Manuals/calci/CORREL

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