STAT 351
Confidence intervals for
Refer to the polynomial regression example
(data on insurance costs). I fit polynomials of
degree 1 through 5. Each model gives a
vector of fitted parameters and to p
STAT 351
The kth moment of a standard normal is
We can do this integral by parts with
and
and
parts
Since
. This makes
so that by integration by
and
we see that
if k is
odd and
if k is even.
We can al
STAT 351
Joint Densities
Suppose and are independent standard
normals. In class I said that their joint
density was
Here I want to show you the meaning of joint
density by computing the density of a
r
STAT 351
Another Extra Sum of Squares Example: two
way layout
We have data
for i from 1 to I, j from 1
to J and k from 1 to K where ilabels the row
effect, j labels the column effect and k labels
the
STAT 351
Edited output:
Dependent Variable: COST
Source
> F
DF
Type I SS
Mean Square
F Value
CODE
0.0001
C2
0.0001
C3
0.0001
C4
0.9678
C5
0.0009
1
3328.3209709
3328.3209709
9081.45
1
298.6522917
298.6
STAT 351
Here is an example of some of the matrix
algebra I was doing in class. Consider the
weighing design where two objects of
weights and are weighed individually and
together. The resulting desig
STAT 351
Multiple Regression
Here is a page of plots:
You will see that the plot of residual against fitted value suggests that we should
consider adding a quadratic term in Fibre:
The model
has ESS=8
STAT 351
I tried, as I was calculating things for the
vectors , and to emphasize which things
needed which assumptions.
So for instance we have following matrix
identities which depend only on the mod
STAT 351
Standardized Residuals
For the insurance data we can look at the residuals after various model fits.
data insure;
infile 'insure.dat' firstobs=2;
input year cost;
code = year - 1975.5 ;
proc
STAT 351
Reparametrization
Suppose X is the design matrix of a linear
model and that is the design matrix of the
linear model we get by imposing some linear
restrictions on the model using X. A good
e
STAT 351
Multiple Regression
In the data set below the hardness of plaster
is measured for each of 9 combinations of
sand content and fibre content. Sand content
was set at one of 3 levels as was fibr
STAT 351
Polynomial Regression
We consider data on average claims paid per
policy for automobile insurance in New
Brunswick in the years 1971-1980:
Year 1971 1972 1973 1974 1975 1976 1977 1978 1979 19