qqplot of studentized residuals with envelopes

Displays a quantile-quantile plot of the quantiles of the sample studentized residuals versus the theoretical quantile values from a normal distribution. If the distribution of residuals is normal, then the data plot appears linear. A confidence level is added to the band.

```
```

qqplot with envelopes for the Wool data.`Y`

=qqplotFS(`res`

,
`Name, Value`

)

This is an example of the use of options X and plots

load('multiple_regression.txt'); y=multiple_regression(:,4); X=multiple_regression(:,1:3); outLM=fitlm(X,y,'exclude',''); res=outLM.Residuals{:,3}; qqplotFS(res,'X',X,'plots',1); title('qqplot of stud. res.') % No outlier appears

Compare the results using untransformed and transformed data.

% This is an example of the use of option h XX=load('wool.txt'); y=(XX(:,end)); lny=log(y); X=XX(:,1:end-1); outLM=fitlm(X,y,'exclude',''); res=outLM.Residuals{:,3}; outLMtra=fitlm(X,lny,'exclude',''); restra=outLMtra.Residuals{:,3}; h1=subplot(1,2,1); qqplotFS(res,'X',X,'plots',1,'h',h1); title('QQplot using untransformed data') h2=subplot(1,2,2); qqplotFS(restra,'X',X,'plots',1,'h',h2); title('QQplot using transformed data')

`res`

— vector containing studentizd residuals.
Vector.Vector with n elements containing the studentized residuals from a regression model

**
Data Types: **`single| double`

Specify optional comma-separated pairs of `Name,Value`

arguments.
`Name`

is the argument name and `Value`

is the corresponding value. `Name`

must appear
inside single quotes (`' '`

).
You can specify several name and value pair arguments in any order as ```
Name1,Value1,...,NameN,ValueN
```

.

```
'intercept',1
```

,```
'X',randn(n,3)
```

,```
'conflev',0.99
```

,```
'nsimul',300
```

,```
'plots',1
```

,```
'tag','mytag'
```

,```
'h',h1 where h1=subplot(2,1,1)
```

`intercept`

—Indicator for constant term.scalar.If 1, a model with constant term will be added to optional matrix X (default), else no constant term will be included.

**Example: **```
'intercept',1
```

**Data Types: **`double`

`X`

—Predictor variables.matrix.Data matrix of explanatory variables (also called 'regressors') of dimension (n x p-1). Rows of X represent observations, and columns represent variables. This is the matrix which has been used to produce stdentized residuals.

If this optional argument is missing we take as matrix X the column of ones.

**Example: **```
'X',randn(n,3)
```

**Data Types: **`double`

`conflev`

—Confidence level which is
used to compute confidence bands of studentized residuals.scalar Usually conflev=0.95, 0.975 0.99 (individual alpha) or 1-0.05/n, 1-0.025/n, 1-0.01/n (simultaneous alpha).

Default value is 0.90

**Example: **```
'conflev',0.99
```

**Data Types: **`double`

`nsimul`

—number of simulations to compute the envelopes.scalar.The default value is 1000.

**Example: **```
'nsimul',300
```

**Data Types: **`double`

`plots`

—Plot on the screen.scalar.If plots = 1, a plot which shows the robust the qqplot of residuals with envelopes is shown on the screen. The confidence level which is used to draw the horizontal lines associated with the bands for the residuals is specified in input option conflev. If conflev is missing a nominal 0.90 confidence interval will be used.

**Example: **```
'plots',1
```

**Data Types: **`double`

`tag`

—handle of the plot which is about to be created.character.The default is to use tag 'pl_qq'. Notice that if the program finds a plot which has a tag equal to the one specified by the user, then the output of the new plot overwrites the existing one in the same window else a new window is created

**Example: **```
'tag','mytag'
```

**Data Types: **`char`

`h`

—the axis handle of a figure where to send the qqplot.this can be used to host the qqplot in a subplot of a complex figure formed by different panels (for example a panel with qqplot from a classical ols estimator and another with qqplot from a robust regression).
**Example: **```
'h',h1 where h1=subplot(2,1,1)
```

**Data Types: **`Axes object (supplied as a scalar)`

```
```

```
```

```
```

```
```## Output Arguments

###
`Y`

—matrix with raws data on which the plot is based.
` n-by-3 `

matrix

1st col = standard normal quantiles.

2nd col = quantiles of input sample of studentized residual.

3rd col = lower confidence band of quantiles of studentized residuals.

4th col = upper confidence band of quantiles of studentized residuals.

## References

Atkinson, A.C. and Riani, M. (2000), "Robust Diagnostic Regression
Analysis", Springer Verlag, New York.

*This page has been automatically generated by our routine publishFS*

```
```

```
```

```
```

```
```

```
```

```
```