Linear regression

Regression analysis can be regarded as a statistical method of investigating the relationship between certain variables (dependent and independent). In this case, independent variables are called "regressors", and dependent ones are "criterial" ones. When performing a linear regression analysis, the representation of the dependent variable is performed in the form of an interval scale. There is a possibility of non-linear relationships between variables related to the interval scale, but this problem is already being solved by non-linear regression methods, which is not the topic of this article.

Linear regression is quite successfully used both in mathematical calculations and in economic studies based on statistical data.

So, let's consider this regression in more detail. From the point of view of the mathematical method of determining the linear relationship between some variables, linear regression can be represented in the form of the following formula: y = a + bx. Decoding of this formula can be found in any textbook on econometrics.

With the expansion of the number of observations (up to n times), a simple linear regression is obtained, represented by the formula:

Yi = A + bxi + ei,

Where ei are independent randomly distributed random variables.

In this article I would like to pay more attention to this concept from the perspective of predicting future prices on the basis of previous data. In this area of calculus, linear regression actively uses the method of least squares, which helps to construct the "most suitable" straight line through a certain series of points of price values. As input data, price points are used that indicate the maximum, minimum, closing or opening, as well as the average values from these values (for example, the sum of the maximum and minimum divided into two). Also, these data can be arbitrarily smoothed before constructing a suitable line.

As noted above, linear regression is often used in analytics to determine the trend based on price and time data. In this case, the regression slope indicator will allow to determine the magnitude of changes in prices per unit of time. One of the conditions for making the right decision when using this indicator is the use of signals in the form of a generator following the trend of the regression slope. If the slope is positive (increasing linear regression), the purchase is carried out if the value of the indicator is greater than zero. During a negative tilt (decreasing regression), the sale should take place with negative indicator values (less than zero).

Used in determining the best line, corresponding to a certain number of price points, the method of least squares involves the following algorithm:

- is the total expression of the squares of the price difference and the regression line;

- is the ratio of the received sum and the number of bars in the range of the regression data series;

- from the result obtained, the square root is calculated , which corresponds to the standard deviation.

The equation of pairwise linear regression has this model:

Y (x) = f ^ (x),

Where y is the resultant attribute represented by the dependent variable;

X is an explanatory or independent variable;

^ Shows the absence of a strict functional relationship between the variables x and y. Therefore, in each particular case the variable y can be composed of such terms:

Y = yx + ε,

Where y is the actual result data;

Yx - theoretical data of the result, determined by solving the regression equation ;

Ε is a random variable that characterizes the deviation between the actual value and the theoretical value.