Correlation Coefficient Calculator
How to use the Correlation Coefficient Calculator?
The instructions to use this calculator are:
- Enter the values of the first dataset.
- Enter the values of the second dataset.
- Click calculate or press enter.
The instructions to use this calculator are:
The correlation coefficient calculator uses Pearson’s method to find the correlation. You will find each step that you will need in the results. Lastly, this tool also analyzes the result and tells how strong a correlation exists between two data sets.
It tells you the nature of the relation between two different sets. The absolute correlation value indicates the strength of this relationship while the positive or negative sign indicates the direction of this relationship.
Scatter plots are also used to get an idea of possible connectivity between two variables. Usually, one variable is plotted against the x-axis while the other is against the y-axis. It is then observed if a linear pattern exists.
The value ranges between +1 and -1. A positive relation will mean one set affects the other set directly while a negative relation means they affect inversely. Zero correlation would mean they are not connected at all.
The formula used for Pearson’s correlation coefficient is
Where
The size of the data set is directly related to the reliability of the correlation coefficient value. A larger set is likely to give a more accurate relation status. The steps to find covariance are:
Set X = 10,34,23,54,9
Set Y = 4,5,11,15,20
Solution:
Step 1: Find the covariance of x and y.
Calculating mean for x and y.
Xmean = 10+34+23+54+9 / 5
= 130/5
=26
Ymean = 4+5+11+15+20/5
= 55/5
= 11
Find covariance.
∑ (xi - X̄) (yi - ȳ) = 23
Step 2: Find the standard deviation of x.
= √ ∑ (xi - X̄)2
Taking the data for the sum of squares from the previous step,
= √ (256 + 64 + 9 + 784 + 289)
= √ (1402)
Step 3: Find the standard deviation of y.
= √ ∑ (yi - ȳ)2
Taking the data for the sum of squares from the first step,
= √ (49 + 36 + 0 + 16 + 81)
= √(182)
Step 4: Use the correlation coefficient formula.
= 23 / √ (1402)√(182)
= 23 /505.1376
= 0.0455
Step 5: Analyze.
Since it is greater than 0, the correlation is positive.
Value is 0.04 hence weak correlation.
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