Correlation Coefficient Formula

About Correlation Coefficient Formula

Correlation is a statistical technique for determining the link or association between two variables. In other words, the correlation coefficient formula aids in the calculation of the correlation coefficient, which measures the relationship between two variables. The correlation coefficient is used to calculate the correlation. Between -1 and 1 is the correlation coefficient. The link between two variables is inverse when the correlation coefficient is negative. A positive correlation coefficient means that the value of one variable is directly influenced by the value of the other. There is no correlation between the two variables if the correlation coefficient is zero. There are several forms of correlation coefficients, the most common of which being the Pearson Correlation Coefficient (PCC). Let's look at how to find the correlation coefficient formula for a specific population or sample

What Is the Correlation Coefficient Formula?

A statistical notion is the correlation coefficient. It provides a link between expected and observed values at the conclusion of a statistical experiment. The correlation coefficient formula aids in the calculation of a link between two variables, and the resulting result explains the precision of the expected and actual values.

Pearson Correlation Coefficient Formula:

1. Sample Correlation Coefficient
   1. 
   2. 
   3. wherecovis the covariance and(cov(X,Y)=σ_Xis standard deviation of Xandσ_Yis standard deviation of Y.
   4. Given X and Y are two random variables.
2. Population Correlation Coefficient
   1. The formula for pearson correlation coefficient for sample of size n(written asr_xy) is given as:
   2. 
   3. wherenis the sample size,x_i & y_iare the i^thsample points and x ?& ?are the sample means for the random variables X and Y respectively.
   4. Given X and Y are two random variables.
3. Linear Correlation Coefficient
   1. It uses pearson's correlation coefficient to determine the linear relationship between two variables. Its value lies between -1 and 1. It is given as:
   2. 
   3. where is the sample size,x_i & y_iare the i^thsample points and x? & ?are the sample means for the random variables x and y respectively.
   4. The sign of r indicates the strength of the linear relationship between the variables.
      • If r is near 1, then the two variables have a strong linear relationship.
      • If r is near 0, then the two variables have no linear relation.
      • If r is near -1, then the two variables have a weak (negative) linear relationship.

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