Linear regression is a statistical tool that has a wide variety of uses. In stock trading, linear regression allows you to quantify the trend of a particular stock, a group of stocks or a broad-based index. Linear regression is also highly useful in assessing the risk profile of stocks.

## Definition

Linear regression is a powerful tool that helps you predict one parameter by plugging the value of another into a simple formula. The parameter that you know is referred to as the independent variable, while the one you can calculate by using linear regression is known as the dependent variable. This is how a regression equation typically looks: Dependent Variable = A + X*Independent Variable. If you are using this equation to estimate the weight of your 2-month-old baby, the dependent variable could be weight and the independent variable could be days since birth. A is the value of the variable when the independent variable equals zero. In the case of the baby's weight, A equals weight at birth. X is referred to as the slope and is the rate at which the dependent variable moves as the independent variable changes.

## Calculation

The best way to calculate a regression equation is to use an online calculator. By simply entering the values of the dependent and independent variables over a sufficiently long time frame, you can obtain both A as well as X -- in other words, the starting value of the dependent variable as well as the slope. When working with stocks, you should use at least one month of daily closing prices.

## Trend Line

If the independent variable in your regression equation is time and the dependent variable is the price of a particular stock, the resulting slope in the regression equation is equal to the slope of the trend line. This slope tells you how fast the stock is advancing or declining. You may have drawn such lines by hand or on your computer screen as well. If the value is positive, the higher the figure, the faster the stock is advancing. For a negative value, higher numbers mean that the stock is dropping fast. By comparing the slopes for various stocks, you can find out which stocks have more positive or negative momentum, or are moving up or down faster.

## Risk

You can also calculate a regression by using the value of a stock index as the independent variable and the price of a particular stock as the dependent variable. Here, the higher the resulting slope, the more volatile the stock in question. A positive slope greater than one indicates that the stock does really well when the market is moving up and outperforms the broad market average, but loses more than the average when the economy is in a recession. Stocks of firms that manufacture luxury goods tend to behave in such fashion. If the value of the slope is positive but less than one, this is a relatively safe stock that moves up or down less than the market. If the slope is negative, you have a counter-cyclical stock that moves in the opposite direction as the general market. Such stocks are very rare.

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Writer Bio

Hunkar Ozyasar is the former high-yield bond strategist for Deutsche Bank. He has been quoted in publications including "Financial Times" and the "Wall Street Journal." His book, "When Time Management Fails," is published in 12 countries while Ozyasar’s finance articles are featured on Nikkei, Japan’s premier financial news service. He holds a Master of Business Administration from Kellogg Graduate School.