Difference between revisions of "Manuals/calci/PEARSON"

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<div style="font-size:30px">'''PEARSON (ar1,ar2)'''</div><br/>
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<div style="font-size:30px">'''PEARSON (Array1,Array2)'''</div><br/>
−
*<math>ar1</math> is the array of independent values and <math>ar2</math> is the array of dependent values.
+
*<math>Array1</math> is the array of independent values  
 +
*<math>Array2</math> is the array of dependent values.
 +
**PEARSON(),returns the Pearson product moment correlation coefficient.
  
 
==Description==
 
==Description==
−
*This function gives the Pearson productmoment correlaton 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 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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*The two variables  X and Y, giving a value between +1 and −1 inclusive.  
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*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  
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*The formula for PPMC,r is defined by:
+
+1 indicates the perfect positive correlation,
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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>     
+
  0 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>     
  
−
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>.
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*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.  
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*In  <math>PEARSON(Array1,Array2)</math>, the value of <math>Array1</math> and <math>Array2</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 ar1 and ar2.
+
*This function will return the result as error when the number of values are different for <math> Array1 </math> and <math> Array2 </math>.
  
 
==Examples==
 
==Examples==
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#Array1          Array2
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{| class="wikitable"
−
5                        8
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|+Spreadsheet
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9                        12
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|-
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10                      15
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! !! A !! B !! C
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PEARSON(B1:B3,C1:C3)=0.968619605
+
|-
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#Array1            Array2
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! 1
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17                    10
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| 5 || 9 || 10  
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0                        11
+
|-
−
19                        7
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! 2
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25                      13
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| 8 || 12 || 15
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PEARSON(D1:D4,E1:E4)=-0.759206026
+
|}
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#Array1            Array2
 
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1                        4
 
−
2                       5
 
−
3
 
−
PEARSON(A1:A3,B1:B2)=NAN
 
  
 +
=PEARSON(A1:C1,A2:C2) = 0.968619605
 +
2.
 +
{| class="wikitable"
 +
|+Spreadsheet
 +
|-
 +
! !! A !! B !! C !!D
 +
|-
 +
! 1
 +
| 17 || 0 || 19 ||25
 +
|-
 +
! 2
 +
| 10 || 11 || 7 ||13
 +
|}
  
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==See Also==
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=PEARSON(A1:D1,A2:D2) = 0.034204238054579846
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*[[Manuals/calci/INTERCEPT  | INTERCEPT ]]
 
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*[[Manuals/calci/SLOPE  | SLOPE ]]
 
  
−
==References==
+
3.
 +
{| class="wikitable"
 +
|+Spreadsheet
 +
|-
 +
! !! A !! B !! C
 +
|-
 +
! 1
 +
| 1 || 2 || 3
 +
|-
 +
! 2
 +
| 4 || 5 ||
 +
|}
  
 +
=PEARSON(A1:C1,A2:B2) = NAN
  
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'''Array1,''' -  represents a set of independent values.
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==Related Videos==
  
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'''Array2''' - represents a of dependent values.
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{{#ev:youtube|JO-Gc5bEG70|280|center|PEARSON}}
  
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</div>
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==See Also==
−
----
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*[[Manuals/calci/INTERCEPT  | INTERCEPT ]]
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<div id="1SpaceContent" class="zcontent" align="left">
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*[[Manuals/calci/SLOPE  | SLOPE ]]
  
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Returns the Pearson product momment correlation coefficient(P).
+
==References==
 +
[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient Pearson]
  
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Formula :-
 
  
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P =
 
  
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</div>
 
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----
 
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<div id="7SpaceContent" class="zcontent" align="left">If Length of Array1 =! Length of Array2 , PEARSON returns the #ERROR.</div>
 
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----
 
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<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
 
  
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PEARSON
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*[[Z_API_Functions | List of Main Z Functions]]
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</div></div>
 
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----
 
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<div id="8SpaceContent" class="zcontent" align="left">
 
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Lets see an example in (Column3, Row1)
 
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UNIQa9cacf80da78a549-nowiki-00000002-QINU
 
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PEARSON returns -0.015.811.
 
−
 
 
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</div>
 
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----
 
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
 
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----
 
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
 
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----
 
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
 
−
----
 
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
 
−
----
 
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<div id="2SpaceContent" class="zcontent" align="left">
 
−
 
 
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{| id="TABLE3" class="SpreadSheet blue"
 
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|- class="even"
 
−
| class=" " |
 
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| class="  " | Column1
 
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| class="  " | Column2
 
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| class="  " | Column3
 
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| Column4
 
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|- class="odd"
 
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| class=" " | Row1
 
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| class=" " | 5
 
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| class="                sshl_f " | 1
 
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| class="sshl_f" | -0.015811
 
−
|
 
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|- class="even"
 
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| class="  " | Row2
 
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| class=" " | 8
 
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| class=" " | 2
 
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| class=" SelectTD ChangeBGColor SelectTD" |
 
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<div id="2Space_Handle" class="zhandles" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="2Space_Copy" class="zhandles" title="Click and Drag over to AutoFill other cells."></div><div id="2Space_Drag" class="zhandles" title="Click and Drag to Move/Copy Area.">[[Image:copy-cube.gif]]  </div>
 
−
|
 
−
|- class="odd"
 
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| Row3
 
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| class=" " | 9
 
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| class=" " | 5
 
−
|
 
−
|
 
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|- class="even"
 
−
| Row4
 
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| class=" " | 7
 
−
| class=" " | 8
 
−
|
 
−
|
 
−
|- class="odd"
 
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| class=" " | Row5
 
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| class=" " | 1
 
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| class=" " | 4
 
−
|
 
−
|
 
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|- class="even"
 
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| Row6
 
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| class=" " | 2
 
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| class=" " | 6
 
−
|
 
−
|
 
−
|}
 
  
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<div align="left">[[Image:calci1.gif]]</div></div>
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*[[ Z3 |  Z3 home ]]
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----
 

Latest revision as of 15:01, 8 August 2018

PEARSON (Array1,Array2)


  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array1} is the array of independent values
  • Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array2} is the array of dependent values.
    • PEARSON(),returns the Pearson product moment correlation coefficient.

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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle X } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle 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.
  • The formula for PPMC, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r } is defined by:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r= \frac{ \Sigma(x-\bar{x})(y-\bar{y})}{\sqrt {\Sigma(x-\bar{x})^2(y-\bar{y})^2}}}

where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{x}} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \bar{y} } are Average of the two Samples Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y } .

  • In Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle PEARSON(Array1,Array2)} , the value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array1} and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array2} 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 Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array1 } and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle Array2 } .

Examples

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) = 0.034204238054579846

3.

Spreadsheet
A B C
1 1 2 3
2 4 5 
=PEARSON(A1:C1,A2:B2) = NAN

Related Videos

PEARSON

See Also

References

Pearson



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