The most common method for fitting a regression line is the method of least-squares. This method calculates the best-fitting line for the observed data by minimizing the sum of the squares of the vertical deviations from each data point to the line. If a point lies on the fitted line exactly, then its vertical deviation is 0. Since the deviations are squared first and then summed, negative and positive do not cancel each other out. The closer the line calculated sits to the data points, the smaller the sum or "error" of a line.

If you think of this trendline as describing an "equilibrium" price, then any moves above or below the trendline indicates overzealous buyers or sellers. Some ways to use a linear regression line are:

• Use the line to forecast prices. The forecast will simply be an extension of the line, so trade in the direction of the line. This can give good results when viewed on a long enough time frame. Use caution as there still can be significant drawdowns as prices fluctuate above and below the line.

• Use the line as a basis and draw two parallel lines above and below it to form a channel. See the entries for Linear Regression Channel for more detail.

Parallel and equidistant lines are drawn two standard deviations above and below a Linear Regression trendline. The distance between the channel lines and the regression line is the greatest distance that any one closing price is from the regression line. Regression Channels contain price movement, the bottom channel line provides support and the top channel line provides resistance. Prices may extend outside of the channel for a short period of time but when prices remain outside the channel for a longer period of time, a reversal in trend may be indicated.

A Linear Regression trendline shows where equilibrium exists but Linear Regression Channels show the range prices can be expected to deviate from a trendline.

Unlike the straight Linear Regression Trendline, the Linear Regression indicator plots the ending values of multiple Linear Regression trendlines. Any point along the Linear Regression Indicator will be equal to the ending value of a Linear Regression Trendline, but the result looks more like a Moving Average.

Unlike a Moving Average, the Linear Regression Indicator does not exhibit as much delay. As the Linear Regression Indicator is fitting a line to the data points rather than simply averaging them, the Linear Regression line becomes more responsive to changes in prices. The Linear Regression Indicator can be thought of as a forecast of the tomorrow's price plotted today.

When prices are persistently higher or lower than the forecasted price, expect them to quickly return to more realistic levels. The Linear Regression Indicator shows where prices should be trading on a statistical basis and any excessive deviation from the regression line is likely to be short-lived.

A typical Linear Regression Indicator will hug the price well, reducing lag time by turning two bars earlier than a normal simple moving average and one sooner than an exponential moving average.

A Linear Regression Reversal differs from the Linear Regression Indicator in that it is a binary indicator that displays +1 when the price direction is up and a -1 when the price direction is down. The movement between +1 and -1 is an indicative of price reversal.

This indicator can provide both long and short term signals. One may view a +1 as a long position and a -1 would be taken as a short position. These entries occur only when the next price bars broke or closed above the high or lower than the high (respectively).

It is a variation on a theme, buying on dips and selling in rallies.

Disadvantages to this indicator are its tendency to reverse more often in sideways trading ranges or with minor corrections in a trend, though it can be advantageous in short term price swings.

Further information on Linear Regression Reversal can be found in the December 2003 issue of Technical Analysis of Stocks and Commodities

http://www.traders.com

As the Slope of a trend first becomes significantly positive, open a long position. Either sell or open a short position as the Slope becomes significantly negative.

For information on more ways to use the linear regression outputs of Slope and combining them with r-squared values it may be helpful to refer to The New Technical Trader by Tushar Chande and Stanley Kroll..

Extend the resulting line and use it to predict future trends. Remember there still can be significant shifts as prices will continue to fluctuate above and below the line.