Chapter 4: Estimating Demand Functions
MULTIPLE CHOICE
1. The inability to isolate a demand curve from observed prices and quantities alone is known as the:
a.
economist’s problem.
b.
inference problem.
c.
regression problem.
d.
identification problem.
e.
timing problem.
2. If an analyst were confident that all factors that shift the supply curve were constant when observing
changing prices and quantities traded:
a.
the analyst would be confident that the demand curve had been identified.
b.
neither the supply nor the demand curve would have been identified.
c.
the analyst should gather more data to find shifts in both curves.
d.
both the supply and demand curves would have been identified.
e.
the analyst would be confident that the supply curve had been identified.
3. The use of consumer interviews to estimate demand functions has been criticized by economists
primarily because:
a.
answering surveys takes too much time.
b.
the answers collected cannot be easily quantified.
c.
respondents don’t have strong incentives to answer accurately.
d.
interviewers are often belligerent.
e.
survey questions are difficult to word clearly.
4. A cost of estimating demand functions particular to the use of market experiments is:
a.
the possibility that customers may be lost and profits cut as a result of the experiment.
b.
the shipping costs to markets across the country.
c.
the need to determine the profit-maximizing discount.
d.
the cost of collecting data.
e.
none of the above.
5. Regression analysis is:
a.
a psychoanalytical tool, often called “regression toward the mean,” used by economists to
estimate consumer reactions.
b.
always preferable to consumer interviews or market experiments.
c.
usually done with a pencil and paper.
d.
a statistical technique that describes how one variable is related to another.
e.
almost never used in practice because of concerns about alienating a firm’s customers.
6. The most frequently used method for estimating demand functions is:
a.
market experiments.
b.
consumer interviews.
c.
regression analysis.
d.
focus groups.
e.
casual introspection.
7. A simple, idealized representation of the real world is called a(n):
a.
function.
b.
illustration.
c.
equation.
d.
diagram.
e.
model.
8. The estimated mathematical relationship between dependent and independent variables derived using
ordinary least squares is called the:
a.
covariance.
b.
sample regression line.
c.
residual demand curve.
d.
goodness of fit.
e.
coefficient of determination.
9. The slope coefficient estimate b from a regression of profits on sales of a number of firms in the coal
industry is 0.075. How should you interpret this coefficient?
a.
Average profit in the coal industry is 7.5%.
b.
If a firm in the coal industry were to increase its sales by $1, its profits would rise on
average by $0.075.
c.
If a firm has 1 more dollar in sales than another firm in the coal industry, it will have 7.5
more cents in profit on average.
d.
Average profit in the coal industry is .75%.
e.
If a firm in the coal industry were to increase its sales by $1, its profits would rise on
average by $0.0075.
10. The vacancy rates for commercial office space in 2001 for selected cities are given in the following
table. What is the intercept coefficient estimate a of the regression of the vacancy rate downtown as a
function of the vacancy rate in the suburbs?
City
Downtown
Suburbs
Los
Angeles
10
16
Boston
9
19
Dallas
19
28
Tampa
12
25
Chicago
20
11.5
a.
5.0.
b.
16.0.
c.
14.0.
d.
18.0.
e.
7.5.
11. The annual mean daily high and low temperatures by selected cities are given in the following table.
What is the estimate of the intercept coefficient a for the regression of the mean daily high temperature
as a function of the mean daily low temperature?
City
High
(degrees)
Mobile
78
Jacksonville
82
Portland
68
Omaha
73
Cincinnati
74
Dallas
75
a.
50.0.
b.
45.0.
c.
47.5.
d.
–47.50.
e.
–50.0.
12. The vacancy rates for commercial office space in 2001 for selected cities are given in the following
table. What is the slope coefficient estimate b of the regression of the vacancy rate downtown as a
function of the vacancy rate in the suburbs?
City
Downtown
Suburbs
Los
Angeles
10
16
Boston
9
19
Dallas
19
28
Tampa
12
25
Chicago
20
11.5
a.
1.0.
b.
0.5.
c.
2.5.
d.
1.5.
e.
0.0.
13. The mean annual precipitation in inches and number of days per year with measurable precipitation by
selected cities are given in the following table. If the average number of days with rain is one greater in
Tupelo than in Tucumcari, what do you estimate the difference in average annual rainfall will be?
City
Rainy
Days
Rainfall
(inches)
Mobile
132
67
Jacksonville
110
53
Portland
128
44
Omaha
91
30
Cincinnati
129
41
a.
0.5 inch.
b.
1.0 inch.
c.
0.8 inch.
d.
1.25 inches.
e.
2.0 inches.
14. The 1991 exports and imports by industry code are given in the following table. What is the
approximate slope coefficient estimate b of the regression of exports as a function of imports?
SIC
Code
Exports (millions of
dollars)
Imports (millions
of dollars)
3088
20
27
3261
41
74
3272
24
70
3275
54
32
3296
85
30
3441
54
22
3448
72
25
a.
–0.5.
b.
–5.0.
c.
–0.3.
d.
–3.0.
e.
0.4.
15. Annual sales and profits in the coal industry are given in the following table. What is the slope
coefficient estimate b of the regression of profits as a function of sales?
Year
Sales (millions
of dollars)
Profits (millions
of dollars)
1996
800
80
1997
688
62
1998
782
64
1999
962
86
a.
0.09.
b.
0.9.
c.
1.2.
d.
0.12.
e.
0.06.
16. The annual mean daily high and low temperatures by selected cities are given in the following table.
What is the R-squared of the regression of the mean daily high temperature as a function of the mean
daily low temperature?
City
Low
(degrees)
High
(degrees)
Mobile
50
78
Jacksonville
50
82
Portland
46
68
Omaha
49
73
Cincinnati
50
74
Dallas
49
75
a.
0.67.
b.
0.25.
c.
0.75.
d.
0.50.
e.
0.85.
17. The mean annual precipitation in inches and number of days per year with measurable precipitation by
selected cities are given in the following table. What is the R-squared of the regression of the mean
annual rainfall as a function of the number of rainy days?
City
Rainy
Days
Rainfall
(inches)
Mobile
132
67
Jacksonville
110
53
Portland
128
44
Omaha
91
30
Cincinnati
129
41
a.
0.28.
b.
0.38.
c.
0.48.
d.
0.58.
e.
0.68.
18. Suppose the labor force and unemployment rate in 2001 are given in the following table. What is the
slope coefficient estimate b of the regression of the unemployment rate as a function of the labor
force?
Country
Labor Force
Unemployment
United
States
122
5.5
Canada
13
7.8
Britain
28
8.6
Germany
29
6.1
a.
–0.20.
b.
–0.020.
c.
–0.0020.
d.
–2.0.
e.
0.020.
19. Suppose the size of the labor force and unemployment rate across countries in 2001 are given in the
following table. What is the intercept coefficient estimate a of the regression of the unemployment rate
as a function of the labor force?
Country
Labor Force
Unemployment
United
States
122
5.5
Canada
13
7.8
Britain
28
8.6
Germany
29
6.1
a.
6.
b.
8.
c.
10.
d.
12.
e.
14.
20. The vacancy rates for commercial office space in 2001 for selected cities are given in the following
table. What is the R-squared of the regression of the vacancy rate downtown as a function of the
vacancy rate in the suburbs?
City
Downtown
Suburbs
Los
Angeles
10
16
Boston
9
19
Dallas
19
28
Tampa
12
25
Chicago
20
11.5
a.
1.0.
b.
0.5.
c.
0.25.
d.
0.75.
e.
0.
21. The 1991 exports and imports by industry code are given in the following table. What is the
approximate intercept coefficient estimate a of the regression of exports as a function of imports?
SIC
Code
Exports (millions
of dollars)
Imports (millions
of dollars)
3088
20
27
3261
41
74
3272
24
70
3275
54
32
3296
85
30
3441
54
22
3448
72
25
a.
30.
b.
40.
c.
50.
d.
60.
e.
70.
22. Coal industry sales and profits are given in the following table. What is the intercept coefficient
estimate a of the regression of profits as a function of sales?
Year
Sales (millions
of dollars)
Profits (millions of
dollars)
1996
800
80
1997
688
62
1998
782
64
1999
962
86
a.
0.12.
b.
0.14.
c.
0.16.
d.
0.18.
e.
0.22.
23. A regression of the mean daily high temperature as a function of mean daily low temperature across
cities yielded High = 21 + Low, R2 = .98, and RMSE = 1.4. Interpret these results.
a.
The regression says that if a city’s average low temperature is 1 degree higher than some
other city’s, their average high temperatures are also likely to be 1 degree different. The
high R2 and low RMSE are inconsistent and suggest a serial correlation problem.
b.
The regression says that if a city’s average low temperature is 10 degrees higher than some
other city’s, their average high temperatures are also likely to be 10 degrees different and
that the average difference between average daily high temperatures and average daily low
temperatures is 21 degrees. The model explains 98% of the variation in average daily high
temperatures, and the standard error of the estimate is quite small.
c.
The regression says that if a city’s average low temperature is 1 degree higher than some
other city’s, their average high temperatures are also likely to be 1 degree different. The
high R2 and low RMSE are inconsistent and suggest a multicollinearity problem.
d.
The regression says that if a city’s average low temperature is 10 degrees higher than some
other city’s, their average high temperatures are also likely to be 10 degrees different and
that the average difference between average daily high temperatures and average daily low
temperatures is 12 degrees. The regression explains all the variation in average daily high
temperatures.
e.
None of the above.
24. A regression of the mean annual precipitation in inches as a function of number of days per year with
measurable precipitation across cities yielded rain = –2 + 0.8 (number of rainy days), R2 = .75, and
RMSE = 11. How do you interpret the intercept coefficient estimate of –2?
a.
There must be 2.5 rainy days before there is any measured rain.
b.
If there are no rainy days in a year, meteorologists report a –2-inch rainfall for the year.
c.
The regression results hold for values of the independent variables that are similar to
values used to estimate the regression and not for extreme values, like 0 rainy days per
year.
d.
Since the RMSE is 5.5 times the intercept coefficient, we can conclude that it is not
significantly different from 0.
e.
The average annual rainfall will be 0.8 inch for every rainy day exceeding 2.
25. The daily mean temperatures in January and July by selected cities are given in the following table. If
the mean temperature in January is 1 degree higher in Tupelo than in Tucumcari, what do you estimate
the difference (Tupelo–Tucumcari) in mean temperatures will be in July?
City
January
(degrees)
July
(degrees)
Mobile
48
80
Jacksonville
49
81
Portland
36
68
Omaha
46
78
Cincinnati
43
75
Dallas
54
86
a.
1.25 degrees.
b.
2.0 degrees.
c.
0.40 degree.
d.
0.80 degree.
e.
1.0 degree.
26. The annual mean daily high and low temperatures by selected cities are given in the following table. If
the mean low temperature is 1 degree higher in Tupelo than in Tucumcari, what do you estimate the
difference in mean high temperatures will be?
City
Low
(degrees)
High
(degrees)
Mobile
50
78
Jacksonville
50
82
Portland
46
68
Omaha
49
73
Cincinnati
50
74
Dallas
49
75
a.
1.0 degree.
b.
1.25 degrees.
c.
0.75 degree.
d.
1.50 degrees.
e.
2.50 degrees.
27. A regression of the average temperature in July as a function of the average temperature in January
across cities yielded the following: July temperature = 20 + 2.0 January temperature, Prob > F = .03,
R2 = .64, and RMSE = 20. If a city has an average temperature of 40 degrees in January, what does this
regression say about its likely July temperature?
a.
The July estimate is 100 degrees, and since the F-statistic has only a 3% chance of being
so large if the January temperature did not affect the July temperature, we would be
confident in this estimate.
b.
The July estimate is 100 degrees, and since the R2 says that variation in the January
temperature explains 64% of the variation in the July temperature, we would be confident
in this estimate.
c.
Since the F-statistic has only a 3% chance of being so large if the January temperature did
not affect the July temperature and the R2 is so high, there is a serial correlation problem
that invalidates any inferences we might draw from the regression.
d.
The July estimate is 100 degrees, and since the RMSE equals 20, normal statistical
confidence intervals would allow for most temperatures from 60 to 140 degrees. Although
the point estimate of 100 degrees is our best estimate, we must accept that the actual
temperature might be quite different; we would not have confidence in this estimate.
e.
Since the F-statistic has only a 3% chance of being so large if the January temperature did
not affect the July temperature and the R2 is so high, there is a multicollinearity problem
that invalidates any inferences we might draw from the regression.
28. In simple regression analysis (Y = a + bX), the estimate of the intercept coefficient a is equal to
a.
Ymean – bXmean.
b.
Xmean – bYmean.
c.
Ymean + bXmean.
d.
Xmean + bYmean.
e.
Ymean – Xmean / b.
29. In simple regression analysis (Y = a + bX), the estimate of the slope coefficient b is equal to
a.
[ [(Xi – Xmean)(Yi – Ymean)] / (Xi – Xmean)]2.
b.
{[(Xi – Xmean)(Yi – Ymean)] / (Xi – Xmean)}2.
c.
[(Xi – Xmean)(Yi – Ymean)] / (Xi – Xmean)2.
d.
[(Xi + Xmean)(Yi + Ymean)] / (Xi + Xmean)2.
e.
[(Xi – Xmean)(Yi – Ymean)] / (Xi – Xmean).
30. The first step in multiple regression analysis is to:
a.
procure a powerful computer.
b.
identify the important variables.
c.
specify a functional form to be estimated.
d.
gather all available data.
e.
select an estimation procedure.
31. Multiple regression differs from simple regression in that:
a.
there can be multiple dependent variables.
b.
the time periods over which observations are taken are multiplied to increase explanatory
power.
c.
a simple regression is done multiple times to increase explanatory power.
d.
the computational requirements are less.
e.
there are multiple independent variables.
32. The standard error of the estimate is also known as:
a.
the root-mean-squared error.
b.
the standard error of the coefficient estimate.
c.
R-squared.
d.
the t-ratio.
e.
t-squared.
33. The root-mean-squared error (RMSE) is:
a.
the proportion of the variation in the dependent variable that is explained by the
regression.
b.
the coefficient estimate divided by the standard error of the estimate.
c.
an increasing function of the number of independent variables.
d.
the square root of the coefficient of determination.
e.
useful for constructing confidence intervals for estimates of the dependent variable.
34. A regression of exports as a function of imports in 1991 across industry types yielded exports = 68 –
0.3(imports), R2 = .25, Prob > F = .26, and RMSE = 30. If imports by an industry equal 60, what is the
estimate of exports from this industry, and how confident are you of your estimate?
a.
Exportsestimated = 50, variation in imports explains 25% of variation in exports, and the
F-test statistic is high, so we are confident in our estimate of exports.
b.
Exportsestimated = 86, variation in imports explains 25% of variation in exports, and the
F-test statistic is high, so we are confident in our estimate of exports.
c.
Exportsestimated = 50, variation in exports explains 25% of variation in imports, and the
F-test statistic is high, so we are confident in our estimate of exports.
d.
Exportsestimated = 86, variation in exports explains 25% of variation in imports, and the
F-test statistic is high, so we are confident in our estimate of exports.
e.
Exportsestimated = 50, but the F-test statistic fails standard significance tests and the RMSE
is large relative to estimated exports, so we are not confident in our estimate.
35. The statistic used to test whether the independent variables taken as a group explain a statistically
significant portion of the variation in the dependent variable is the:
a.
R-squared statistic.
b.
t-statistic.
c.
Durbin-Watson statistic.
d.
F-test statistic.
e.
standard error of the estimate.
36. The statistic that tests an individual coefficient for statistical significance is the:
a.
R-squared statistic.
b.
t-statistic.
c.
Durbin-Watson statistic.
d.
F-test statistic.
e.
standard error of the estimate.
37. When the t-ratio statistics on individual coefficients are all near 0 but the F-test statistic is greater than
20:
a.
multicollinearity is suggested.
b.
nonconstant variance of the error terms is suggested.
c.
serial correlation is suggested.
d.
the root-mean-squared error will be large.
e.
the Durbin-Watson statistic will be near 0.
38. When the coefficient of determination is near 1 but the t-statistics are all insignificant, the regression
likely suffers from:
a.
nonconstant variance of the error terms.
b.
multicollinearity.
c.
serial correlation.
d.
randomness.
e.
nonidentifiability.
39. Serial correlation occurs when:
a.
independent variables are correlated across observations.
b.
dependent variables are correlated across observations.
c.
error terms are correlated across observations.
d.
R-squared is near 1 and the t–statistics are near 0.
e.
R-squared is near 0 and the t–statistics are near 1.
40. The statistic used to test for serial correlation is the:
a.
R-squared statistic.
b.
t-statistic.
c.
Durbin-Watson statistic.
d.
F-test statistic.
e.
standard error of the estimate.
41. If the Durbin-Watson statistic is near 0, we can conclude that there is:
a.
positive serial correlation.
b.
negative serial correlation.
c.
no serial correlation.
d.
a multicollinearity problem.
e.
not enough data to estimate the regression.
42. If the Durbin-Watson statistic is 2, we can conclude that:
a.
there is no serial correlation.
b.
the error terms have constant variances.
c.
there is negative serial correlation.
d.
there is positive serial correlation.
e.
there is multicollinearity.
43. When the error terms are correlated across observations, one way to address the resulting econometric
problem is to:
a.
use weighted least squares.
b.
use first differences rather than levels of the variables.
c.
gather more data.
d.
transform the independent variable.
e.
eliminate covarying variables.
44. If the Durbin-Watson statistic is near 4, we can conclude that there is:
a.
positive serial correlation.
b.
negative serial correlation.
c.
no serial correlation.
d.
a multicollinearity problem.
e.
not enough data to estimate the regression.
45. The difference between the observed value of a dependent variable and the value we estimate using
regression analysis is known as a(n):
a.
aberration.
b.
correlation.
c.
dependent variable.
d.
mistake.
e.
residual.
46. The coefficient of determination from a regression represents the:
a.
proportion of variation in the dependent variable explained by variation in the independent
variables.
b.
proportion of variation in the independent variables explained by variation in the
dependent variable.
c.
variation in the dependent variable.
d.
proportion of the variation in the dependent variable.
e.
proportion of the variation in the independent variable.
47. The total variation in the dependent variable Y is:
a.
(Yi – Ymean)2.
b.
(Yi – Yestimated)2.
c.
(Yi – Ymean)2 / (Yi – Yestimated)2.
d.
(Yi – Yestimated)2 / (Yi – Ymean)2.
e.
1 – (Yi – Yestimated)2 / (Yi – Ymean)2.
48. The coefficient of determination, or R-squared, is defined as:
a.
1 – (Yi + Yestimated)2 / (Yi + Ymean)2.
b.
1 – (Yi – Yestimated)2 / (Yi – Ymean)2.
c.
(Yi + Yestimated)2 / (Yi + Ymean)2.
d.
1 – (Yi – Yestimated) / (Yi – Ymean).
e.
1 – [ (Yi – Yestimated) / (Yi – Ymean)]2.