What is Correlation
Correlation
What is Correlation?
In statistics, a correlation estimates how closely two variables are related. This sums up the correlation definition. The measure works best with variables that have a linear connection. A scatterplot is used to check how well the data fits together. We may analyse the association between the factors and decide if they are correlated or not using a scatterplot.
A correlation coefficient is a value that shows a strong link existing between two variables. The coefficient might be any figure between -1 and 1. The following are the values' interpretations:
-1: The greatest possible negative correlation. Variables tend to move in opposing directions (i.e., one variable increases, the other decreases).
0: There is no correlation. The variables don't have any link.
1: There is a perfect positive correlation here. The variables tend to follow the same path (i.e., an increase in one variable leads to a rise in the other).
What is the difference between correlation and causation?
It's important to distinguish between correlation and causation. The statement "correlation does not imply causation" is critical to comprehending the two statistical notions.
Correlation between two variables does not mean that one causes changes in the other. Correlation merely evaluates correlations between variables, and various circumstances may cause the associations. Causation is one plausible explanation for the association, but this is not the only one.
The formula to obtain the Correlation coefficient
Between two variables, To calculate the correlation coefficient, we need to use the following formula:
r = n× (∑(X,Y)− (∑(X) × ∑(Y))) /
√(n×∑ ( X2 )-∑( X) 2) × ( n× ∑( Y2 )-∑(Y)2 )
Where
r= correlation coefficient
n = Number of observations
x,y= types of Variables
What are the main types of correlation?
There are mainly four types of correlation. They are as follows:
Kendall Rank correlation
It is a non-parametric test that determines how two variables are interdependent. We know that the total combinations with a b are n(n-1)/2 if we take two samples, a and b, each with a sample size of n. The value of Kendall rank correlation is calculated using the following formula:
𝘁= nc-nd / 1/2n (n-1)
Where
nc stands for the number of (concordant; positioned in the same way)
nd denotes the number of (discordant; differently ordered)
Pearson correlation
The Pearson r correlation is the most extensively used correlation statistic for determining the degree of linearly linked variables' association. For example, in the share market, then it is used to determine how closely two stocks are connected. The formula is used for the point-biserial correlation, but one of the variables is dualistic.
The Pearson r correlation is calculated using the following formula:
r= NΣxy-(Σx) (Σy)/
√ [NΣx2-(Σx)2] [NΣy2 - (Σy)2]
Where:
N = number of pairs of scores
Σxy = a sum of the products of paired scores
Σy = the sum of y scores
Σx = the sum of x scores
Σy2 = the sum of squared y scores
Σx2 = the sum of squared x scores
Spearman rank correlation
It is a non-parametric test used to determine the relationship between two variables. When the variables are assessed on a level that is at least ordinal, the Spearman rank-order correlation test is the proper correlation analysis since it makes no assumptions about the data distribution.
Calculate Spearman rank correlation using the following formula:
𝘱= 1- 6 Σ di2 / n(n2-1)
Where,
ρ= Spearman rank correlation
n= number of observations
di= the difference between corresponding variables ranks
Point-Biserial correlation
This is another type of correlation where the strength and direction of the link between one continuous function and one dichotomous variable are measured. It's a variant of Pearson's product-moment correlation, which is used when two continuous variables are compared; however, one of the variables is examined on a dichotomous scale in this case.
Therefore, point-biserial correlation measures the strength of a relationship between two variables where one variable of interest includes one continuous while the other is a binary variable.
rpb = M1-M0
√ pq
Sn
Where
M1= Mean of the total group receiving a positive binary variable( 1)
M0= Mean of the whole group receiving a negative binary variable (0)
Sn= Standard derivation for the entirety of the test
p= proportional cases in the 0 group
q= proportional cases in the 1 group
Relevance of Correlation in business
Business executives may use regression and correlation analysis to make accurate forecasts based on data trends. This strategy may assist lead corporate procedures, perspective, and effectiveness in the right direction, resulting in better management, consumer experience strategies, and operations. Therefore, correlation plays a holistic role in business.
What is the significance of correlation in finance?
Correlations are crucial in finance since they are used to anticipate future trends and manage portfolio risks. Correlations between commodities can now be easily calculated using various software and internet platforms. In the construction and price of derivatives and other complex financial products, correlations, including different concepts, play a critical role in finance.
What is the correlation definition?
In the financial and investment sectors, correlation is a measure that quantifies how closely two commodities move concerning one another. Advanced portfolio management employs correlations, calculated as the correlation coefficient, that must lie between -1.0 and +1.0.
When is point-biserial correlation used?
The use of point-biserial is applicable in the following scenario:
To know about the relationship between two variables
When there is one continuous and one binary variable present
When there are only two variables present
What does a correlation tell you numerically?
Since the value of correlation ranges between 1 and -1, the correlation coefficient is 1 in a total positive correlation. The other security travels up and down in response to the movement of one security. An absolute negative correlation indicates that two commodities move in opposing directions, whereas a zero correlation indicates that there is no linear link.
Disclaimer: This content is authored by an external agency. The views expressed here are that of the respective authors/ entities and do not represent the views of Economic Times (ET). ET does not guarantee, vouch for or endorse any of its contents nor is responsible for them in any manner whatsoever. Please take all steps necessary to ascertain that any information and content provided is correct, updated and verified. ET hereby disclaims any and all warranties, express or implied, relating to the report and any content therein.
What is Correlation?
In statistics, a correlation estimates how closely two variables are related. This sums up the correlation definition. The measure works best with variables that have a linear connection. A scatterplot is used to check how well the data fits together. We may analyse the association between the factors and decide if they are correlated or not using a scatterplot.
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Correlation Coefficient valueA correlation coefficient is a value that shows a strong link existing between two variables. The coefficient might be any figure between -1 and 1. The following are the values' interpretations:
-1: The greatest possible negative correlation. Variables tend to move in opposing directions (i.e., one variable increases, the other decreases).
0: There is no correlation. The variables don't have any link.
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1: There is a perfect positive correlation here. The variables tend to follow the same path (i.e., an increase in one variable leads to a rise in the other).
What is the difference between correlation and causation?
It's important to distinguish between correlation and causation. The statement "correlation does not imply causation" is critical to comprehending the two statistical notions.
Correlation between two variables does not mean that one causes changes in the other. Correlation merely evaluates correlations between variables, and various circumstances may cause the associations. Causation is one plausible explanation for the association, but this is not the only one.
The formula to obtain the Correlation coefficient
Between two variables, To calculate the correlation coefficient, we need to use the following formula:
r = n× (∑(X,Y)− (∑(X) × ∑(Y))) /
√(n×∑ ( X2 )-∑( X) 2) × ( n× ∑( Y2 )-∑(Y)2 )
Where
r= correlation coefficient
n = Number of observations
x,y= types of Variables
What are the main types of correlation?
There are mainly four types of correlation. They are as follows:
Kendall Rank correlation
It is a non-parametric test that determines how two variables are interdependent. We know that the total combinations with a b are n(n-1)/2 if we take two samples, a and b, each with a sample size of n. The value of Kendall rank correlation is calculated using the following formula:
𝘁= nc-nd / 1/2n (n-1)
Where
nc stands for the number of (concordant; positioned in the same way)
nd denotes the number of (discordant; differently ordered)
Pearson correlation
The Pearson r correlation is the most extensively used correlation statistic for determining the degree of linearly linked variables' association. For example, in the share market, then it is used to determine how closely two stocks are connected. The formula is used for the point-biserial correlation, but one of the variables is dualistic.
The Pearson r correlation is calculated using the following formula:
r= NΣxy-(Σx) (Σy)/
√ [NΣx2-(Σx)2] [NΣy2 - (Σy)2]
Where:
N = number of pairs of scores
Σxy = a sum of the products of paired scores
Σy = the sum of y scores
Σx = the sum of x scores
Σy2 = the sum of squared y scores
Σx2 = the sum of squared x scores
Spearman rank correlation
It is a non-parametric test used to determine the relationship between two variables. When the variables are assessed on a level that is at least ordinal, the Spearman rank-order correlation test is the proper correlation analysis since it makes no assumptions about the data distribution.
Calculate Spearman rank correlation using the following formula:
𝘱= 1- 6 Σ di2 / n(n2-1)
Where,
ρ= Spearman rank correlation
n= number of observations
di= the difference between corresponding variables ranks
Point-Biserial correlation
This is another type of correlation where the strength and direction of the link between one continuous function and one dichotomous variable are measured. It's a variant of Pearson's product-moment correlation, which is used when two continuous variables are compared; however, one of the variables is examined on a dichotomous scale in this case.
Therefore, point-biserial correlation measures the strength of a relationship between two variables where one variable of interest includes one continuous while the other is a binary variable.
rpb = M1-M0
√ pq
Sn
Where
M1= Mean of the total group receiving a positive binary variable( 1)
M0= Mean of the whole group receiving a negative binary variable (0)
Sn= Standard derivation for the entirety of the test
p= proportional cases in the 0 group
q= proportional cases in the 1 group
Relevance of Correlation in business
Business executives may use regression and correlation analysis to make accurate forecasts based on data trends. This strategy may assist lead corporate procedures, perspective, and effectiveness in the right direction, resulting in better management, consumer experience strategies, and operations. Therefore, correlation plays a holistic role in business.
What is the significance of correlation in finance?
Correlations are crucial in finance since they are used to anticipate future trends and manage portfolio risks. Correlations between commodities can now be easily calculated using various software and internet platforms. In the construction and price of derivatives and other complex financial products, correlations, including different concepts, play a critical role in finance.
What is the correlation definition?
In the financial and investment sectors, correlation is a measure that quantifies how closely two commodities move concerning one another. Advanced portfolio management employs correlations, calculated as the correlation coefficient, that must lie between -1.0 and +1.0.
When is point-biserial correlation used?
The use of point-biserial is applicable in the following scenario:
To know about the relationship between two variables
When there is one continuous and one binary variable present
When there are only two variables present
What does a correlation tell you numerically?
Since the value of correlation ranges between 1 and -1, the correlation coefficient is 1 in a total positive correlation. The other security travels up and down in response to the movement of one security. An absolute negative correlation indicates that two commodities move in opposing directions, whereas a zero correlation indicates that there is no linear link.
Disclaimer: This content is authored by an external agency. The views expressed here are that of the respective authors/ entities and do not represent the views of Economic Times (ET). ET does not guarantee, vouch for or endorse any of its contents nor is responsible for them in any manner whatsoever. Please take all steps necessary to ascertain that any information and content provided is correct, updated and verified. ET hereby disclaims any and all warranties, express or implied, relating to the report and any content therein.
