Manuals/calci/MCORREL

MCORREL (ArrayOfArrays)

$ArrayOfArrays$ is set of values.

Description

This function is showing the result for multiple correlation.
In $MCORREL(ArrayOfArrays)$ , $Arrayofarrays$ are set of values.
Correlation is a statistical technique which shows the relation of strongly paired variables.When one variable is related to a number of other variables, the correlation is not simple.
It is multiple if there is one variable on one side and a set of variables on the other side.
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 $Y$ .
The above formula is used for simple correlation.
Now consider the variables x,y and z we define the multiple correlation as:

$R_{zxy}={\sqrt {\frac {r_{xz}^{2}+r_{yz}^{2}-2r_{xz}r_{yz}r_{xy}}{1-r_{xy}^{2}}}}$

$r_{xy}$ is the correlation of x and y.
$r_{yz}$ is the correlation of y and z.
$r_{zx}$ is the correlation of z and x.
Here x and y are viewed as the independent variables and z is the dependent variable.
This function will give the result as error when