Difference between revisions of "Manuals/calci/CORREL"

Latest revision as of 03:26, 25 August 2020

CORREL(Array1,Array2)

and are the set of values.
- CORREL(), returns the correlation coefficient between two data sets.

Description

This function gives the correlation coefficient of the 1st set( $Array1$ ) of values and 2nd set( $Array2$ ) 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 $r_{xy}$ .
The main result of a correlation is called the Correlation Coefficient( $r$ )which ranges from -1 to +1.
The correlation calculation only works well for relationships that follow a straight line.
The $r$ value is positive i.e +1 when the two set values increase together then it is the perfect Positive Correlation.
The $r$ 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 $n$ measurements of $X$ and $Y$ written as $x_{i}$ and $y_{i}$ where $i=1,2,...n$ then the Sample Correlation Coefficient is:

 $CORREL(X,Y)=r_{xy}={\frac {\sum _{i=1}^{n}(x_{i}-{\bar {x}})(y_{i}-{\bar {y}})}{\sqrt {\sum _{i=1}^{n}(x_{i}-{\bar {x}})^{2}\sum _{i=1}^{n}(y_{i}-{\bar {y}})^{2}}}}$

${\bar {x}}$ and ${\bar {y}}$ are the sample means of $X$ and $Y$ .
This function will give the result as error when

1. $Array1$  and  $Array2$  are non-numeric or different number of data points.
2. $Array1$  or  $Array2$  is empty
3.The denominator value is zero.

Suppose $Array1$ and $Array2$ contains any text, logical values, or empty cells, like that values are ignored.

ZOS

The syntax is to calculate CORREL in ZOS is .
- $Array1$ and $Array2$ are the set of values.
For e.g.,CORREL([(-5)..(-1)],[10..15])

Correlation Coefficient

Examples

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

2. 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

3. 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

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-<div style="font-size:30px">'''CORREL(ar1,ar2)'''</div><br/>
+<div style="font-size:30px">'''CORREL(Array1,Array2)'''</div><br/>
-*<math>ar1</math> and <math>ar2 </math>are the set of values.
+*<math>Array1</math> and <math>Array2 </math> are the set of values.
+**CORREL(), returns the correlation coefficient between two data sets.
 ==Description==
-*This function gives the correlation coefficient of the 1st set(ar1) of values and 2nd set(ar2) 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 time more to study they will get high marks and spending less time for studies their Average will goes down.
+*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 measuring the degree of correlation.
+*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 most common of these is the Pearson Correlation Coefficient  denoted by <math>r_{xy}</math>.
-*The main result of a correlation is called the correlation coefficient (or "r")which  ranges from -1 to +1.
+*The main result of a correlation is called the Correlation Coefficient(<math>r</math>)which  ranges from -1 to +1.
-*The r value is positive i.e.+1  when the two set values increase together then it is the perfect positive correlation.
+*The correlation calculation only works well for relationships that follow a straight line.
-*The r value is negative i.e. (-1)  when one value decreases as the other increases then it is called negative correlation.
+*The <math>r</math> value is positive i.e +1  when the two set values increase together then it is the perfect Positive Correlation.
-*Suppose the r value is 0  then there is no correlation (the values don't seem linked at all).
+*The <math>r</math> value is negative i.e. (-1)  when one value decreases as the other increases then it is called Negative Correlation.
-*If we have a series of n measurements of X and Y written as xi and yi where i = 1, 2, ..., n, then the sample *correlation coefficient is: CORREL(X,Y)= r xy=[ summation(i=1 to n)(xi-x(bar))(yi-y(bar))]/ SQRT{ summation(i=1 to n)(xi-x(bar))^2 summation(i=1 to n)(yi-y(bar))^2], where x(bar) and y(bar) are the sample means of X and Y. *This function will give the result as error when
+*Suppose the <math>r</math> value is 0 then there is no correlation (the values don't seem linked at all).
-#ar1 and ar2 are nonnumeric or different number of data points.
+*If we have a series of <math>n</math> measurements of <math>X</math> and <math>Y</math> written as <math>x_i</math> and <math>y_i</math> where <math>i = 1, 2,...n</math> then the Sample Correlation Coefficient is:
-#ar1 or ar2 is empty
+ <math>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}}</math>
-#The denominator value is zero.
+*<math>\bar x</math> and <math>\bar y</math> are the sample means of <math>X</math> and <math>Y</math>.
-*Suppose ar1 and ar2 contains any text, logical values, or empty cells, like that values are ignored.
+*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> 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.
+==ZOS==
+*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.
+*For e.g.,CORREL([(-5)..(-1)],[10..15])
+{{#ev:youtube|Il4jCpJy0IA|280|center|Correlation Coefficient}}
 ==Examples==
-#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}
+. 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
+=CORREL(A4:A8,B4:B8)=0.99890610723867
-#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
+. 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
+==Related Videos==
+{{#ev:youtube|s2TVkYmmCAs|280|center|Correlation Coefficient}}
 ==See Also==
 *[[Manuals/calci/COVAR  | COVAR ]]
 *[[Manuals/calci/FISHER  | FISHER ]]
+==References==
+[http://en.wikipedia.org/wiki/Pearson_product-moment_correlation_coefficient  Correlation]
-==References==
-[http://en.wikipedia.org/wiki/Bessel_function| Bessel Function]
+*[[Z_API_Functions | List of Main Z Functions]]
+*[[ Z3 |   Z3 home ]]

Difference between revisions of "Manuals/calci/CORREL"

Latest revision as of 03:26, 25 August 2020

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Description

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Examples

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References

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