Difference between revisions of "Manuals/calci/CORREL"

Revision as of 14:45, 14 June 2018

CORREL(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} 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 } 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 Array1} ) 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 Array2} ) 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 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_{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 correlation calculation only works well for relationships that follow a straight line.
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 $r$ 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 x_i} 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_i} 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 i = 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 (x_i-\bar x)(y_i-\bar y)}{\sqrt{ \sum_{i=1}^n (x_i-\bar x)^2 \sum_{i=1}^n (y_i-\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 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}
 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 Array1}
 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 Array2}
 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 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} contains any text, logical values, or empty cells, like that values are ignored.

ZOS

The syntax is to calculate CORREL in ZOS 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(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} and $Array2$ are the set of values.
For e.g.,CORREL([(-5)..(-1)],[10..15])

Correlation Coefficient

Examples

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

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

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

References

Correlation

List of Main Z Functions

Z3 home

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''CORREL(array1,array2)'''</div><br/>
+<div style="font-size:30px">'''CORREL(Array1,Array2)'''</div><br/>
-*<math>array1</math> and <math>array2 </math> are the set of values.
+*<math>Array1</math> and <math>Array2 </math> are the set of values.
 ==Description==
-*This function gives the correlation coefficient of the 1st set(<math>array1</math>) of values and 2nd set(<math>array2</math>) of values.
+*This function gives the correlation coefficient of the 1st set(<math>Array1</math>) of values and 2nd set(<math>Array2</math>) 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.
@@ Line 17: / Line 17: @@
 *<math>\bar x</math> and <math>\bar y</math> are the sample means of <math>X</math> and <math>Y</math>.
 *This function will give the result as error when
-.<math>array1</math> and <math>array2</math> are non-numeric or different number of data points.
+.<math>Array1</math> and <math>Array2</math> are non-numeric or different number of data points.
-.<math>array1</math> or <math>array2</math> is empty
+.<math>Array1</math> or <math>Array2</math> is empty
 .The denominator value is zero.
-*Suppose <math>array1</math> and <math>array2</math> contains any text, logical values, or empty cells, like that values are ignored.
+*Suppose <math>Array1</math> and <math>Array2</math> contains any text, logical values, or empty cells, like that values are ignored.
 ==ZOS==
-*The syntax is to calculate CORREL in ZOS is <math>CORREL(array1,array2)</math>.
+*The syntax is to calculate CORREL in ZOS is <math>CORREL(Array1,Array2)</math>.
-**<math>array1</math> and <math>array2 </math> are the set of values.
+**<math>Array1</math> and <math>Array2 </math> are the set of values.
 *For e.g.,CORREL([(-5)..(-1)],[10..15])
 {{#ev:youtube|Il4jCpJy0IA|280|center|Correlation Coefficient}}

Difference between revisions of "Manuals/calci/CORREL"

Revision as of 14:45, 14 June 2018

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