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:

Failed to parse (syntax error): {\displaystyle R_{zxy}=\sqrt{\frac{r_{xz}^2+r_{yz}^2-2 r_{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

1.$ArrayofArrays$ are non-numeric or different number of data points. 2.$ArrayofArrays$is empty 3.The denominator value is zero. 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 \sqrt{\frac{r_{xz}^2+r_{yz}^2-2 r_{xz} r_{yz} r_{xy}}{1-r_{xy}^2}}

See Also

• CORREL
• MINVERSE
• MMULT

References

• Multiple Correl

• List of Main Z Functions

• Z3 home