Problem Set 2
Introduction to Econometrics  Fall 2006
Due Date: Thursday, October 5th, BEFORE CLASS.
Each student is responsible for handing one handwritten solution. If working in groups, indicate the
members of the group (to facilitate grading).
PLEASE SHOW YOUR WORK
.
1. A random sample of 400 ants is taken from an anthill and their length and speed are recorded. Length
is measured in inches and speed in miles per hour. A regression of speed on length yields:
\
speed
=
−
1
.
1+4
.
28
∗
length
R
2
=0
.
92
SER
=1
5
.
1
(a) Say that a speci
f
cantis
1
.
2
inches long. What is the regression speed prediction for it? What if
it was
0
.
5
inches long?
(b) If an ant grew by
3
inches, how much would its regression predicted speed increase?
(c) Now, say that length was recorded in centimeters and speed in kilometers per hour. What are the
regression estimates from this new regression? (Specify all estimated coe
ﬃ
cients,
R
2
and
)
1
2. A professor decides to run an experiment to measure the e
f
ect of time pressure on
f
nal exam scores.
He gives each of the 400 students in his course the same
f
nal exam, but some students have 90 minutes
to complete the exam while others have 120 minutes. Each student is randomly assigned one of the
examination times based on the
F
ip of a coin. Let
Y
i
denote the number of points scored on the exam
by the
i
th
student
(0
≤
Y
i
≤
100)
,let
X
i
denote the amount of time that the student has to complete
the exam
(
X
i
=90
or
120)
, and consider the regression
Y
i
=
β
0
+
β
1
X
i
+
u
i
.
(a) Explain what the term
u
i
represents. Why will di
f
erent students have di
f
erent values of
u
i
?
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '08
 Staff
 Statistics, Econometrics, Variance, Null hypothesis, Yi, following hypothesis

Click to edit the document details