Enter the X and Y values as comma-separated numbers into the calculator to determine the correlation factor. This calculator helps to evaluate the strength and direction of the relationship between two variables.
Correlation Factor Formula
The following formula is used to calculate the correlation factor (r):
r = Σ[(xi - x̄)(yi - ȳ)] / [√(Σ(xi - x̄)²) * √(Σ(yi - ȳ)²)]
Variables:
- r is the correlation factor
- xi are the X values
- yi are the Y values
- x̄ is the mean of the X values
- ȳ is the mean of the Y values
To calculate the correlation factor, first find the mean of the X values and the mean of the Y values. Then, for each pair of X and Y values, subtract the mean of X from X and the mean of Y from Y, multiply these results together, and sum them up. Finally, divide this sum by the product of the square root of the sum of squared differences from the mean for X and Y values.
What is a Correlation Factor?
A correlation factor, also known as the Pearson correlation coefficient, measures the strength and direction of the linear relationship between two variables. It ranges from -1 to 1, where 1 indicates a perfect positive correlation, -1 indicates a perfect negative correlation, and 0 indicates no linear correlation.
How to Calculate Correlation Factor?
The following steps outline how to calculate the correlation factor.
- First, input the X and Y values as comma-separated numbers.
- Next, calculate the mean of the X values (x̄) and the mean of the Y values (ȳ).
- Then, for each pair of X and Y values, calculate (xi – x̄)(yi – ȳ) and sum these values.
- Calculate the sum of squared differences from the mean for X and Y values, and take the square root of each.
- Finally, divide the sum from step 3 by the product of the results from step 4 to get the correlation factor (r).
- Use the calculator above to check your calculations.
Example Problem :
Use the following variables as an example problem to test your knowledge.
X values = 1,2,3,4
Y values = 2,3,4,5
