Erindale College - University of Toronto
Faculty of Arts and Science
December Examinations 1995
STA 301F
Duration - 3 hours
Aids allowed:  Calculator.  Computer printout will be supplied.
 
Name (Please print) _____________________
Signature _____________________________
Student Number ________________________

1.	(10 points)	Answer the following questions T for true
or F for false; write the letters on the lines.  Assume the
significance level is alpha = .05 in all cases.  You must get at
least 10 out of 11 right in order to get any marks at all on this
question.

____	In an observational study, a significant relationship between
the independent variable and the dependent variable provides good
evidence of a causal relationship.

____	We observe r = -0.041, p = .762.  We conclude that there
is a nonlinear relationship between X and Y.

____	We would like to predict type of automobile (North American vs.
Japanese vs. other) from income, education and sex.  It does not make
sense to use the SPSS Regression procedure to do this.

____	An experimental study is one in which cases are randomly
assigned to the different values of an independent variable.

____	In simple regression, a negative regression coefficient
b1 (if it is significant) implies that high values of X go with low
values of Y and low values of X go with high values of Y.

____	If P > .05 we say the results are statistically significant at
the .05 level.

____	We attempt to predict the independent variable from the
dependent variable.

____	In a study seeking to predict income from education and
race, there is a significant interaction between education and race. 
This means that education and race are related.

____	We observe r = 0.50, p = .002.  This means that 50% of
the variation in the dependent variable is explained by a linear
relationship with the independent variable.

____	When a relationship between the independent variable and
the dependent variable is statistically significant, we conclude that
the two variables are actually related.

____	We observe r = -0.70, p = .009.  We conclude that X and Y
are related.


2.	(30 pts for 3 tables) Please fill in the tables below and on
the following pages.  Use my variable names from Section A of the
printout.  Infection risk always refers to infrisk, not riskcat.
Write the letter of the best technique, using
A = Matched t-test
B = Independent t-test
C = One-way anova
D = Chisq test of ind.
E = Simple regression
F = Multiple regression  
G = Logistic regression 
H = Factor or PC analysis
I = None of the above


Question	                   IV(s)	DV(s)   Letter of best test
	
Is there a linear
relationship
between the average
patient age in a
hospital and the
average length of
time a patient
stays?			

Is the average of
xratio different
from the average of
culratio?	

Do the geographic
regions differ in
average length of
patient
stay?			

Once we control for
number of nurses
and length of stay,
can the geographic
region of a
hospital be
predicted from
medical school
affiliation?			

Once we control for
number of patients,
do the geographic
regions differ in
average number of
nurses?			

Do patients in
hospitals with
medical schools
have a lower risk
of getting an
infection?			

Once we control for
number of patients,
number of beds and
length of stay, is
there a
relationship
between medical
school affiliation
& infection
risk?			

Do the geographic
regions differ in
how likely a
patient is to
acquire an
infection while in
the
hospital?			

Can
percent of
facilities and
services be
predicted from the
number of patients
in a
hospital?			

Once we control for
size of hospital
(represented by
nbeds and census),
do the geographic
regions differ in
how likely a
hospital is to be
affiliated with a
medical
school?			

Do hospitals with a
medical school
affiliation tend to
have more
patients?			

Do the geographic
regions differ in
how likely a
hospital is to be
affiliated with a
medical
school?			

Do patients in
hospitals with
medical schools
stay a shorter
length of time on
average?			

Once we control for
number of patients,
can medical school
affiliation be
predicted from
number of
nurses?			

Do hospitals with
more nurses tend to
have higher
infection risk? 
			

3.	(4 points)	Refer to Section B of the printout.  In
everyday language, what do we learn from this analysis? (If you just
say something is "related" to something else, you get no credit.  Be
specific about what the results are -- but don't quote numbers).

4.	(4 points)	Refer to Section C of the printout.  In
everyday language, what do we learn from this analysis?  (If you just
say something is "related" to something else, you get no credit.  Be
specific about what the results are -- but don't quote numbers).

5.	(4 points)	Refer to Section D of the printout.  In
everyday language, what do we learn from this analysis?

6a.	(3 pts)	In the table below, set up indicator dummy
variables for geographic region so that SOUTH is the reference
category.

Region	                      D1	D2	D3
NORTHEAST			
NORTH CENTRAL			
SOUTH			
WEST			

b.	(8 pts)	Representing infection risk by Y, age by the variable X, and
your three dummy variables by D1, D2 and D3, write a regression
equation in which the linear relationship of age to infection risk
might depend on geographic region. Complete the equation below.

	= b0 + b1X + 



c.	(4 pts)	Using your notation from parts (a) and (b) above, write the
equations of the 4 regression lines (one for each region) in the table
below.  You may want to do some scratch work on the (mostly blank)
sheet of paper that has your name, but DO NOT HAND IN THE SCRATCH
PAPER.  All I want are the answers.

Region	Equation: = (Intercept) + (Slope) X
NORTHEAST	
NORTH CENTRAL	
SOUTH	
WEST	

7.	Refer to Section E of the printout: Ordinary Multiple Regression. 
We are always using nondirectional tests (two-sided, if it's a t-test) 
with significance level alpha = 0.05.

a.	(1 point)	Without considering any other variables, are
number of beds and number of patients (together) significant predictors
of infection risk?  Write your answers in the boxes.

		Answer Yes or No 	P - Value
	

b. (1 point) When we control for number of beds in the hospital, is the
number of patients a significant predictor of infection risk?  Write your
answers in the boxes. 

		Answer Yes or No 	P - Value
	

c. (1 point) When we control for number of patients, is number of beds in
the hospital a significant predictor of infection risk?  Write your
answers in the boxes. 


		Answer Yes or No 	P - Value
	

d. (5 points) Explain the apparent inconsistency between your answer to
(a) and your answers to (b) and (c).  Don't worry about "everyday
language;"  just convince me that you understand what's going on. 



7e.	(1 point)	When we control for number of beds and
number of patients, do medical school affiliation and number of nurses
(considered together) predict infection risk?  Write your answers in
the boxes.

		Answer Yes or No 	P - Value
	

7f.	(1 point)	Controlling for number of beds and number of
patients (but NOT for number of nurses), does medical school
affiliation predict infection risk?  Write your answers in the boxes.

		Answer Yes or No 	P - Value
	

7g.	(1 point)	What percentage of the variation in infection risk is
explained by the 4 independent variables together?


7h..	(1 point)	Taken all together, do the 4 independent
variables explain a significant amount of variation in the dependent
variable?  Write your answers in the boxes.

		Answer Yes or No 	P - Value
	

7i.	(1 points)	Which variable or variables explains a
significant amount of variation in the dependent variable once you
control for the other three?  Just name the variable or variables.


8.	Refer to Section F of the printout:  Logistic Regression.  We
are always using nondirectional tests with significance level alpha =
0.05.  If both a Wald test and a likelihood ratio test answer the same
question, use the likelihood ratio test.

a. (1 point) Without considering any other variables, is average length of
stay a significant predictor of infection risk category?  Write your
answers in the boxes. 

		Answer Yes or No 	P - Value
	

b. (1 point) When we control for average length of stay, are number of
patients and number of beds (together) significant predictors of infection
risk category?  Write your answers in the boxes. 

		Answer Yes or No 	P - Value
	

c. (1 point) When we control for average length of stay, number of
patients and number of beds, is geographic region a significant predictor
of infection risk category?  Write your answers in the boxes. 

		Answer Yes or No 	P - Value
	

d. (1 point) When we control for number of beds, number of patients and
geographic region, and the average length of stay increases by one day,
the odds of being above the median in infection risk are ___________ times
as great (fill in the blank). 

e. (1 point) When we control for average length of stay, number of beds
and number of patients, the odds of being above the median in infection
risk are ___________ times as great for a hospital in the West as a
hospital in the South (fill in the blank). 


9.	This is about principal components analysis, and you don't want to see
it, I believe.