# GUIcorr

GUIcorr shows the necessary calculations to obtain the correlation in a GUI.

## Syntax

• out=GUIcorr(x,y)example
• out=GUIcorr(x,y,w)example

## Description

 out =GUIcorr(x, y) Example of unweighted covariance.

 out =GUIcorr(x, y, w) Example 1 of weighted correlation.

## Examples

expand all

### Example of unweighted covariance.

The data below are referred to monthly income of 13 families and their corrisponding free time expenditure (See page 223 of [MRZ]).

% x= monthly income of 13 families.
% y= free time expenditure.
x=[1330 1225 1225 1400 1575 2050 1750 2240 1225 1730 1470 2730 1380];
y=[120 60 30 60 90 150 140 210 30 100 30 270 260];
GUIcorr(x,y)

### Example 1 of weighted correlation.

In this example vectors x y and w are supplied. (See Covariance from Wikipedia)

x=[  8     8     9     9];
y=[6     7     5     7];
w=[0.4000    0.1000    0.3000    0.2000];
y=GUIcorr(x,y,w);

## Related Examples

expand all

### Example 2 of weighted correlation.

In this example first input argument is a table and only this argument is passed. (See Covariance from Wikipedia)

N=[0 0.4 0.1
0.3	 0	0.2];
colnames={'5' '6'	'7'};
rownames={'8','9'};
Ntable=array2table(N,'RowNames',rownames,'VariableNames',colnames);
out=GUIcorr(Ntable);

### Another example of weighted correlation.

In this example first input argument is a table and only this argument is passed. (See Correlation from Wikipedia)

N=[0 1/3 0
1/3	 0 1/3];
colnames={'-1' '0' '1'};
rownames={'0','1'};
Ntable=array2table(N,'RowNames',rownames,'VariableNames',colnames);
out=GUIcorr(Ntable);

## Input Arguments

### x — vector of numeric data or table. Vector or table.

Vector containing strictly numerical data. If x is table it contains the contingency table associated with the joint probability distribution. In this case, the second input argument y is not necessary. If x is a table, weighted correation is computed where the weights are the values inside the contingency table.

Data Types: vector of doubles or table

### y — vector of numeric data. Vector.

Vector containing strictly numerical data.

This input argument is not requested if previously input argument x is a table.

Data Types: vector of doubles

### w — weights. Vector.

Vector of the same length of x containing the weights (frequencies) assigned to each observation.

Example: 1:10 

Data Types: vector of doubles

## Output Arguments

### out — description Structure

detailed output to compute the index. struct.

Structure containing the following fields.

Value Description
data

table with n+1 rows (where n is the length of x) containing what is shown in the GUI.

Last row contains the totals.

corr

scalar containing the correlation coefficient.

## References

Milioli, M.A., Riani, M., Zani, S. (2019), "Introduzione all'analisi dei dati statistici (Quarta edizione ampliata)". [MRZ]

Cerioli, A., Milioli, M.A., Riani, M. (2016), "Esercizi di statistica (Quinta edizione)". [CMR]