Geoscience Reference
In-Depth Information
which is the change in the residuals of a model if this specii c data point is
removed. h e larger the Cook's distance of a particular data point the more
likely it is to be an outlier. h e diagnostic plot again displays a dashed line,
which marks a recommended threshold of three times the mean Cook's
distance
3*mean(mdl.Diagnostics.CooksDistance)
which yields
ans =
0.1144
According to this plot there are three data points above the critical value
marked by the dashed line, one each in rows 22, 27 and 35. Since the data
point
HF49
in the 22nd row also has a high leverage on the model it should
be removed as an outlier and the improved model then run. We can also
examine the residuals of the model using
plotResiduals(beta)
which suggests that the measurements above 9 are outliers. As the last
diagnostic plot in this exercise we display the normal probability plot of the
residuals
plotResiduals(beta,'probability')
where the black line represents the probability of the residuals in the case
of an ideal normal distribution. In our example, the tails of the normal
distribution plot of the residuals do not match a normal distribution and
our linear regression model is therefore good (but not perfect) without
having removed the outliers. h e regression coei cients calculated from the
regression analysis (including the outliers) are, however, similar to those
reported on page 347 of Swan and Sandilands (1995).
h e linear regression model can now be used to predict the permeability
of a new sample from the values of the other petrophysical parameters. h e
ef ect that each predictor variable has on the model can be examined using
one of several functions included in the Statistics Toolbox. As an example
plotSlice(beta)
yields a slice plot of the responses displaying each predictor variable separately.
Within this plot we can drag the lines or insert values for the individual
predictor variables and examine the resulting value of the response variable.
