trend established by the regression analysis (using period specified).
 

All three line values can be accessed in RTL using the LRF token.  To access the middle regression band, check only the "Regression Band" checkbox (uncheck Upper and Lower Band).  To access the upper band, check only the "Upper Band" checkbox.  To access the lower band, check only the "Lower Band" checkbox.