Difference between revisions of "Manuals/calci/CORREL"

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*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>xi</math> and <math>yi</math> where <math>i</math> = 1, 2,...n then the Sample Correlation Coefficient is:
 
*If we have a series of <math>n</math> measurements of <math>X</math> and <math>Y</math> written as <math>xi</math> and <math>yi</math> where <math>i</math> = 1, 2,...n then the Sample Correlation Coefficient is:
−
  <math>CORREL(X,Y)= r_{xy}= \frac{\sum_{i=1}^n (xi-\bar x)(yi-\bar y)}{\sqrt{ \sum_{i=1}^n (xi-\bar x)^2 \sum{i=1}^n (yi-\bar y)^2}}</math>, where x(bar) and y(bar) are the sample means of X and Y. *This function will give the result as error when  
+
  <math>CORREL(X,Y)= r_{xy}= \frac{\sum_{i=1}^n (xi-\bar x)(yi-\bar y)}{\sqrt{ \sum_{i=1}^n (xi-\bar x)^2 \sum{i=1}^n (yi-\bar y)^2}}</math>
−
#ar1 and ar2 are nonnumeric or different number of data points.
+
*<math>\bar x</math> and <math>\bar y</math> are the sample means of <math>X</math> and <math>Y</math>.
−
#ar1 or ar2 is empty
+
*This function will give the result as error when  
−
#The denominator value is zero.
+
1.<math>ar1</math> and <math>ar2</math> are non-numeric or different number of data points.
−
*Suppose ar1 and ar2 contains any text, logical values, or empty cells, like that values are ignored.
+
2.<math>ar1</math> or <math>ar2</math> is empty
 +
3.The denominator value is zero.
 +
*Suppose <math>ar1</math> and <math>ar2</math> contains any text, logical values, or empty cells, like that values are ignored.
  
 
==Examples==
 
==Examples==

Revision as of 23:30, 9 December 2013

CORREL(ar1,ar2)


  • 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 ar1} 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 ar2 } are the set of values.

Description

  • This function gives the correlation coefficient of the 1st set(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 ar1} ) of values and 2nd set(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 ar2} ) 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 r xy.
  • The main result of a correlation is called the Correlation Coefficient(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} )which ranges from -1 to +1.
  • The 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} value is positive i.e +1 when the two set values increase together then it is the perfect Positive Correlation.
  • The 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} value is negative i.e. (-1) when one value decreases as the other increases then it is called Negative Correlation.
  • Suppose the 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} value is 0 then there is no correlation (the values don't seem linked at all).
  • If we have a series 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 n} measurements 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 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} written as 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 xi} 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 yi} where = 1, 2,...n then the Sample Correlation Coefficient is:
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 CORREL(X,Y)= r_{xy}= \frac{\sum_{i=1}^n (xi-\bar x)(yi-\bar y)}{\sqrt{ \sum_{i=1}^n (xi-\bar x)^2 \sum{i=1}^n (yi-\bar y)^2}}}
  • 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 the sample means 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 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} .
  • This function will give the result as error when
1.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 ar1}
 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 ar2}
 are non-numeric or different number of data points.
2.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 ar1}
 or 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 ar2}
 is empty
3.The denominator value is zero.
  • Suppose 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 ar1} 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 ar2} contains any text, logical values, or empty cells, like that values are ignored.

Examples

  1. 1. 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

  1. 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
  2. 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


References

Bessel Function

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