Biostatistics 100B, Midterm 1, Practice Set 2
General Comments:
•
These problems are taken from old exams from some of my past classes.
I have picked a
selection of problems that I think will be useful.
I do not guarantee that I have here a
problem on every subject that is fair game for the exam or that the balance is exactly right.
A few of the regression problems contain questions about confidence intervals and hypothesis
tests that may not be fair game for our exam depending on how far I get on Monday. I have
left these pieces in (a) in case they are fair game and (b) so you can see the original structure
of the questions. At the moment this list does not incllude examples of Fisher’s exact test
and McNemar’s test. I will add a problem or two on these topics later but this should get
you well started.
•
In addition to practice problems it is worth reviewing the problems from HW13 as the
assignments more accurately reflect what I think are the key topics we have covered so far.
•
The exam will be closed book. However, you may use two pages, front and back, of notes
and formulas. Write your answers on the exam sheets. If you need more space, continue your
answer on the back of the pages. Normal and chisquared tables will be provided for you at
the end of the exam and I will have scratch paper available if you want it.
•
You must show your work
on the exam to obtain full credit.
If you use a result from
class, state what result you are using. If you can’t complete a problem for any reason, explain
what concepts are at issue, and how you would attack the problem. If you can’t work out a
number you need for a later part of a problem give it a symbol and show how you would do
the calculations with a symbol in place of the missing number. It is, in any case, a good idea
to explain
briefly
what your reasoning is in English. If I can’t tell that you understood what
you were doing, I can’t give you credit, particularly if you get the wrong numerical answer.
HAPPY STUDYING!
(1) Regress a Wreck
A statistician is trying to learn what factors affect the price of a used car.
Her Y variable is the price of the car. She is considering several possible predictor variables. They
are
X
1
, the original value of the car,
X
2
, the mileage on the car,
X
3
, the number of repairs that
have been done on the car, and
X
4
, the number of seat belts in the car.
(a)
For each of the four possible predictor variables the statistician has obtained the covariance
and correlation.
Cor
(
Y, X
1
) =
.
795
Cov
(
Y, X
1
) = 3
,
688
,
147
Cor
(
Y, X
2
) =

.
789
Cov
(
Y, X
2
) =

149
.
155
Cor
(
Y, X
3
) =

.
539
Cov
(
Y, X
3
) =

1186
.
4
Cor
(
Y, X
4
) =

.
004
Cov
(
Y, X
4
) =

7
.
6
Note:
For each variable described what a plot of X versus Y would look like and why.
(b)
Rank the variables
X
1
, X
2
, X
3
, X
4
in terms of how good a job you expect them to do of pre
dicting Y based on the values given in part (a) (NOT on your common sense opinion!) Order them
1