# Assignment #1 due 4/12 - DOC

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```							ECON 497 Assignment 2                                                                Page 1 of 4

Metropolitan State University
ECON 497: Research and Forecasting
Bellas, Spring 2011
Assignment #2, due 2/15

1. Pity the poor farmer. As in any industry with free entry, there will always be those
who are at the margin, only barely covering their opportunity cost. It's one of the very
most dangerous industries in the U.S. (second only to construction) and while its proud
tradition of child labor continues from the middle ages to today, cheap food from abroad
threatens to feed the poor at lower cost than domestic farmers can manage. This is all
basically true in every country around the world. Anyhow, even the seemingly
omnipotent econometrician may be unable to aid the farmer. Consider this equation from
Studenmund:

ˆ
Yt   = -120 + 0.10Ft + 5.33Rt

Y = yield per acre
F = fertilizer per acre, in pounds
R = rainfall

A. How does output per acre increase if an additional pound of fertilizer per acre is
B. Explain why this information is of little or no use to farmers. If you find this question
confusing, imagine that the price of corn is \$1.50/bushel. What does this equation suggest
that farmers should do if the price of fertilizer is:
i. \$0.10/pound
ii. \$0.15/pound
iii. \$0.20/pound
C. What does this equation suggest is the correct (profit maximizing) amount of fertilizer
for a farmer to use?
D. Now, imagine instead that the model estimated is:

ˆ
Yt = -120   + 0.50Ft - 0.013 Ft2 + 5.33Rt

In this case, what will be the profit maximizing quantity of fertilizer to use per acre if the
price of fertilizer is \$0.15/pound and the price of corn is \$1.50/bushel?

2. We all love hypothesis testing. When a software package calculates a t-statistic for an
estimated coefficient, that statistic is associated with a hypothesis test, which must have
associated with it a null and alternative hypothesis.
A. Explain what the null and alternative hypotheses are when you do a regression and
get a t-statistic.
B. Explain the null and alternative hypotheses underlying the F-test (which, according to
Studenmund, virtually every computer regression package routinely provides).

3. Multicollinearity and heteroskedasticity are big words that are fun to use.
ECON 497 Assignment 2                                                            Page 2 of 4

A. How many syllables are there in the words “multicollinearity” and
“heteroskedasticity”?
B. The best way to detect multicollinearity in a regression model is to calculate VIF
numbers. Explain where these numbers come from and how you use them to determine if
multicollinearity is present in your model.
C. Explain briefly how to conduct a Park test for heteroskedasticity.

In SPSS
4. (From Studenmund) What attributes make a car accelerate well? If you're like most
people, you'd answer that the fastest accelerators are high-powered, light, manual
transmission cars with aerodynamic shapes. To test this, use the data available on the
web site for 1995 model vehicles to estimate the following equation:

S i   0   1Ti   2 E i   3 Pi   4 H i   i

Where

S = the number of seconds it takes to accelerate from 0 to 62 mph
T = a dummy variable equal to 1 if the car has a manual transmission, 0 if not
E = the coefficient of drag of the car
P = curb weight (in pounds) of the car
H = the bhp horsepower of the car

A. According to Studenmund’s four criteria for inclusion of explanatory variables,
should E, the drag coefficient, be included in the linear model described above? Explain
why or why not.
B. Suppose your neighbor is a physics major who also races motorcycles, and she tells
you that horsepower can be expressed in terms of the following equation: H = MDA/S
where M=mass, D=distance, A=acceleration and S and H are as defined above. Based on
this conversation with your neighbor, you decide to change the functional form of the
relationship to include 1/H rather than H as an explanatory variable because that's the
appropriate theoretical relationship between the two variables. What would the expected
sign of the coefficient of 1/H be? Explain.
C. Estimate the above equation, substituting 1/H for H. Which of the two models do you
prefer and why?
D. Since the two equations have different functional forms, can the adjusted R2 be used
to compare the overall fit of the equation? Why or why not?
E. Use correlation coefficients and VIF figures to look for multicollinearity in the data.
Present your results and discuss what you should do if you find multicollinearity in the
data.

5. Among the determinants of a house's price or value are such factors as its size in
square feet, the number of bathrooms it has, the neighborhood it is in and its age.
A. Do a linear regression of house price on these factors.
ECON 497 Assignment 2                                                              Page 3 of 4

B. Look for heteroskedasticity in the results. Provide output to support your
conclusions.
C. Look for evidence of multicollinearity using the following approaches:
i. Scatterplots
ii. Correlation coefficients
iii. VIFs

6. Use the data set associated with this exam on the web site to examine coffee sales at
the New Kingdome, an open air baseball stadium with a hat.
A. Estimate the following model and report the estimated coefficients, t-stats and p-
values:

Ci  0  1 Ti  2 Ai  3Ni  i

where

Ci = coffee sales at the ith game
Ti = temperature at the start of the ith game
Ai = attendance at the ith game
Ni = a dummy variable equal to 1 if the ith game was a night game and 0 otherwise

B. Estimate a semi-log model with ln Ci as the dependent variable. Are your results
robust to changes in the model specification?
C. Heteroskedasticity is a big word that is fun to use.
i. Using scatterplots and the Park test, look for heteroskedasticity associated with the
linear model and describe what you find.
ii. Do another regression correcting for heteroskedasticity (you probably want to use the
Zen approach) and present your results. How have they changed from the original
regression?

7. There is fake data available on the web site the lists the charge and the tip for 1000
customers at an imaginary coffee shop somewhere in Nowheresville. Do a regression of
the tip on the charge. The results will be crap. Explain what the real relationship is and
try to estimate it.

Happy Fun Questions – Not required, but fun!
A. When a software package calculates a t-statistic for an estimated coefficient, that
statistic is associated with a hypothesis test, which must have associated with it a null and
alternative hypothesis. Explain what the null and alternative hypotheses are when you do
a regression and get a t-statistic, which you then look at on a page of output.

B. Explain the null and alternative hypotheses underlying the F-test (which, according to
Studenmund, virtually every computer regression package routinely provides).
ECON 497 Assignment 2                                                             Page 4 of 4

C. (From Studenmund) Create null and alternative hypotheses for the following
coefficients:
A. the impact of height on weight
C. all the coefficients in Y=f(X1,X2,X3) where Y is total gasoline used on a trip, X1 is
miles travelled, X2 is the weight of the car and X3 is average speed.
D. the impact of the decibel level of the grunt of shot putters on the length of the throw
involved. Assume all relevant "non-grunt" variables are included in the equation.

D. (From Studenmund) It turns out that the F-ratio can be expressed as a function of R2.
A. As an exercise, substitute equation 2.21 into equation 5.11 to derive the exact
relationship between F and R2.
B. If one can be expressed as a function of the other, why do we need both? What
reason is there for computer regression packages to typically print out both R2 and the F-
ratio?

E. Read through and answer the questions for the case on the web site regarding gender
and credit in rural Paraguay. Pay particular attention to the parallels between regression
analysis and other forms of analysis (comparison of means and correlations).

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