# The Linear Regression of Time and Price

Since its start, technical and quantitative analysts have used statistical concepts to the financial market. Some initiatives have been quite successful, while others have proved disastrous. The challenge is to discover a mechanism to recognize pricing patterns without relying on the human mind’s fallibility and prejudice. Linear regression is an effective strategy for investors that is accessible in most charting software.

Linear regression examines two distinct variables to identify a single connection. This refers to the price and time variables in chart analysis. Using charts, investors and traders may see the ups and downs of price displayed horizontally from day to day, minute to minute, or week to week, depending on the time period being analyzed. The many market methods are what make linear regression analysis appealing.

### Key Takeaways

- Linear regression is a valuable technique for technical and quantitative research in financial markets that analyzes two different variables to determine a single connection.
- Plotting stock values along a normal distribution (the bell curve) may help traders identify whether a stock is overbought or oversold.
- A trader may use linear regression to discover crucial price points such as entry, stop-loss, and exit prices.
- The system parameters for linear regression are determined by the price of a stock and the time period, making the procedure generally applicable.

## Bell Curve Basics

The bell curve approach, commonly known as the normal distribution, has been used by statisticians to analyze a specific collection of data points. The dark blue line in Figure 1 is an example of a bell curve. The shape of the different data point occurrences is represented by the bell curve. The majority of the points are generally located towards the center of the bell curve, but with time, the points wander, or diverge from the population. Points that are unusual or uncommon are often way beyond the “normal” population.

Figure 1: The Normal Distribution (Bell Curve)

It is usual practice to average the results to provide a mean score as a reference point. The mean does not always indicate the centre of the data, but rather the average score that includes all outlying data points. After establishing a mean, analysts assess how often price deviates from the mean.

A standard deviation to one side of the average is normally 34% of the data, or 68% of the data points if we look at one positive and one negative standard deviation, as shown by the first dark blue arrow segment in Figure 1. Two standard deviations include about 95% of the data points and are the sum of the three dark blue arrowed regions. The very unusual events, depicted by the light blue arrows, occur near the bell curve’s tails. Because any data point that comes outside of two standard deviations is very unusual, it is often expected that the data points will regress, or move back toward the average.

## Stock Price as a Data Set

Consider flipping the bell curve on its side and applying it to a stock chart. This would enable us to detect when a security has been overbought or oversold and is about to return to the mean. The linear regression research is added to the chart in Figure 2, providing investors with the blue outer channel and the linear regression line running through the centre of our price points. This channel displays the current price trend and offers a mean value to investors. Using variable linear regression, we may produce green channels by setting a narrow channel at one standard deviation, or 68%. While there is no bell curve, we can observe in Figure 1 that pricing now reflects the bell curve’s divisions.

Figure 2: Four-point mean reversion trading illustration. ProphetCharts is the source.

## Trading the Mean Reversion

This setup is simple to trade utilizing four points on the chart, as shown in Figure 2. No. 1 is the starting point. This becomes an entry opportunity only once the price has traded out to the outer blue channel and returned to the one standard deviation line. We don’t just depend on the price being an anomaly since it may get another farther out. Instead, we want the outlier event to occur and the price to return to the norm. The regression is confirmed by a shift back inside the first standard deviation.

No. 2 establishes a stop-loss position in the event that the cause of the outliers continues to have a negative impact on the price. Setting the stop-loss order clearly identifies the risk of the transaction.

For lucrative exits, two price objectives will be established at Nos. 3 and 4. Our initial anticipation with the trade was that it would return to the mean line, and the goal in Figure 2 is to exit half of the position approximately $26.50, or the current mean value. The second objective is based on the premise of a continuing trend, thus another target for the other standard deviation line, or $31.50, will be established at the other end of the channel. This technique defines the potential profit for an investment.

Figure 3: Filling the mean price. Source: ProphetCharts

The price will fluctuate over time, and the linear regression channel will alter as old prices fade and new ones arise. However, goals and stops should stay unchanged until the mean price objective is reached (see Figure 3).A profit has been locked in at this stage, and the stop-loss should be raised to the original entry price. Assuming the market is efficient and liquid, the rest of the deal should be risk-free.

Figure 4: Filling the mean price. Source: ProphetCharts

Remember that a security does not have to close at a certain price in order for your order to be filled; it just needs to reach the price intraday. You may have been filled on the second target in any of the three regions shown in Figure 4.

## The Bottom Line

Technicians and quant traders often use one strategy for a certain asset or stock only to discover that the same parameters do not work on other securities or equities. The beauty of linear regression is that the system parameters are determined by the security’s price and time period. Use these tools and the criteria outlined in this article on a variety of securities and time periods, and you’ll be astonished at how universal they are.

Investopedia does not provide tax, investment, or financial advice. The material is offered without regard for any individual investor’s investing goals, risk tolerance, or financial circumstances, and may not be appropriate for all investors. Investing entails risk, including the possibility of losing money.

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