Department of Economics
Vanderbilt University
Adnan Kasman
Spring 2001
Econ 308
Problem Set 1
Due: 01-26-2001
1) (Gujarati 2.11) Determine whether the following models are linear in the parameters, or the
variables, or both. Which of these models are linear regression models?
 1
 Xi

  i


Yi  1   2 ln X i   i
a) Yi  1   2 
b)
c) ln Yi  1   2 X i   i
d) ln Yi  ln 1   2 ln X i   i
e)
 1
ln Yi  1   2 
 Xi

  i


2) Are the following models linear regression models? Why or why not?
a) Yi  e 1   2 X i  i
b) Yi 
c)
1
1 e
1   2 X i  i
 1
ln Yi  1   2 
 Xi

  i


d) Yi  1  (0.75  1 )e  2 ( X i  2)   i
e) Yi  1   23 X i   i
3) Explain carefully the meaning of each of the following terms
a) Population regression function (PRF)
b) Sample regression function (SRF)
c) Stochastic PRF
d) Stochastic error term (  i )
e) Residual term ( ei )
f) Conditional expectation
g) Regression coefficients or parameters
h) Estimators of regression coefficients
4) What is the difference between a stochastic population regression function (PRF) and
stochastic sample regression function (SRF)?
5) State with reasons whether the following statements are true, false, or uncertain. Be precise.
a) The stochastic error term  i and the residual term ei mean the same thing.
b) A linear regression model means a model linear in the variables.
c) In the linear regression model the explanatory variable is the cause and the dependent
variable is the effect.
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6) Suppose you have the following data on the price of orange and the quantity sold:
Price per
Dollars)
0.50
0.75
1.00
1.25
1.50
Pound
(in Quantity
Pounds)
10
7
6
5
2
Sold
(in
Assume that the quantity sold (Y) is a linear function of the price (X), i.e.
Yi  1   2 X i   i
Estimate the population regression coefficients. (Do not use Computer)
7) In television’s early years, most commercials were 60 seconds long. Now, however,
commercials can be any length. The objective of commercials remains the same-to have as
many viewers as possible remember the product in a favorable way and eventually buy it. In
an experiment to determine how the length of a commercial affects people’s memory of it, 60
randomly selected people were asked to watch a one-hour television program. In the middle
of the show, a commercial advertising a brand of toothpaste appeared. Each viewer watched a
commercial whose length varied between 20 and 60 seconds. The essential content of the
commercials was the same. After the show, each person was given a test to measure how
much he or she remembered about the product. The commercial times and test scores (on a
30-point test) are stored in file Data308#1. (use computer)
a) Draw a scatter diagram of the data to determine whether a linear model appears to be
appropriate.
b) Determine least squares line.
c) Interpret the coefficients.
8) Ramanathan (textbook page 144) question # 3.31 (only part a)
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