Difference between revisions of "Manuals/calci/PEARSON"

Revision as of 03:00, 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 $PEARSON(ar1,ar2)$ , the value of $ar1$ and $ar2$ 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 $ar1$ and $ar2$ .

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 1: / Line 1: @@
 <div style="font-size:30px">'''PEARSON (ar1,ar2)'''</div><br/>
-*<math>ar1</math> is the array of independent values
+*<math>ar_1</math> is the array of independent values
-*<math>ar2</math> is the array of dependent values.
+*<math>ar_2</math> is the array of dependent values.
 ==Description==
-*This function gives the Pearson product-moment correlation coefficient.
+*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  <math> X </math>  and <math> Y </math>, 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.
+*Here
+ +1 indicates the perfect positive correlation,
+indicates no correlation
+ -1 indicates the perfect negative correlation.
 *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>