Least Sq. Linear Regression (LIN)

FutureSource uses the least squares technique to fit a straight line to the data. In simple terms, the software system computes the linear trend with 1 to time. Is the market trending lower or higher with respect to time? Once the calculations are completed, FutureSource draws the trendline on the screen.

In practical use, the regression line indicates the dominant market trend relative to time. It can inform you when the market is diverging from an established trend, but only when prices fluctuate uniformly around the trendline and within a narrow range. The better the fit of the equation to the data the more reliable the linear trend.

Do not rely on this study when prices deviate widely about the trendline. The fit of the trend to the data is most likely not very reliable. If the price chart flows uniformly about the regression line, the market should have a tendency to continue in the direction of the statistically fit trendline. Any large deviation from the regression line implies a change in the dominant market trend.

Parameters:

• Period (10) - the number of bars, or interval, used to calculate the study.

Computation

The least squares methodology can be found in most books on basic statistics. It is a rather intense calculation process. This manual includes the formula for computing the slope and intercept using standard statistical notation. Given the linear equation:

Y = a + bX

• Y is the dependent variable.
• a is the intercept of the equation.
• b is the slope of the equation.
• X is the independent variable.

You can solve the equation using the method of least squares:

• S is the Greek alphabet symbol for Sigma which statisticians use to represent summation or a group of sums.
• n is the number of data points or total number of intervals used to estimate the equation.
• Ybar is the mean of the dependent variable.
• Xbar is the mean of the independent variable.

Note: If you are unfamiliar with the formulas above, do not use this study without seeking assistance from a good statistics book. Regression analysis is a powerful statistical method when used properly. However, it is easily abused in the hands of a novice statistician.