Linear Regression Trend Line

The linear regression is the purest form of trendline we can draw. We say “pure” because it is an arithmetic calculation that entails no judgment by the person preparing the chart. A linear regression is the line that minimizes the distance between itself and a series of prices, in this case the close. Anyone drawing a linreg off a high or a low will get the same line.

There’s the clue that that a linear regression line involves some judgment—the starting and ending points. You can draw different linregs on any chart depending on your starting and ending point. Mathematically, they are all “scientifically correct” but of course to the trader, they have very different meanings. See the figure below.

A linreg drawn arbitrarily from the left hand side of the chart tot the last data point is sloping a little upward. A linreg drawn from the high to the next obvious high slopes downward. A linreg drawn from the lowest low to the most recent highest high is a steep uptrend, almost exactly 45 degrees, in fact.

No one linreg is correct. They are all correct. We find in practice, however, that it’s most useful to draw linregs from an obvious low to a succession of highs, or from low to low, or the opposite for a downtrend.

Going back to the question of slope, we have the tools to measure slope, but that only adds a veneer of scientific respectability to what is still a subjective representation of trendedness. In the figure below, we drew a series of linear regressions from the bar that has the first lower high in a series of higher highs. You can see the trend losing slope with every passing day until the linreg line slopes downward.

This is useful to identify that the pullback in occurring, but laborious, and only makes the same point that we can see from plain old bar-reading, that despite the price making higher highs, it is also making lower closes and with the close under the open. Those two bar characteristics more than offset the higher highs.

The next figure shows a 5-day measure of slope itself in the top window. Clearly the price series was already losing slope before it peaked. This is only a little useful (as a warning to tighten stops) but doesn’t give a buy/sell signal itself. When the slope indicator spikes up, then you have confirmation of what the upside breakout bar is telling you, higher high and close at high (buy).

Another way of depicting the shift in slope and thus trendedness is with an indicator (brilliantly called the linear regression indicator in Metastock). This is a moving average of several days worth of linreg readings, in this case 5 days. On the next figure you can see that the indicator goes flat on that first day with a lower high, but then tracks the prices. The usefulness of this indicator lies in accepting the assumption that when the close is under the indicator, the price will have a tendency to rise to the indicator, and vice versa. If the close is under the indicator, it will drag the indicator down tomorrow. You can use the indicator to help set stops and targets.

If linregs are useful to keep your head screwed on straight, linreg channels are even better.