# The Slope of the Linear Regression Line

**What is Linear Regression?**

Linear regression is a statistical tool commonly used in conjunction with other technical indicators to better identify the underlying trend and most importantly, to evaluate the sustainability of the existing trend.

A linear regression line utilizes the least square method to plot a straight line through prices to shorten the distances between the straight line and the price. The slope of the trendline can be rising, falling, or sideways to flat.

**The Slope of the Linear Regression Line**

The slope of the linear regression line measures the angle of the acceleration of the prevailing linear regression trend based on a defined timeframe (i.e., 20-month, 20-weeks, 20-days, etc.). By taking the current price and the price from x periods ago and drawing a straight line between the two, it can quantify the strength and sustainability of the trend. It is helpful to filter the shorter-term fluctuations during increased market volatility. Although it may resemble the moving average indicator, unlike a moving average – which is often curved and conforms to price over a specified range, a linear regression line is linear. The slope denotes the steepness of the current trend, the strength, and possibly the duration.

**Technical Interpretation**

From the March 2009 market bottom in SPX (666.79), the slope of the monthly linear regression line has accurately forecasted the underlying trends of SPX. When the slope of the monthly linear regression line (grey line) is rising this has led to a sustainable SPX price (black line) rally. On the other hand, when the monthly linear regression line declines it has warned the pace of the SPX rally is beginning to slow and SPX may be vulnerable to a correction or a downturn.

Since July 2010, the slope of the monthly linear regression line in SPX has peaked and bottomed every three to four years. The slope of the linear regression line bottomed during July 2012, April 2016, and May 2019. It peaked during July 2010, June 2014, and February 2018. The next peak in the slope of the regression trend may occur as early as 2022. The next bottom may not occur until 2023-2024.

**SPX Linear Regression Line Confirming Current Structural Bull**

Since March 2020 low, the slope of the SPX linear regression line (20-month period) continues with its uptrend, confirming a structural bull trend in SPX Index. A higher-low and a higher-high on the slope of the monthly linear regression line reaffirms the long-term bullish technical trend.

*The pertinent question is not if the structural trend will continue but at what point does this trend transition toward a more aggressive and parabolic uptrend that ends in a potential bubble?*

The steepness of the slope of the monthly regression trend may give us clues to the transition phase.

For instance, from the March 2009 bottom, a very steep uptrend developed as evidenced by the sharp rise in the slope of the monthly linear regression trend line. The linear regression trend peaked in July 2010, transitioning toward a 2-year correction. Although the SPX price trend continues to climb higher, the pace and the steepness of the rally dramatically slowed. The slope of the monthly regression line peaked again during June 2014, resulting in another correction. SPX price trend entered a sideways trading range for the next 2-years until the linear regression line bottomed in April 2016. The recent February 2018 to May 2019 correction in the slope of the linear regression trend line also coincided with a trading range trend in the SPX Index. Since May 2019 bottom the slope of regression trend has resumed its primary uptrend. It has recorded new all-time highs as the slope has steepened dramatically since March/April 2020. As mentioned before, the steepness of the slope will help determine whether this may lead to the start of the speculative phase to the current structural bull.

**Bottom-up Analysis of Large Market-cap Names in SPX and NDX**

Because the S&P 500 Index (SPX) and the NASDAQ NDX 100 Index (NDX) are both market capitalization-weighted indexes, the largest weightings names can influence the underlining trends. The collective market capitalizations of AAPL (5.91%/11.29% of SPX/NDX), MSFT (5.30%/9.51%), AMZN (3.92%/8.28%), FB (1.96%/3.52%), GOOG (1.84%/3.65%)/GOOGL (1.79%/3.31%), and TSLA (1.60%/4.45%) currently comprised 20.36% of the overall SPX Index and over 44% of the NDX Index.

The primary reason SPX and NDX have outperformed domestic and international equities over the past decade is the market leadership roles of these mega-cap technology names. It is reasonable to expect SPX and NDX will continue to be influenced by these seven stocks.

**The slope of the Linear Regression Trends of the top Seven Large-cap Names**

**AAPL** – It appears AAPL's monthly price trend has become increasingly volatile as it attempts to reaffirm new all-time highs. A new record high would help to reassert its leadership role. In the meantime, the flattening of the monthly linear regression slope hints of further price consolidation is likely over the near-term to medium-term before the start of the next sustainable rally.

**MSFT** – The monthly price trend continues to trend higher to new all-time highs. It appears the slope of the linear regression trend is no longer as steep as before, reaffirming a sustainable MSFT price uptrend and the possible emergence of leadership.

**AMZN** – AMZN's monthly price trend may have peaked during Aug 2020 as a lower-high pattern has developed. The monthly linear regression slope is also beginning to show signs of a near-term peak. However, it may be too early to confirm an intermediate-to-longer term top in AMZN.

**FB** – FB may still be consolidating its recent rally as it has yet to record new all-time highs. However, the monthly linear regression line continues to trend higher, suggesting new price highs are still likely.

**GOOG/GOOGL** – Both technology names have assumed market leadership roles within the large-cap Technology arena. The steepening of the linear regression lines and all-time price highs reinforce leadership roles.

**TSLA** – Although TSLA is not a classic technology name, it has outperformed the Technology sector over the past year. The steepness and the speed of the linear regression line have led to an overbought condition. Despite the recent price correction, the slope of the linear regression line continues to trend higher, suggesting this may be a near-term correction rather than a major top.