Difference between revisions of "Manuals/calci/PEARSON"
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==Description== | ==Description== | ||
| − | *This function gives the Pearson | + | *This function gives the Pearson product-moment correlation coefficient. |
*It is denoted by PPMC, which shows the linear relationship between two variables. | *It is denoted by PPMC, which shows the linear relationship between two variables. | ||
*It is a measure of the strength of a linear association between two variables . | *It is a measure of the strength of a linear association between two variables . | ||
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<math> r= \frac{ \Sigma(x-\bar{x})(y-\bar{y})}{\sqrt {\Sigma(x-\bar{x})^2(y-\bar{y})^2}}</math> | <math> r= \frac{ \Sigma(x-\bar{x})(y-\bar{y})}{\sqrt {\Sigma(x-\bar{x})^2(y-\bar{y})^2}}</math> | ||
| − | where <math> \bar{x} and \bar{y} </math> are Average of the two Samples x and y. | + | where <math> \bar{x}</math> and <math>\bar{y} </math> are Average of the two Samples <math>x </math> and <math>y </math>. |
| − | *In <math>PEARSON(ar1,ar2)</math> , the value of <math> ar1</math> and <math> ar2</math> must be either numbers or names, array,constants or references that contain numbers. | + | *In <math>PEARSON(ar1,ar2)</math>, the value of <math> ar1</math> and <math> ar2</math> must be either numbers or names, array,constants or references that contain numbers. |
*Suppose the array contains text,logicl values or empty cells, like that values are not considered. | *Suppose the array contains text,logicl values or empty cells, like that values are not considered. | ||
*This function will return the result as error when the number of values are different for <math> ar1 </math> and <math> ar2 </math>. | *This function will return the result as error when the number of values are different for <math> ar1 </math> and <math> ar2 </math>. | ||
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==References== | ==References== | ||
| + | [http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Pearson] | ||
Revision as of 02:00, 7 January 2014
PEARSON (ar1,ar2)
- is the array of independent values
- is the array of dependent values.
is the array of independent values
is the array of dependent values.Description
- This function gives the Pearson product-moment correlation coefficient.
- It is denoted by PPMC, which shows the linear relationship between two variables.
- It is a measure of the strength of a linear association between two variables .
- The two variables and , giving a value between +1 and −1 inclusive.
- Here +1 indicates the perfect positive correlation, 0 indicates no correlation and -1 indicates the perfect negative correlation.
- The formula for PPMC, is defined by:
and 
, giving a value between +1 and −1 inclusive.
is defined by:
where and are Average of the two Samples and .
and 
are Average of the two Samples 
and 
.
- In , the value of and must be either numbers or names, array,constants or references that contain numbers.
- Suppose the array contains text,logicl values or empty cells, like that values are not considered.
- This function will return the result as error when the number of values are different for and .
, the value of Examples
- 1.Array1 Array2
5 8 9 12 10 15 PEARSON(B1:B3,C1:C3)=0.968619605
- 2.Array1 Array2
17 10
0 11 19 7 25 13 PEARSON(D1:D4,E1:E4)=-0.759206026
- 3.Array1 Array2
1 4 2 5 3 PEARSON(A1:A3,B1:B2)=NAN