Difference between revisions of "Manuals/calci/CORREL"
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*The <math>r</math> value is negative i.e. (-1) when one value decreases as the other increases then it is called Negative Correlation. | *The <math>r</math> value is negative i.e. (-1) when one value decreases as the other increases then it is called Negative Correlation. | ||
*Suppose the <math>r</math> value is 0 then there is no correlation (the values don't seem linked at all). | *Suppose the <math>r</math> value is 0 then there is no correlation (the values don't seem linked at all). | ||
| − | *If we have a series of <math>n</math> measurements of <math>X</math> and <math>Y</math> written as <math> | + | *If we have a series of <math>n</math> measurements of <math>X</math> and <math>Y</math> written as <math>x_i</math> and <math>y_i</math> where <math>i = 1, 2,...n</math> then the Sample Correlation Coefficient is: |
| − | <math>CORREL(X,Y)= r_{xy}= \frac{\sum_{i=1}^n ( | + | <math>CORREL(X,Y)= r_{xy}= \frac{\sum_{i=1}^n (x_i-\bar x)(y_i-\bar y)}{\sqrt{ \sum_{i=1}^n (x_i-\bar x)^2 \sum_{i=1}^n (y_i-\bar y)^2}}</math> |
*<math>\bar x</math> and <math>\bar y</math> are the sample means of <math>X</math> and <math>Y</math>. | *<math>\bar x</math> and <math>\bar y</math> are the sample means of <math>X</math> and <math>Y</math>. | ||
*This function will give the result as error when | *This function will give the result as error when | ||
Revision as of 22:28, 10 December 2013
CORREL(ar1,ar2)
- and are the set of values.
and 
are the set of values.Description
- This function gives the correlation coefficient of the 1st set() of values and 2nd set() of values.
- Correlation is a statistical technique which shows the relation of strongly paired variables.
- For example, test average and study time are related; those who spending more time to study will get high marks and Average will go down for those who spend less time for studies.
- There are different correlation techniques to measure the Degree of Correlation.
- The most common of these is the Pearson Correlation Coefficient denoted by .
- The main result of a correlation is called the Correlation Coefficient()which ranges from -1 to +1.
- The value is positive i.e +1 when the two set values increase together then it is the perfect Positive Correlation.
- The value is negative i.e. (-1) when one value decreases as the other increases then it is called Negative Correlation.
- Suppose the value is 0 then there is no correlation (the values don't seem linked at all).
- If we have a series of measurements of and written as and where then the Sample Correlation Coefficient is:
.
)which ranges from -1 to +1.
measurements of 
and 
written as 
and 
where 
then the Sample Correlation Coefficient is:
- and are the sample means of and .
- This function will give the result as error when
and 
are the sample means of 1. and are non-numeric or different number of data points. 2. or is empty 3.The denominator value is zero.
- Suppose and contains any text, logical values, or empty cells, like that values are ignored.
Examples
- Find the correlation coefficients for X and Y values are given below :X={1,2,3,4,5}; Y={11,22,34,43,56}
=CORREL(A4:A8,B4:B8)=0.99890610723867
- The following table gives the math scores and times taken to run 100 m for 10 friends:SCORE(X)={52,25,35,90,76,40}; TIME TAKEN(Y)={11.3,12.9,11.9,10.2,11.1,12.5}
=CORREL(A5:A10,B5:B10)= -0.93626409417769
- Find the correlation coefficients for X and Y values are given below :X={-4,11,34,87};Y={9,2,59,24}
=CORREL(A1:A4,B1:B4)=0.353184665607273
See Also