Regression analysis can be added to the statistical methods of research the relationship between certain variables (dependent and independent).At the same independent variables are called "covariates" and associates - "criterial".During the presentation of linear regression analysis the dependent variable takes the form of an interval scale.There is a possibility of having non-linear relationships between variables related to the interval scale, but this task has been solved by nonlinear regression, that is not the subject of this article.
Linear regression is used successfully as in mathematical calculations, as well as in economic studies based on statistical data.
So, consider this a regression more.From the viewpoint of a mathematical method of determining the linear relationship between the linear regression of some variables can be represented as a formula: y = a + bx.For an explanation of this formula can be found in any textbook on econometrics.
In expanding the number of observations (before the n-th number of times) is obtained by a simple linear regression, presented in the form of the formula:
yi = A + bxi + ei,
where ei - independent, identically distributed, random variables.
In this article I would like to pay more attention to this concept from the standpoint of the future price forecasting based on historical data.In this area, estimates a linear regression is actively using the least squares method, which helps to build the "most appropriate" straight line through a certain number of points of price values.As the input data used price point, meaning high, low, open or closed, and the average of these values (for example, the sum of the maximum and minimum, divided by two).Also, these pre-build appropriate lines can be arbitrarily smoothed.
As mentioned above, the linear regression is often used by analysts to determine a trend on the basis of price and time.In this case, the indicator will determine the slope of the regression value of price changes per unit time.One of the conditions for making the right decision when using this indicator is the use of a signal generator, following the slope of the regression trend.With a positive slope (rising linear regression) the purchase is carried out, if the indicator value is greater than zero.During the negative slope (decreasing regression) the sale should be carried out with negative value of the indicator (less than zero).
used to determine the best line corresponding to a certain number of price points, the least squares method involves the following algorithm:
- is an expression of the total price and the difference of the squares of the regression line;
- is the ratio of the amount received and the number of bars in the range of regression series of data;
- the result of the square root, which corresponds to the standard deviation.
linear regression equation of the pair has a model:
y (x) = f ^ (x),
where - productive features presented the dependent variable;
x - explaining or independent variable;
^ shows no strong functional relationship between the variables x and y.Therefore, in each particular case may have a variable shape of these terms:
y = yx + ε,
where - the actual result data;
uh - theoretical result data determined by solving the regression equation;
ε - random variable, which characterizes the deviation between the actual value and the theoretical.
