STAT 352
Categorical covariates
Data
; i labels level of covariate.
Additive Model:
Alternative form of same model:
Possible linear restrictions on
's.
or
Example
Consider a small version of the car m
STAT 352
Interaction effects
If a model contains terms
then we define the UV interaction term
to be
, that is, we define a new column of the design matrix which is
the product of the U column and the
STAT 352
Diagnostics
In addition to the residual plots already discussed there are a number of formal
statistical procedures available for diagnosing problems with the fitted model.
Problems with indi
STAT 352
Goodness-of-fit: Pure Error Sum of Squares
If, for each (or at least sufficiently many)
combination of covariates in a data set, there are
several observations, we can carry out an extra
sum
STAT 352
Goodness-of-fit: Pure Error Sum of Squares, An Example
Plaster hardness data of Lecture 12.
9 different covariate patterns: 3 levels of SAND and 3 levels of FIBRE.
Two ways to compute pure er
STAT 352
Fitting Interactions: Two Way ANOVA
Influence of SCHOOL, REGION on STAY
data scenic;
infile 'scenic.dat' firstobs=2;
input Stay Age Risk Culture Chest Beds
School Region Census Nurses Facil;
STAT 352
The SCENIC data set, continued
See Lecture 18 for plots of the data and Lecture 19 for our first analysis.
We have found that STAY, CULTURE and CHEST are significant and that we must
retain o
STAT 351
The SCENIC data set
The data set is described in the Appendix of the text. Here I reproduce a page of pairwise scatter plots for all variables except the categorical variables Region and Scho
STAT 352
The SCENIC data set, continued
See Lecture 18 for plots of the data. Here we fit several models and discuss
interpretation of the coefficients.
I begin by thinking about how the variables sho
STAT 352
Quadratic forms, Diagonalization and Eigenvalues
The function
is a quadratic form. The coefficient of a cross product term like
is
so
the function is unchanged if each of
and
is replaced by t
STAT 352
Instructions: This is an open book test. You
may use notes, text, other books and a
calculator. Your presentations of statistical
analysis will be marked for clarity of
explanation. I expect