Plot of slices through fitted linear regression surface
plotSlice(
creates a figure
containing one or more plots, each representing a slice through the regression
surface predicted by mdl
)mdl
. Each plot shows the fitted response
values as a function of a single predictor variable, with the other predictor
variables held constant.
plotSlice
also displays the 95% confidence bounds for the
response values. Use the Bounds menu to choose the type
of confidence bounds, and use the Predictors menu to
select which predictors to use for each slice plot. For details, see Tips.
Use the Bounds menu in the figure window to choose the type of confidence bounds. You can choose Simultaneous or Non-Simultaneous, and Curve or Observation. You can also choose No Bounds to have no confidence bounds.
Simultaneous or Non-Simultaneous
Simultaneous (default) — plotSlice
computes confidence bounds for the curve of the response values
using Scheffe's method. The range between the upper and lower
confidence bounds contains the curve consisting of true response
values with 95% confidence.
Non-Simultaneous — plotSlice
computes
confidence bounds for the response value at each observation.
The confidence interval for a response value at a specific
predictor value contains the true response value with 95%
confidence.
Simultaneous bounds are wider than separate bounds, because requiring the entire curve of response values to be within the bounds is stricter than requiring the response value at a single predictor value to be within the bounds.
Curve or Observation
A regression model for the predictor variables X and the response variable y has the form
y = f(X) + ε,
where f is a function of X and ε is a random noise term.
Curve (default) —
plotSlice
predicts confidence
bounds for the fitted responses f(X).
Observation —
plotSlice
predicts confidence
bounds for the response observations y.
The bounds for y are wider than the bounds for f(X) because of the additional variability of the noise term.
Use the Predictors menu in the figure window to
select which predictors to use for each slice plot. If the regression model
mdl
includes more than eight predictors,
plotSlice
creates plots for the first five predictors
by default.
Use predict
to return the predicted
response values and confidence bounds. You can also specify the confidence level
for confidence bounds by using the 'Alpha'
name-value pair
argument of the predict
function. Note that
predict
finds nonsimultaneous bounds by default whereas
plotSlice
finds simultaneous bounds by default.
A LinearModel
object provides multiple plotting functions.
When creating a model, use plotAdded
to understand the effect of adding or removing a predictor
variable.
When verifying a model, use plotDiagnostics
to find questionable data and to understand the
effect of each observation. Also, use plotResiduals
to analyze the residuals of the model.
After fitting a model, use plotAdjustedResponse
, plotPartialDependence
, and plotEffects
to understand the effect of a particular predictor. Use
plotInteraction
to understand the
interaction effect between two predictors. Also, use plotSlice
to plot slices through the prediction surface.