What is correlation and how to interpret the meaning of the coefficient. Relatively apply it

What is correlation? The meaning of the word “Corelation” in popular dictionaries and encyclopedias, the use of the term in everyday life.

Correlation - Medical dictionary

(In statistics) stage, whereby one characteristic flows into another, and these characteristics are interconnected and create a pair. Such characteristics can be represented on the graphics at a low level. If all points on the scatter diagram fall on a straight line (not horizontal or vertical), then the correlation coefficient can be changed to +1 (to increase no change is accompanied by corresponding increases in the other) up to -1 (as an increase in one change is accompanied by permanent changes in another); The correlation coefficient is equal to 0, to determine that between the two characteristics that are considered, there is no significance and they fit on the same straight line. The regression coefficient is the average indicator of the degree to which an increase in one characteristic leads to an increase/change in another. If it is necessary to evaluate the contributions of several factors in the development of a particular illness, then the contribution of each of them can be calculated using statistical methods, for example, multivariate analysis.

Correlation - Psychological dictionary

Correlation - Sociological Dictionary

There is a stable relationship between the two, either variable or changeable values, as expressed in statistical form. Correlations can be either positive or negative.

Correlation - Psychological Encyclopedia

A foot that has two or more alternating ones is connected one to the other.

Correlation - Economic dictionary

The size and level of statistical position between the two are more variable.

Correlation (in Economic Statistics) – Economic dictionary

an understanding that represents the obvious connection between phenomena, processes and quantities characterizing them.

Correlation Biserial - Sociological Dictionary

The correlation between the dichotomous and multivariate variables conveys that the dichotomous variable was established as a result of grouping the multivariate at two intervals. Shows that there was a linear correlation between these variables, as if the dichotomous variable was different. Referring to assistant co-respondent K.B. rbis, which is calculated using the Pearson linear correlation coefficient formula. O.V. Tereshchenko

Correlation Biserial - Psychological Encyclopedia

Corelatsiya J. – Tlumachny Dictionary of Efremova

1. Mutual connection, relationship of objects, clearly understandable.

Correlation and regression – Psychological dictionary

(correlation and regression) View Before. that R. will be near the offensive foundations. food: a) what is there between the changeable X and Y of this kind of connections, so that behind the values ​​of X we know, we could, with a reasonable level of accuracy, transfer the value of Y? b) What is the strength (or tightness) of the connection between the variables X and Y? c) In your opinion, based on such a connection between X and Y, what is the optimal rule (or, mathematically determined, equal) for transferring Y along X and how well is it wired? When we are concerned with assessing the tightness or the degree of bonding (strictly apparent, the stage of linear bonding), we can see to the right of the K. Term “R.” add to the power supply associated with the transfers the value of one change after the value of another. Correlation coefficient Coefficient Do. +1 to -1. The zero value of the coefficient of K. Pearson indicates the presence of a linear connection between X and Y; The positive value of this coefficient indicates the beginning of an increasing trend in Y in the world, an increase in X, while the negative value indicates the beginning of a protracted trend: a change in Y world increase X. Straightforward K. between X and Y is small in that case, as if the value of Y It was possible to easily transfer the values ​​of X, vikorista and equal to the forecast of the form Y = aX + b, where a and b are a similar method for selecting a constant. When a > 0 it is completely positive. (+1), and with a correlation (-1). The equation of the form Y = аХ + b is called linear equations, since when the graph of the function Y is displayed in X, all points (X, Y) that satisfy this equation lie on a straight line. The coefficient of K. Pearson is not an indicator of the stage of a linear connection, but also a non-linear connection. For example, you can indicate the renewed relevance of Do. (r = 0) between two variables associated with a functional nonlinear relationship. Through this exchange, the coefficient of K. Pearson has a tendency to underestimate the level of communication between the variables. They don’t care about those who fall asleep on December. different, although equivalent, formulas for calculating the coefficient Do. Pearson, the most common scaling formula is: , where N is the number of paired estimates for X and Y. When interpreting the coefficient Do. The trace shows caution. De facto Before. Between the changeable X and Y is still not enough to automatically establish a causal connection between them. X can correlate with Y, fragments: a) change X call change Y; b) change Y call change X; c) change it. Changes are caused by changes like X, and Y. For example, in primary school students, their vocabulary knowledge positively correlates with their growth, while resentment and change are associated with age. Moreover, the Pearson coefficient may decrease as a result of the “sampling breadth reduction.” Establishment of correlational and experimental studies Experiment. to last transfers the manipulation of one or more independent variables and often results in the formulation of causal and hereditary statements so as to infuse independent variables onto the stale variable. The correctness of such assertions, therefore, will be ensured by the development of three such minds: a) at the initial stage of investigation. Let's experiment. The groups are not guilty of systematically dividing according to all control measures; b) these groups are subject to the continued influx of all control officials, as well as the influx of independent change; c) after the experiment. Due to the manipulation of the independent exchange, the groups reliably fight among themselves behind the equal of the independent exchange. Correlation research. does not transfer the manipulation of independent variables and, in its simplest form, is reduced to the reduction of a number of variables and the strength of connections between them. I want this kind of investigation. keep us informed. The link and link stage allow you to transfer the values ​​of one change after another, which can be changed at any time. changeable ones, as a rule, do not allow us to work on the causal-hereditary connections between the changeable ones. However, in our time, methods of statistical analysis are available to prehistorians, which allow us to verify the extent to which a particular correlative constellation fits with the specific model of causal-hereditary connections. Private coefficient K. rXY.W is an indicator of the strength of the linear connection between the changeable X and Y when the injection of the changeable W is turned off. It also allows you to “clean” the pair of K. by injecting more than one and changeable. Multiple correlation It is acceptable that we want to achieve the shortest transfer of variable Y (criterion, or stale, variable) based on a series of others. For example, we wanted to transfer the level of success in graduate school based on student badges and a number of Graduate Record Examination (GRE) scores. Using the methods of random multiply regression, we can derive the form: b0 + b1Х1 + ... + bpXp, where b0, b1, ... bp - the appropriate choice of constant, which optimally transfers Y. Coefficient of multiply representation K., r, є itself is a coefficient of Do. the addition of Pearson moments between the shortest transfers and the actual values ​​of the transferred variable, as well as the measure of the correctness of the transfer based on multiple regression. also Correlation methods, Statistics in psychology A. D. Well

Correlation and regression – Psychological Encyclopedia

(correlation and regression) View Before. that R. will be near the offensive foundations. ask: a) what kind of connections exist between the changeable X and Y, so that behind the values ​​of X we know, we could, with a reasonable level of accuracy, transfer the value of Y? b) What is the strength (or tightness) of the connection between the variables X and Y? c) In your opinion, based on such a connection between X and Y, what is the optimal rule (or, mathematically determined, equal) for transferring Y along X and how well is it wired? When we are concerned with assessing the tightness or the degree of bonding (strictly apparent, the stage of linear bonding), we can see to the right of the K. Term “R.” add to the power supply associated with the transfers the value of one change after the value of another. Correlation coefficient Coefficient Do. +1 to -1. The zero value of the coefficient of K. Pearson indicates the presence of a linear connection between X and Y; The positive value of this coefficient indicates the beginning of an increasing trend in Y in the world, an increase in X, while the negative value indicates the beginning of a protracted trend: a change in Y world increase X. Straightforward K. between X and Y is small in that case, as if the value of Y It was possible to easily transfer the values ​​of X, vikorista and equal to the forecast of the form Y = aX + b, where a and b are a similar method for selecting a constant. When a > 0 it is completely positive. (+1), and with a correlation (-1). The equation of the form Y = аХ + b is called linear equations, since when the graph of the function Y is displayed in X, all points (X, Y) that satisfy this equation lie on a straight line. The coefficient of K. Pearson is not an indicator of the stage of a linear connection, but also a non-linear connection. For example, you can indicate the renewed relevance of Do. (r = 0) between two variables associated with a functional nonlinear relationship. Through this exchange, the coefficient of K. Pearson has a tendency to underestimate the level of communication between the variables. They don’t care about those who fall asleep on December. different, although equivalent, formulas for calculating the coefficient Do. Pearson, the most common scaling formula is: , where N is the number of paired estimates for X and Y. When interpreting the coefficient Do. The trace shows caution. De facto Before. Between the changeable X and Y is still not enough to automatically establish a causal connection between them. X can correlate with Y, fragments: a) change X call change Y; b) change Y call change X; c) change it. Changes are caused by changes like X, and Y. For example, in primary school students, their vocabulary knowledge positively correlates with their growth, while resentment and changes are associated with age. Moreover, the Pearson coefficient may decrease as a result of the “sampling breadth reduction.” Establishment of correlational and experimental studies Experiment. to last transfers the manipulation of one or more independent variables and often results in the formulation of causal and hereditary statements so as to infuse independent variables onto the stale variable. The correctness of such assertions, therefore, will be ensured by the development of three such minds: a) at the initial stage of investigation. Let's experiment. The groups are not guilty of systematically dividing according to all control measures; b) these groups are subject to the continued influx of all control officials, as well as the influx of independent change; c) after the experiment. Due to the manipulation of the independent exchange, the groups reliably fight among themselves behind the equal of the independent exchange. Correlation research. does not transfer the manipulation of independent variables and in its simplest form is reduced to the reduction of a number of variables and the strength of connections between them. I want this kind of investigation. keep us informed. The link and link stage allow you to transfer the values ​​of one change after another, which can be changed at any time. changeable ones, as a rule, do not allow us to work on the causal-hereditary connections between the changeable ones. However, in our time, methods of statistical analysis are available to prehistorians, which allow us to verify the extent to which a particular correlative constellation fits with the specific model of causal-hereditary connections. Private coefficient K. rXY.W is an indicator of the strength of the linear connection between the changeable X and Y when the injection of the changeable W is turned off. It also allows you to “clean” the pair of K. by injecting more than one and changeable. Multiple correlation It is acceptable that we want to achieve the shortest transfer of variable Y (criterion, or stale, variable) based on a series of others. For example, we wanted to transfer the level of success in graduate school based on student badges and a number of Graduate Record Examination (GRE) scores. Using the methods of random multiply regression, we can derive the form: b0 + b1Х1 + ... + bpXp, where b0, b1, ... bp - the appropriate choice of constant, which optimally transfers Y. Coefficient of multiply representation K., r, є itself is a coefficient of Do. the addition of Pearson moments between the shortest transfers and the actual values ​​of the transferred variable, as well as the measure of the correctness of the transfer based on multiple regression. also Correlation methods, Statistics in psychology A. D. Well

Correlation Canonical - Sociological Dictionary

English correlation, canonic(al); Nyumu. Correlation, kanonische. Uralization of pairwise correlations, which shows the significance of the relationship between two groups of characters.

Correlation Canonical - Sociological Dictionary

Uralization of pairwise correlations, which shows the significance of the relationship between two groups of characters. Kanonich. analysis, i.e., the method of finding K.K., bases on the basis of such linear combinations is a sign of one other group, so that the highest coefficient of pairwise correlation between these combinations is has the greatest significance. Such a maximum coefficient is called the first canon. correlation coefficient, and the corresponding linear combinations of two groups of sound signs. first canon. quantities. Dive Kendall M.J., Stewart A. Biometric static analysis of time series. M., 1976; Vold R. Road models with latent variables // Mathematics in sociology: modeling and information processing M., 1977; Bolch B., Huan K.J. There are a wide variety of statistical methods of economics. M., 1979; Dubrovsky S.A. Applied Rich World Statistical Analysis 1982; Lipovetsky S.S. Various models of canonical analysis as extremals of quadratic and bilinear forms//Comprehensive application of mathematical methods in sociological research. M., 1983; Van den Wollenberg A.L. Redundancy: An alternative for canonical correlation analysis//Psychometrica. 1977. Vol. 42 No. 2. C.C. Lipovetsky, L.G. Badalyan.

Correlation Linear - Sociological Dictionary

English correlation, linear; Nyumu. Correlation, lineare. Correlation, when the relation between the stage of change of one variable and the stage of change of another variable is a constant value.

Scientific concepts have become increasingly popular. The word “correlate” is widely used by journalists and politicians, but is sometimes not used correctly. Call the term "correlation" to mean any connection.

People have long noticed that all the phenomena that appear on our planet flow together like a singing world. Before long, the connections between them can be easily revealed, but they disappear. When talking about mutual dependence, the word “correlation” is often used. Most often, economists and analysts use it.

Let's figure out what this really means.

Correlation: meaning

Perhaps paleontologist Georges Cuvey was the first to speak about correlation in the scientific world. At the turn of the 18th-19th century, he developed a number of findings in the galusa of the ovarian anatomy. As a result of these findings, Cuvey formulated the law of the reciprocal relationship of parts, whereby changes in one of the organs of the creature lead to changes in other organs. Lurking on this knowledge, Cuvey has learned to recreate the image of the ancient creatures behind the surrounding fragments that have been preserved.

As for statistics, this scientific understanding of correlations was consolidated later - for example, in the 19th century, thanks to the English biologist Francis Galton.

Correlation- This is not just a connection (relation), but rather, mutuality or mutual dependence (co-relation).

The formula for determining the correlation coefficient was derived by Galton's scientist, mathematician and biologist K. Pearson.

Correlation coefficient

Correlation is the name given to statistical connections between quantities that are independent of each other. It is transferred when the values ​​of one of the parameters are changed, and the values ​​of another are changed. Since changes depend on other statistical characteristics, connections of this kind are important for statistical purposes. There is no mention of correlation in this case.

To express the level of mutuality, the correlation coefficient is used. The coefficient value range is from -1 to +1.

• Since the correlation is absolute and positive (+1), then when one valuable paper becomes more expensive, another one in the same world becomes more expensive.
• Speaking about the absolute negative correlation, we take into account that as the wariness of one valuable paper increases, the wariness of the negatively correlated one decreases.
• Since the correlation coefficient is zero, there is no interdependence between the aroma of valuable papers: the stench of the fall.

The greater the significance of the coefficient, the greater the mutual dependence. If the coefficient value is greater than 0.5, the interactions are clearly visible.

It is necessary to clarify that the absolute correlation of valuable papers is less than ideal light. In real life, the shares are simply not the same.

Parna correlation

This term is used mutually between two simple quantities. Apparently, what you spend on advertising in the United States significantly contributes to the GDP of this country. The correlation coefficient between these values ​​behind the precautionary bags, which was tested over a period of 20 years, becomes 0.9699.

More “landing” butt – connections between the promotion of the site to the online store and the obligation of its sale.

And now, of course, it is unlikely to notice the presence of staleness that occurs between the air temperature and the sale of beer and frost.

Correlation is the interdependence of two quantities; The correlation coefficient is an objective indicator that indicates the level of price interdependence. The correlation coefficient can be positive or negative. Although there are valuable papers, the smells are rarely completely corroded.

06.06.2018 15 091 0 Igor

Psychology and matrimony

Everything in the world is mutual. The skin of a person, on an equal level of intuition, tries to know the relationships between objects, so that they can react to them and deal with them. The concept that separates these relationships is called correlation. What does won mean in simple words?

Zmist:

Concepts of correlation

Correlation (from the Latin "correlatio" - relationship, interconnection)– a mathematical term that means a measure of statistical significance between variable values ​​(variables).

Butt: Let’s take two types of interconnection:

1. First- A hand in a person’s hand. In which way the hand collapses, in the same way the pen collapses. If the hand remains calm, then the pen does not write. If people put more pressure on it, then the mark on the paper will be more intense. This type of interconnection eliminates rigidity and correlation. This relationship is functional.
2. Another look- the importance of studying people and reading literature. From afar, it is unknown which people read more: with or without the light. This link is purely stochastic, which is why statistical science deals with mass phenomena inclusively. If the statistical analysis allows us to establish a correlation between the level of awareness and reading of the literature, then I will be able to make any forecasts, conveying the current situation to the world. In this case, with great confidence, it can be confirmed that people with more knowledge read books more, those who are more enlightened. However, some connections between these parameters are not functional, we can apologize. It is then possible to evaluate the validity of such a reduction, which will be clearly small and is called the level of statistical significance (p).

Examples of interconnection between natural phenomena: The lantern of food in nature, the human body, which consists of organ systems interconnected with each other and functioning as a single whole.

Today we come to grips with the correlation in everyday life: between the weather and a good mood, the correct formulation of goals and their achievements, a positive attitude and good luck, happiness and financial well-being . Ale we are looking for a connection, spiraling not so on mathematical developments, but in myths, intuition, concerns, empty speculations. It’s very difficult to translate these things mathematically, put them in numbers, and put them into perspective. It’s different when we analyze the items that can be examined, given in the form of numbers. In this case, we can determine the correlation using the correlation coefficient (r), which reflects the strength, degree, density and direction of the correlation between the variable variables.

Strong correlation between fall values– evidence of the presence of a statistical connection between these entities, but the connections cannot be transferred to the same entities, or in other situations. Often, investigators who have found a significant correlation between two variables in their relationships, relying on the simplicity of correlation analysis, dispel strange intuitive assumptions about the origin of causal-inherited relationships And between the signs, we forget about those that the correlation coefficient is of a universal nature.

Butt: the number of people injured due to ice and the number of accidents involving motor vehicles. These values ​​correlate with each other, although the stench is absolutely not mutually related to each other, and there are only connections due to the underlying cause of these episodes - ice. Although the analysis did not reveal a correlational relationship between the objects, there is still no evidence of the presence of relationships between them, which may be complex nonlinear, which is not revealed by additional correlation patterns NKiv.

The first person to introduce the concept of correlation in science is French. paleontologist Georges Cuvey. VIN in the XVIII Ts VIVIV Law of the Korelitsyi Part, 17- Ta Organizov Organism, Zadakoi Zamiyviliyvyvyvati in the recognizable parts of the TIL (remains) VIGUSY VIKOPNOTYS, TETVRINI. In statistics, the term correlation was first established in 1886 by English teachings Francis Galton. Ale vin was not able to derive the exact formula for the expansion of the correlation coefficient, but without completing his student. The most famous mathematician and biologist Karl Pearson.

Types of correlation

For significance- Highly significant, significant and insignificant.

Negative(The change in the value of one variable to an increase in the level of another: the more phobias a person has, the less likely they are to experience a bad attitude) and positive (as the same value increases This brings with it a greater level of anxiety: the more nervous you are, the more likely you are to get sick). Since there is no connection between the variables, such a correlation is called zero.

Linea(if one value increases and changes, the other also increases and changes) and non-linear (if, when changing one value, the nature of the change cannot be described by another using a linear sequence, then it becomes stagnant other mathematical laws – polynomial, hyperbolic law).

Behind the force.

Coefficients

It is important to determine to what scale the changes that are being monitored are applied to different types of correlation coefficients:

1. The Pearson correlation coefficient, the pairwise linear correlation coefficient, or the moment correlation coefficient are calculated for changes with an interval and scale scale.
2. Kendall's rank correlation coefficient – ​​if one of the values ​​is on an ordinal scale or normally distributed.
3. The point-noise correlation coefficient (the Fechner sign correlation coefficient) is made up of two quantities and is dichotomous.
4. The coefficient of multi-field correlation (the coefficient of multiple rank correlation (concordance)) is like two variable dichotomies.

The Pearson coefficient is used for parametric correlation indicators, and for non-parametric ones.

The values ​​of the correlation coefficient between the boundaries range from -1 to +1. For a completely positive correlation r = +1, for a completely negative correlation – r = -1.

Formula ta roserahunok

Apply it

It is necessary to evaluate the interrelationships between two variables: the level of intellectual development (based on the testing data) and the amount of learning per month (based on the initial journal entries) for schoolchildren.

The output data is presented in the table:

To give a correct interpretation of the extracted indicator, it is necessary to analyze the sign of the correlation coefficient (+ or -) and its absolute value (behind the module).

It is consistent with the table of classification of the correlation coefficient based on the strength of the positive correlation, rxy = -0.827 – this is a strong negative correlation. Thus, the amount of lateness of schoolchildren may have a very strong impact on the level of intellectual development. We can say that students with a high IQ level are more likely to meet in class than students with a low IQ.

The correlation coefficient can be used both to confirm or state the assumption about the occurrence of two quantities or to demonstrate their strength, significance, and by students to conduct empirical and statistical research on various subjects iv. It is necessary to remember that this indicator is not an ideal instrument, it will be too expensive to change the strength of linear position and will later become an incredible value, which may lead to death.

Correlation analysis is limited in the following areas:

• economic science;
• astrophysics;
• social sciences (sociology, psychology, pedagogy);
• agrochemistry;
• metal science;
• industry (control of vigor);
• hydrobiology;
• biometrics, etc.

Reasons for the popularity of the correlation analysis method:

1. The simplicity of developing correlation coefficients is remarkable, for which no special mathematical background is required.
2. Allows you to explore the relationships between mass variable quantities, which are the subject of analysis of statistical science. In connection with this method, there is a wide expansion in statistical research.

I hope that now you can distinguish the functional relationship from the correlational one, and you know that if you hear on TV or read about correlation in the press, then you can see it in a positive light I mean mutuality between two boxes.

The correlation between two quantities is called a statistical relationship, in which a change in one quantity leads to a systematic change in the other. As a result of the correlation, there is a linear correlation coefficient (also called the Pearson correlation coefficient), which is calculated using the formula:

• r xy – correlation coefficient of the values ​​of x and y;
• d x - Addition of the actual value to the row x from the middle value of the row;
• d y - Addition of the current value to the row y from the middle value of the row.

The range of possible correlation coefficient values ​​is between +1 and -1. In which case the following options are possible:

• +1 - Direct deposit between values;
• |r xy| > 0.7 – the depth between values ​​is clearly visible;
• 0.4 < |r xy| >0.7 – average depth between values;
• |r xy|< 0.4 – слабо выраженная зависимость между величинами;
• -1 - Return value between values.

It is important to note that the larger the selection value, so with a smaller value of the module of the correlation coefficient, we can talk about the correlation between x and y. It’s a pity that the formula has a paste in it, so that a hundred financial instruments can play evil with the investor. For a number reader, the values ​​can be both different and different signs, so the sign can be both positive and negative. The banner has a square, which guarantees the positiveness of the banner. For now, we’re just brutally at this point, and then we’ll turn around to where we can get out.

A practical sense of calculating the correlation between financial instruments lies in the extraction of important fundamental data, the necessary adoption of trading decisions. The market's reaction to the release of important economic news is reflected in the fact that the prices of major assets (gold, naphtha, industrial index futures) are immediately collapsing, at the same time as income. As a result, exchange rates and stock quotes change. Through the interrelationships of other instruments, and the creation of causal connections between price changes, you can quickly revise your trading and investment plans. In addition, the correlation analysis is integrated into the controlled part.

It is possible to visually detect the correlation of two quantities as a graph in hour-amplitude coordinates. For example, with a negative correlation we get the following picture:

Knowing the correlation of assets reduces portfolio risk

Come on, for example, there are 2 assets. For simplicity, it is assumed that their prices lie according to the sine law. Then, with a correlation of +1, the overlay is taken away from the outside and the expansion of interests in both assets will be equivalent to a subordinate position in one of them. Correlation -1, however, means mutual compensation for gains and losses in assets. It is understandable that we have decided not to go around the same level, but to continue the trend until it grows over time. In addition, with some assets, growth in others allows you to minimize the total risk of the portfolio:

The process, called portfolio rebalancing, allows you to trim income by alternately changing the portion of assets in the portfolio. The easiest way to achieve this is with clear expressions of negative correlation. Let’s assume that the portfolio contains assets A and B with a reversal correlation and relationship of 1:1, for a total amount of 1 million rubles. We will hand over the asset A, having dropped the price by 20% and its value from the cob 500 thousand. rubles became 400 thousand. rubles Asset B, for example, increased by 20% and its value rose to 600 thousand. rubles The total value of the portfolio has not changed and, as before, remains 1 million rubles. Now 50% of the asset (300 thousand) is transferred to A and its risk is now 700 thousand, and the asset – 300 thousand.

At the beginning of the week, a protracted process begins: assets return to their initial price. Now asset A is worth 700 thousand. The cost is 840 thousand, and the asset is 300 thousand. - 240 thousand. The total value of the portfolio, in this manner, amounted to 1 million 80 thousand. rub., then The profitability of the rebalancing accounts is 8% of the current ones. Without rebalancing, the portfolio profitability would become 0%. Real situations are very complex, because The correlations of most instruments are between +0.5 and -0.5. As soon as we look at the risk-gain graph for different correlations between two instruments for different correlation values, we can see the following picture:

Apparently, the lower the value of the correlation coefficient of instruments, the greater the possible return of the portfolio with the same significant risk, and the lower the risk with the same significant return.

Correlation in Forex

The strategy has been expanded, based on the correlation of currency pairs, so that at times of a sharp increase in the correlation coefficient from the flow value, the interests are supported by the updated value. For example, if the EURUSD and GBPUSD bets have been collapsing in one direction for the past three hours, then with their strong divergence, convergence will occur, as the divergence is not caused by the long-term (for example, a change in the investment rate).

In addition, the correlation of currency pairs is analyzed for a comprehensive assessment of the market. For example, before the mortgage crisis of 2008-2009, when the Australian and New Zealand dollars, as well as the British pound, were at a low key rate, a trading strategy called the carry trade took off. Vaughn believed that during favorable conditions for stock markets, pairs of these currencies against the yen grew especially actively, which traditionally rises even at a low rate, while they also actively decreased during unfavorable conditions.

Given that the same correlation cannot be applied to absolutely all hourly intervals and possible multi-directional currency movements, except for the clear expressions of single-directional currency movements, as a rule, we can talk about the presence of a hidden fundamental “driver”. This makes planning easier. Zokrema, there is no sense of jokes, and in the middle of the day, practice, as all bets that clearly correlate, go in one direction.

You can view the correlation table of currency pairs and other instruments in real time at myfxbook.com/forex-market/correlation. This table shows that EURUSD and AUDCAD bets practically do not correlate with each other. In case of instantaneous discovery of these pairs, there is no need to be afraid of the addition of refills, or the interruption of the flow of one pair of refills over another.

This chart shows how the Australian and New Zealand dollars, which back correlate with the “buy currencies” the yen and the Swiss franc, were actively growing during the period of the greatest differential in key rates. This trend reversed itself after a period of rising rates began as the mortgage crisis subsided.

There are no inheritances without a reason

The correlation of asset prices is similar to trends: the longer the hourly interval for its development, the more it changes. There are also those that clearly contradict the correlation of many other methods. It can be developed for such pairs of assets that are not traded on the stock exchange (nafta-gas, nafta-gold), which allows you to supplement the analyst’s arsenal with valuable information, which allows you to read the market between charts.

Any correlation between two or more quantities will always lead to a causal link. One of the quantities is the initial one that lies in one (or another). Correlation in the stock market is not to blame. For example, the Naftogaz pair had a difficult time with the initial price of nafta. In the graph below, it can be noted that the widening of the spread between naphtha and gas due to the sharp changes in the gas flow rate changed with the sharp turns of the flow rate:

At the same time, in another pair of assets, gold-naphtha, initially gold. With a significant expansion (sharp rise or fall of naphtha with more stable gold), naphtha itself renews the broken balance:

By following this behavior of “domestic” assets, it is possible to improve the balance. Before speaking, correlation often underlies the linking of certain currencies to foreign assets. They are called so: “virgin currencies”. For example, the Canadian dollar and ruble are heavily dependent on oil. In both cases, the correlation is direct: the more expensive nafta is, the higher the exchange rate of these currencies in terms of the US dollar.

What is the difference between the ruble and the correlation of charts on the table, which can be used in a trading strategy. Let's take a look at the cob of 2014 rock. Nafta is trading at around $110 per barrel, after which it rises slightly higher every hour. This hour, however, the ruble quickly drops from 33 per US dollar to 36. At this point, the correlation almost turns into a reversal, but soon the ruble reverses and the ruble turns to the rate of 33 per dollar, reportedly following the naphtha. An even brighter butt, especially at the end of 2014, was when there was a sharp weakening of the ruble due to oil, which is gradually decreasing even more. And this time the ruble was destroyed due to the sudden depreciation of the ruble. Over time, the correlation can show strong changes and go from direct to reverse. This was particularly evident in the correlation between the Dow Jones Industrial Average and RTS indices.

For example, at the end of 2007, when the first signs of the mortgage crisis in the US began to appear, the DJ index flared down, and the RTS index, due to the active growth of naphtha quotations, was still climbing to a historical maximum. However, there was a sharp collapse in all stock indices around the world and in oil prices. This led to the fact that the RTS index, following the rate of decline, almost doubled the DJ rate. In oil, at a rate of decline in the RTS index, there has been a significant outflow of capital from markets that are developing.

The crisis was not long lasting and at the beginning of 2009 economic growth changed. The high correlation between DJ and RTS was observed right up until the end of 2012, which was marked by the exhaustion of the possibilities of the Syrian model for the development of the Russian economy. As this fate began, the naphtha road no longer ensured economic growth. In the future, the economic downturn in Russia was no longer supported by oil, which is cheaper, as the American economy lost additional incentive for growth. The correlation between i has become a turning point.

Of course, the obviousness of the correlation between assets also means that one can have a trading and investment strategy. Let's take a look at the correlation between IBM shares over the past 12 months (div. impactopia.com/correlation). Also, in 4th place behind the correlation value is Banco Santander (close to 0.43). Shvidshe for everything, it’s just a shortcoming or a systemic shortcoming of the correlation method.

Mathematical pasta

As you know, the formula for the development of the correlation coefficient is very sensitive to the signs of change in the value of the quantities from their average values. Since these signs are most often visible, the correlation coefficient is found to have a high value. Ale chi bude tse znachennya mati sens? The answer is not at all obvious. Look at the practical butt. Let’s say on the graphs there are two values ​​simultaneously:

Then new values ​​of these quantities will systematically appear on one side of their average values. This causes a high positive correlation. Unfortunately, there is nothing to gain from this information, because Apart from the obviousness of the gap, there is nothing special between the graphs. It is more important to note that, due to the expansion of correlation, it is allowed to use stationary series of values ​​inclusively. rows, in which there is no trendy warehouse. This means that the development of correlations in the world of financial assets will inevitably lead to a reassessment of the significance of factors, which indeed may be of a phased nature. Understand correctly: it is important not to exaggerate these factors and introduce special amendments to them, but to show the very essence of the phenomenon and not joke about the Holy Grail where there is none.

However, it’s not so bad. A way to bypass the influx of trends is by decoupling the correlation not of the prices themselves, but of the increases. Then, the guesswork of the GEP will appear as a statistical wiki, which practically does not affect the result. There was no longer any need to wait until such an approach climbed the mountain. New data will soon be available to correlate assets. They can be analyzed using Microsoft Excel. For this quote, two ranges of middles are written in the view, and then in one of the other middles the function of the approach is written: =CORREL (array 1; array 2). The massif can be seen, for example, like this: A1: A100. To release the correlation for increased prices, this program is dependent on each other, and even based on closing prices, it is necessary to immediately release the increases themselves.

Summary

Correlation between asset prices is an important tool for both data analysis and risk management in portfolio investments. However, like all statistical approaches, they do not eliminate serious shortcomings:

• the presence of a pronounced correlation between data in the past cannot be guaranteed in the future;
• The mathematical model used by Wikoristov has great consequences during the trend.

The use of the correlation approach will bring maximum profit in addition to other methods of analysis and capital management. In the comments, please discuss how to make money on the correlation of specific assets. I brought my butts to the statistics, I check yours for negotiations.

Profit to all!

Publication date: 09/03/2017 13:01

The term “correlation” is actively used in the humanities and medicine; blink frequently at snakes. Correlation plays a key role in psychology. Zokrem, correlation analysis is an important stage in the implementation of empirical research when writing a research paper in psychology.

Materials with correlation at the limit of science. It is important for non-Fakhivtsevs to understand the formulas. At this very moment, understanding the sense of correlation is necessary for a marketer, sociologist, physician, psychologist - everyone who conducts research on people.

This article, in a simple way, explains the essence of the correlation link, the types of correlation, the methods of distribution, the specifics of the correlation correlation in psychological research, as well as the writing of dissertations in psychology.

Zmist

What is correlation?

Correlation is not a connection. Never mind. What is special? Let's take a look at the butt.

Detect that you are driving a car. You press the gas pedal - the car is moving forward. If you change the gas, the car will move smoothly. People who are not familiar with the structure of a car say: “There is a direct connection between the gas pedal and the fluidity of the car: the harder the pedal is pressed, the fluidity of the car.”

This is functional - fluidity acts as a direct function of the gas pedal. Please explain that the pedal is pressurized by supplying fuel to the cylinders, which causes combustion of the mixture, which leads to increased tension on the shaft. This connection is strong, deterministic, and does not allow for blame (for the mind that the machine is in good working order).

Now understand that you are the director of a company that sells goods. You hope to increase sales in exchange for salary increases for healthcare workers. You increase your salary by 10%, and sales for the average company increase. After an hour, move up another 10% and increase again. Then another 5% and the effect is again. There is a need for a reversal - between the company's sales and the salaries of the military workers, there is a direct correlation - whichever is higher, the higher the salary, then the higher the sale of the organization. The same connection as between the gas pedal and the speed of a car? What is the key importance?

That's right, the gap between salary and sales is not great. This means that for some of the workers, sales could have decreased, regardless of the increase in salary. Who will lose their irreplaceable ones? But on average across the company, sales have grown, and we are talking about the relationship between sales and the salaries of employees, and the correlation.

The basis of the functional connection (gas pedal - speed) is a physical law. The correlation link (sale - salary) is based on the simple convenience of changing two indicators. There is no natural law (there is no physical word) behind correlation. This is a less than universal (stochastic) pattern.

Numerical expression of correlation

Also, the correlative connection reveals the content between the boxes. Since these objects can be measured, the numerical expression is taken away.

For example, the role of reading plays a role in people’s lives. The investigators took a group of 40 individuals and measured two indicators from each person tested: 1) how many hours does he read per day; 2) in what way he considers himself prosperous (on a scale from 1 to 10). In recent years, these data have been collected from two specialists and, using additional statistical programs, they have analyzed the correlation between reading and well-being. Let's say the stinks won an offensive result of -0.76. What does this number mean? How should we interpret it? Let's get along.

The resulting number is called the correlation coefficient. For this correct interpretation, it is important to read as follows:

1. The "+" or "-" sign indicates the location.
2. The size of the coefficient influences the strength of the deposit.

Right at the gateway

A plus sign in front of the coefficient indicates that the connection between the boxes and indicators is direct. So the more one showman, the more the other. The highest salary is the highest for sales. This correlation is called direct or positive.

If the coefficient has a minus sign, it means the correlation is positive or negative. Whichever type has one display, then the lower one has another. In the case of reading and well-being, the score was -0.76, which means that the more people read, the lower their level of well-being.

Strong is the weak

The correlation link in a numerical expression is a number in the range from -1 to +1. Indicated by the letter "r". The higher the number (without the order of the sign), the stronger the correlation link.

The lower the numerical value of the coefficient, the less interconnection between the components and indicators.

The maximum possible force of storage is 1 or -1. How can this be understood and revealed?

Let's take a look at the butt. They took 10 students and measured their intelligence (IQ) and success rates for the semester. The tributes were exchanged in front of two staunch figures.

It is important to look at the data in the table. From 1 to 10 tests, the level of IQ increases. Also, the rate of success is growing. Either way, success will be with the one with the higher IQ. There will be no common faults with this rule.

Before us is the butt of a new, 100% customized change of two members of the group. And this is an example of the most possible positive interaction. So the correlation between intelligence and success is equal to 1.

Let's take a look at a different butt. These 10 students assessed the degree of stench they felt was successful in people with chronic illness (on a scale from 1 to 10).

It is important to see the data in the table. From 1 to 10 tests, the level of IQ increases. In this case, the success rate of amalgamation with the protracted state is consistently decreasing. For any two students, the one with the lower IQ will be more successful. There will be no common faults with this rule.

This means that the change in the two indicators of the group means the maximum possible negative interaction. The correlation between IQ and the success of the study with a long-term status is equal to -1.

How can we understand sense correlations that are equal to zero (0)? This means that there is no connection between the indicators. Once again, let’s turn to our students and take a look at another extinct display among them - the end of the day’s haircut from the place.

Don't be afraid of the same convenience between changing IQ from person to person and having a long haircut. It is important to note the existence of the correlation. The correlation coefficient of IQ and the final cut from the place among students is 0.

We saw extreme outbursts. In real worlds, the coefficients rarely reach exactly 1 or 0. When the scale is taken:

• if the coefficient is more than 0.70 – the relationship between the indicators is strong;
• from 0.30 to 0.70 - the connection is dead,
• less than 0.30 - the sound is weak.

If we evaluate on this scale the higher correlation between reading and well-being, we find that this correlation is strong and negative -0.76. Then beware of strong negative connections between being well-read and being successful. Once again confirming the biblical wisdom about spiritual wisdom and confusion.

The gradation given gives even approximate estimates, and they rarely seem to be consistent with investigations.

Most often, there are gradations of coefficients based on levels of significance. And here, in reality, the negative coefficient may be significant and significant. The value can be calculated by comparing this value with the critical values ​​of the correlation coefficient taken from a special table. Moreover, these critical values ​​depend on the number of samples (the greater the value, the lower the critical value).

Correlation analysis in psychology

The correlation method is one of the main ones in psychological research. And this is not true, even psychology is not an exact science. Should I go out?

Why are there special laws in the exact sciences? For example, the law of gravity in physics is true: the greater the body weight, the stronger the attraction of other bodies. This physical law reflects the relationship between body mass and gravity.

Psychology has a different situation. For example, psychologists publish data about the bonding of warm containers in childhood with parents and the level of creativity in adults. What does it mean that the skin from the last few years, with very warm mothers and fathers, has very high creativity? The answer is clear – no. There is no law similar to the physical here. There is no mechanism for infusing children's desire for the creativity of adults. These are our fantasies! The convenience of data (the term is creativity), but there is no law behind it. And this is just a correlative connection. Psychologists often call relationships, which are revealed by psychological patterns, underpinning their universal character - not cruelty.

An example of a study on students from the first section well illustrates the strong correlation in psychology:

1. Analysis of the relationship between psychological indicators. Our IQ application has the same success in combining with a protracted article – these are psychological parameters. The revealed correlation between them expands the findings about the mental organization of a person, about the interactions between different parties and characteristics - between the intellect and the sphere of sleep.
2. Analysis of the relationship between IQ and success and stripes - an example of the connection between a psychological parameter and non-psychological ones. The results reveal the peculiarities of the infusion of intelligence into initial and sports activities.

The axis could be seen as a short summary of the results of the conducted research on students:

1. It was revealed that there is a positive impact on students’ intelligence and their success.
2. There is a negative significant relationship between IQ and academic success.
3. There was no connection between the IQ of students and the time taken from the place.

Thus, the respect for the intelligence of students is a positive factor in their academic success, but at the same time it is negatively reflected in the academic performance and does not have a significant impact on sports success, academic performance, mistya.

As a matter of fact, intelligence helps students get started, and prevents them from having hundreds of years of work. Which does not affect their sporting successes.

The ambiguous infusion of intelligence into the characteristics and activity of students reflects the complexity of this phenomenon in the structure of special characteristics and the importance of continued investigation of this phenomenon directly. Zokrem, it is important to analyze the relationship between intelligence and psychological characteristics and the activity of students with their status.

Pearson and Spearman coefficients

Let's take a look at two methods of rozrakhunku.

p align="justify"> Pearson's coefficient is a special method of analyzing the interrelationship of indicators between the expression of numerical values ​​in one group. It’s quite easy to bring things down to the offensive:

1. The values ​​of two parameters are taken from the sample group (for example, aggression and perfectionism).
2. The average value of the skin parameter of the group is found.
3. There is a difference in the parameters of the skin tested and the average value.
4. These differences must be submitted to a special form for the Pearson coefficient breakdown.

Spearman's rank correlation coefficient is calculated as follows:

1. The values ​​of the two indicators in the group below are taken.
2. The ranks of the skin official of the group are known, so the place is on the list of growth.
3. Differences in ranks are found, squared and summed.
4. Further differences in ranks are presented in a special form for calculating the Spearman coefficient.

In the case of Pearson, the size of the eggs is of average value. Also, the results of the data (the difference in value from the average), for example, through the correction of processing or inaccurate evidence can completely spoil the result.

In Spearman's version, the absolute values ​​of the data do not play a role, so it is ensured that there is no mutual expansion in relation to one to one (ranks). Please delete the data or other inaccuracies will not affect the final result.

Although the test results are correct, the differences between the Pearson and Spearman coefficients are insignificant, and the Pearson coefficient shows more accurately the significance of the relationship between the data.

How to develop the correlation coefficient

The Pearson and Spearman coefficients can be calculated manually. This may be necessary when using statistical methods.

However, in most cases of increased applied tasks, such as in psychology, it is possible to carry out developments with the help of special programs.

Rozrahunok for help with Microsoft Excel electronic spreadsheets

Let's turn again to the students and look at the data about the level of their intellect and the recent eradication of the place. Enter this data (two columns) into the Excel table.

Having moved the cursor to the empty box, click on the “Insert function” option and select “CORREL” from the “Statistical” section.

The format of this function transmits two data arrays: Corel (array 1; array "). Apparently there is a player with IQ and a lot of stripping.

Excel tables have a growth formula based on the Pearson coefficient.

Rozrahunok for additional help with the STATISTICA program

We enter data on intelligence and last row in the output data field. Next, select the option “Nonparametric criteria”, “Spearman”. The parameters for the development are visible and the resulting result is visible.

Apparently, the expansion yielded a result of 0.024, which differs from the result of Pearson - 0.038, calculated using Excel. Proceedings are insignificant.

Victimization of correlation analysis in graduate students in psychology (example)

Most of the subjects of graduate qualifications in psychology (diplomas, coursework, master's) are subject to correlational research (otherwise related to the identification of the significance of psychological indicators in them groups).

The term “correlation” itself is rarely heard in the names of topics - it is usually found in such formulations:

• “The relationship between subjective self-esteem and self-actualization in women of mature age”;
• “The influence of managers’ vitality on the success of their interactions with clients in conflict situations”;
• "Special factors of stress resistance in MNS patients."

Also, the words “interconnections”, “inflow” and “officials” are sure signs that by analyzing the data, empirical research can lead to correlation analysis.

Let’s take a brief look at the stages of my work during the writing of my thesis in psychology on the topic: “The relationship between special anxiety and aggression in children.”

1. For the development of the necessary data, which depends on the results of testing below. They are entered into the table and placed in additions. This table is set up like this:

• leather row to place tribute on one tried;
• Skin care should be taken to place indicators on the same scale for all tests.

2. It is necessary to decide which of the two types of coefficients - Person or Spearman - is victorious. It is likely that Pearson gives a more accurate result, but is more sensitive to data loss. Spearman's coefficients can be compared with any data (other than the nominative scale), which is why they are most often used in psychology degrees.

3. Enter a table of the data into a statistical program.

4. Insurance value.

5. At the next stage, it is important to consider how important the relationship is. The statistical program highlighted the results in red, which means that the correlation is statistically significant at a significance level of 0.05 (higher is indicated).

However, it’s worth knowing how to determine significance manually. Therefore, you need a table of Spearman's critical values.

Spearman's table of critical coefficient values

We have a significance level of 0.05 and our sample size is 10 individuals. Based on these data, the critical Spearman value is found: Rcr = 0.63.

The rule is this: if Spearman's empirical significance is greater than one critical, it is statistically significant. In our case: Ramp (0.66) > Rcr (0.63), however, the interaction between the aggressiveness and anxiety of the subgroup is statistically significant.

5. For the thesis text, you need to insert data into a table in Word format, rather than a table in statistical programs. Below the table we describe the results and interpret them.

Table 1

Coefficients of aggression and anxiety in a group of children

* - statistically significant (p≤ 0,05)

Analysis of the data from Table 1 shows that there is a statistically significant positive relationship between the aggression and anxiety of the subordinates. This means that the greater the special anxiety of the sublinguals, the greater the level of their aggressiveness. This result suggests that aggression for teenagers is one of the ways to relieve anxiety. Knowing their own insecurity and anxiety in connection with threats to self-esteem, which are especially sensitive in adolescents, adolescents often engage in aggressive behavior, thus reducing anxiety in an unproductive way.

6. How can we talk about inflow when interpreting connections? Can we say that anxiety leads to aggressiveness? Strictly apparent, no. We have shown that the correlation between the phenomena is of a unique nature and undermines the convenience of changing the sign of the group. At the same time, we cannot say that this is the benefit of the wickedness because one manifestation is the cause of another that flows into the other. Thus, the presence of a correlation between psychological parameters does not provide a basis for talking about the existence of a causal link between them. However, practice shows that the term “influx” is often used when analyzing the results of correlation analysis.