Midterm Two Solutions
General Comments:
•
The average on this exam was 82.3, a little lower than midterm 1 (84.5) but not much.
The median was 83.5, low score 36, high score 100 (wow!)
and standard deviation 11.4.
I
have given approximate grade distributions below.
As always remember that they do not
necessarily represent the score necessary for a particular grade overall in the course as you
get to drop your lowest homework and drop the weight on your lower midterm to 10% if
you do better on the final. These are mostly designed to give you an idea of your relative
performance on this exam.
•
People struggled a lot on the last question–partly this may have been time, but historically
people have difficulties when I give a problem like this so make sure you read the solutions
carefully. In addition I recommend you look carefully at the solutions to the second half of
problem 2, especially the part about (g) about multicollinearity and overfitting, and the parts
on interactions. There seem to be some common misconceptions about these concepts.
Grade
Score
Number In Range
A
89+
30
A
8488.5
19
B+
8083.5
18
B
7079.5
20
B
6569.5
3
C+
6064.5
3
C
5559.5
3
C
5054.5
1
F
¡ 50
2
THE STORY BEHIND THE EXAM:
As we all know from class my baby has not been sleep
ing well...perhaps that has something to do with the exam theme! A professor of pediatrics at the
University of Calculationally Learned Adults is interested in knowing what factors affect how well
an infant sleeps at night. During the course of the exam you will help her analyze the data from a
study she has conducted.
Question 1: Drinking the Milk of Paradise (45 points, 45 minutes)
A common story among parents of young babies is that if you can get them to drink a lot of milk
before going to bed they will sleep longer. Our pediatric researcher decides to test this. She has
collected information on Y, the number of minutes a baby sleeps and X, the number of ounces of
1
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
milk the baby has consumed. Some summary statistics, a simple linear regression printout and sev
eral corresponding plots are shown below. Use them to answer the questions on the following pages.
¯
Y
= 562
¯
X
= 4
.
75
SSX
= 755
n
= 100
. reg Sleep Milk
Source 
SS
df
MS
Number of obs =
100
+
F( 1,
98) =
28.98
Model  1034501.63
1 1034501.63
Prob > F
= 0.0000
Residual  3497999.72
98 35693.8747
Rsquared
= 0.2282
+
Adj Rsquared = 0.2204
Total  4532501.35
99 45782.8419
Root MSE
= 188.93

Sleep 
Coef.
Std. Err.
t
P>t
[95% Conf. Interval]
+
Milk 
37.02467
6.877371
5.38
0.000
23.37675
50.67259
_cons 
385.8047
37.77206
10.21
0.000
310.8473
460.7621

Part a (3 points)
Is there a significant linear relationship between sleeping time and amount of milk drunk? Justify
your answer with an appropriate test using
α
=
.
05. You do not need to write out all the details.
Just give your basic reasoning.
Solution:
Yes, the pvalue for the F test (or the ttest for the Milk variable) is 0.0000 which is
certainly much less than
α
=
.
05 so we reject the null hypothesis that
β
1
= 0 and conclude that
there is a significant relationship between amount of milk drunk and length of time slept.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '07
 Sugar
 Regression Analysis, Coef, sleep time

Click to edit the document details