Difference between revisions of "Manuals/calci/PEARSON"

Revision as of 02:01, 22 January 2014

PEARSON (ar1,ar2)

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 $X$ and $Y$ , giving a value between +1 and −1 inclusive.
Here

+1 indicates the perfect positive correlation,
 0 indicates no correlation 
-1 indicates the perfect negative correlation.

$r={\frac {\Sigma (x-{\bar {x}})(y-{\bar {y}})}{\sqrt {\Sigma (x-{\bar {x}})^{2}(y-{\bar {y}})^{2}}}}$

where ${\bar {x}}$ and ${\bar {y}}$ are Average of the two Samples $x$ and $y$ .

In $PEARSON(ar_{1},ar_{2})$ , the value of $ar_{1}$ and $ar_{2}$ 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 $ar_{1}$ and $ar_{2}$ .

Spreadsheet
	A	B	C
1	5	9	10
2	8	12	15

=PEARSON(A1:C1,A2:C2) = 0.968619605

2.

Spreadsheet
	A	B	C	D
1	17	0	19	25
2	10	11	7	13

=PEARSON(A1:D1,A2:D2) = -0.759206026

3.

Spreadsheet
	A	B	C
1	1	2	3
2	4	5

=PEARSON(A1:C1,A2:B2) = NAN

@@ Line 12: / Line 12: @@
 indicates no correlation
   -1 indicates the perfect negative correlation.
-*The formula for PPMC,<math> r </math> is defined by:
+*The formula for PPMC, <math> r </math> is defined by:
 <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}</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(ar_1,ar_2)</math>, the value of <math> ar_1</math> and <math> ar_2</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> ar_1 </math> and <math> ar_2 </math>.
 ==Examples==