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Correlation Coefficient is used to understand and establish a relationship between variables. In finances, it is used to analyze and understand the set variables. In business, the correlation coefficient helps determine future sales and market trends.
A correlation coefficient is a statistical approach that measures the strength and direction of the relationship between the two variables. It is used to measure the dependency of the response variable on the explanatory variable.
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Pearson correlation is used to examine the linear relationship between the two separate variables. The correlation coefficient will show values closer to + 1 and -1 when the relationship is stronger between the variables.
It is the most used type of correlation coefficient. We will be using the Pearson Correlation formula to explain how you can calculate Correlation Coefficient.
The Spearman Correlation helps to determine the monotonic nature of the relationship between the variables. This method does not use the dataset that follows a normal distribution. Instead, it uses ordinal variables.
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ρX,Y = cov(X,Y)σXσY
= ∑ni=1(Xi−¯X) (Yi−¯Y)/ √ΣnΣi=1(Xi−¯X)2√∑nΣi=1(Yi−¯Y)2
σX: standard deviation of x
σY: standard deviation of y
rx,y = ∑ni=1(xi−¯x)(yi−¯y) / √ΣnΣi=1(xi−¯x)2√∑nΣi=1(yi−¯y)2
r = n(Σxy)−(Σx)(Σy) / √[nΣx2−(Σx)2][nΣy2−(Σy)2]
This is the formula that you may have seen the most. It is the Pearson Correlation formula applied to a sample.
Explaining the terms:
When we rearrange the formula, we get:
Further rearranging the formula gives us a simplified formula for Correlation Coefficient:
Now with the simplified formula, we will begin the steps to calculate the correlation coefficient.