3. Assessing The Regression Model
Two Important Questions
Does the model fit the
observed data well, or is
it influenced by a small
number of cases?
Can my model Generalize
to other samples?
Question 1 Question 2
4. Answering the Model Fit
Outliers Influential Cases
The one different
from others
A case which stands
out
Case with Large
Residual
5. Outliers With Residuals
Standardized Residuals Un standardized Residuals
Can not tell how big residual
will be considered big.
Using the Properties of
Normal Distribution helps us
in making a rule for deciding
large or small
Rule of 3.28
Rule of 2.58
Rule of 1.96
There be no value with more than 3.28 SR
Model is unacceptable if more than 5% cases
have Standardized Residual>2.58
Model is unacceptable if more than 1% cases
have Standardized Residual>2.58
7. Influential Cases
By Excluding a certain case, the slope and intercept of the
regression line is affected.
It means the model is not stable and changes its coefficients
from one sample to another.
8. Residual Statistics to Assess the Effect of a
Particular CaseDeleted
Residual
Adjusted
predicted
Value
Studentized
Deleted
Residual A new model is calculated with using a particular case.
Then that particular case is predicted. This value is
called APV. If the case is not an influential one, then the
adjusted predicted value will be very near the originally
predicted value.
difference between the adjusted predicted value and
the original observed value = DR
Studentized Deleted Residual = DR/ Standard Deviation
This residual can be compared across different
regression analyses because it is measured in standard
units.
9. Residual Statistics to Assess the Effect of a
Particular Case
Deleted Residuals Can not
Provide any information about
how a case influences the
model as a whole
Deleted Residuals Can
Assess the influence of a case
on the ability of the model to
predict that case.
So how we can assess the influence
Cook’s Distance
Mahalanobis
Distances
Leverage
