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# RGRAPH procedure

Draws a graph to display the fit of a regression model (P.W. Lane).

### Options

`GRAPHICS` = string token Type of graphics to produce (`lineprinter`, `highresolution`); default `high` Title for the graph; default `'Fitted and observed relationship'` Which high-resolution graphics window to use; default 4 (redefined if necessary to fill the frame) Whether to clear the graphics screen before plotting (`clear`, `keep`); default `clea` Whether to plot confidence intervals (`no`, `yes`); default `no` Probability for confidence interval; default 0.95 What back-transformation to make (`link`, `none`, `axis`); default `link` Save structure of the model to display; default `*` uses the most recently fitted regression model

### Parameters

`INDEX` = variate Which explanatory variate to display; default `*` if `GROUPS` is set, otherwise `INDEX` is set to the first variate in the fitted model (must be set for nonlinear models other than standard curves) Which explanatory factor to display; default `*` if `INDEX` is set, otherwise `GROUPS` is set to the first factor in the fitted model (ignored for nonlinear models)

### Description

Procedure `RGRAPH` displays the fit of either a linear regression, a generalized linear model, a generalized additive model, a standard curve or a nonlinear model.

For models other than the nonlinear models fitted by `FITNONLINEAR` or `FIT` with the `CALCULATION` option set, the graph shows the relationship between the response variate and either one explanatory variate or one explanatory factor or one of each. If no parameters are set, `RGRAPH` takes the first explanatory variate and the first factor in the model, and the predicted relationship is represented by a line for each level of the factor. The display represents the observed relationship as points, plotting the response (adjusted for further explanatory terms in the model, if any) against the chosen explanatory variate, with each point labelled according to the corresponding factor level. If no factor has been fitted, a single line is drawn, while if no variate has been fitted the graph simply shows the predicted mean for each level of the factor.

If a linear, generalized linear, or generalized additive model has been fitted, the `INDEX` and `GROUPS` parameters can be used to specify which explanatory variate and factor, respectively, should be used. If `INDEX` is set and `GROUPS` is not, a single line is drawn even if there are factors in the model; similarly if `GROUPS` is set and `INDEX` is not, the effect of the factor alone is shown. With generalized linear models, the relationship is usually plotted on the original scale, but you can set option `BACKTRANSFORM` to either `none` or `axis`, to plot on the scale of the linear predictor. These settings are useful, for example, if you want to check for potential non-linearity in the response. They differ in that the `axis` setting includes axis markings, back-transformed onto the natural scale, on the right-hand side of the y-axis. However, this is not available for log-ratio, power, reciprocal or calculated links.

For nonlinear models fitted by the `FITNONLINEAR` directive, a single line is drawn by joining the fitted values, and the response values are shown as points. Any setting of the `GROUPS` parameter is ignored. For curves fitted by the `FITCURVE` directive, settings of the `INDEX` and `GROUPS` parameters are ignored.

No graph can be drawn if the `REG` function has been used for any variate in the model. If the `SSPLINE` function has been used for any variate whose relationship with the response is not actually displayed, then the only adjustment for its effect will be the linear component of the fitted smooth curve. If the displayed variate itself is smoothed, then the curve is formed by interpolation between adjusted fitted values. The `POL` function is dealt with correctly.

The `TITLE` option can be used to supply a title for the graph. By default the graph is plotted on the current high-resolution device, but the `GRAPHICS` option can be set to `line` for a line printer plot. The `WINDOW` option can be used to select a pre-defined window for high-resolution plots; otherwise window 4 is used, and is redefined if necessary to fill the frame. The `SCREEN` option allows the graph to be added to an existing high-resolution plot. The colours and symbols used in the displays can be controlled by setting the attributes of the following pens with the `PEN` directive before calling the procedure:

    pen 1 labels for lines when drawn for each level of a factor, fitted lines and means, points, and back-transformed axis marks and labels.

By default the current regression model is displayed, but option `SAVE` can be set to specify the save structure (from a `MODEL` statement) of some other model.

When there are no groups with a linear or generalized linear model, you can set option `CIPLOT=yes` to include confidence intervals for the fitted relationship. The `CIPROBABILITY` option sets the size of the interval. The default is 0.95 (i.e. 95%).

Options: `GRAPHICS`, `TITLE`, `WINDOW`, `SCREEN`, `CIPLOT`, `CIPROBABILITY`, `BACKTRANSFORM`, `SAVE`.

Parameters: `INDEX`, `GROUPS`.

### Method

For a linear or generalized linear model, fitted lines are drawn by joining predicted values calculated by a `PREDICT` statement at 21 equally spaced values spanning the range of the explanatory variate. Alternatively, `PREDICT` provides adjusted means at each level of the factor, if the effect of the factor is to be displayed alone. If all the effects in the current model are displayed, the response is plotted against the explanatory variable (or against the factor level) as points. But if adjustment has to be made for some effects, adjusted response values (known as “partial residuals”) are calculated by adding the simple residuals to predictions produced for all observations.

For generalized additive models, no predictions are used if the explanatory variate is smoothed: the nonlinear component of the smooth is extracted using `RKEEP`. For curves and general nonlinear models no predictions are made, and fitted values are used.

If a linear or generalized linear model is constrained to pass through the origin, the display will extend the range of the explanatory if necessary to include the origin.

The back-transformed axis markings, given by `BACKTRANSFORM=axis`, are added by using `AXIS` to including an additional (oblique) axis alongside the y-axis.

### Action with `RESTRICT`

Any restriction that was in force when the model was fitted will apply also to the graphs. Problems may occur, however, if the response variate is not restricted and an explanatory variate or factor is restricted.

Procedures: `RCHECK`, `RDESTIMATES`, `AGRAPH`, `DTABLE`, `VGRAPH`.

Commands for: Regression analysis.

### Example

```CAPTION 'RGRAPH example',!t('Experiments on cauliflowers in 1957 and 1958',\
'provided data on the mean number of florets in the plant and the',\
'temperature during the growing season (expressed as accumulated',\
'temperature above 0 deg C.).'); STYLE=meta,plain
FACTOR  [LEVELS=!(1957,1958); VALUES=7(1957,1958)] Year
VARIATE [NVALUES=14] MnCount,AccTemp
3.8  2.5    6.2  4.2    7.2  5.3    8.7  5.8
10.2  7.2   13.5  8.9   15.0 10.0
6.0  2.5    8.5  4.4    9.1  5.3   12.0  6.4
12.6  7.2   13.3  7.8   15.2  9.2 :
" Fit a linear regression model of the mean count of florets on
accumulated temperature - first ignoring the division into two years."
MODEL  MnCount
TERMS  AccTemp*Year
FIT    AccTemp
" Display single fitted line."
RGRAPH
" Fit separate regressions for the two years."