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| m66907 | a. Use the data given in Table 9-5 (on the textbook s Web site) to develop a
multiple regression model to explain daily calorie intake for the 20 countries shown in the table.
b. Does this model suffer from heteroscedasticity? Show the necessary test(s).
c. If there is heteroscedasticity, obtain White s heteroscedasticity-corrected standard errors and t statistics (see if your software does this) and compare and comment on the results obtained in part (a) above. |
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| m66908 | a. Use the method of restricted least squares to find out if it is worth adding the Pop (population) variable to the model.
b. Divide both Educ and GDP by Pop to obtain per capita Educ and per capita GDP. Now regress per capita Educ on per capita GDP and compare your results with those given in Example 4.5. What conclusion can you draw from this exercise?
For Information: Refer to Example 4.5. |
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| m66910 | a. Using a statistical package of your choice, confirm the regression results given in Eq. (2.24) and Eq. (2.25).
b. For both regressions, get the estimated values of Y (i.e., Ŷi) and compare them with the actual Y values in the sample. Also obtain the residual values, ei. From this can you tell which is a better model, Eq. (2.24) or Eq. (2.25)?
For Information: Refer to Example 2.3, for which the data are as shown in Table 2-6. |
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| m66949 | According to Chebyshev s inequality, what percentage of any set of data must lie within c standard deviations on either side of the mean value if
(a) c = 2.5 and
(b) c = 8? |
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| m67003 | After eliminating one or more X variables, what is your final demand function for passenger cars? In what ways is this "final" model better than the initial model that includes all X variables? |
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| m67032 | Although popularly used, what are some limitations of the Durbin-Watson d statistic? |
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| m67033 | Although the logit and probit models may be superior to the LPM model, in practice, we should choose the LPM model because of its simplicity per Occam s razor principle. Do you agree with this statement? Why or why not? |
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| m67140 | An r.v. X has the following PDF
a. What is the value of b? Why?
b. Find the P(X ≤ 2); prob(X ≤ 3); prob(2 ≤ X ≤ 3). |
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| m67176 | Are the following models linear in the parameters? If not, is there any way to make them linear-in-parameter (LIP) models?
a.
b. |
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| m67179 | Are the following variables quantitative or qualitative?
a. U.S. balance of payments.
b. Political party affiliation.
c. U.S. exports to the Republic of China.
d. Membership in the United Nations.
e. Consumer Price Index (CPI).
f. Education.
g. People living in the European Community (EC).
h. Membership in General Agreement on Tariffs and Trade (GATT).
i. Members of the U.S. Congress,
j. Social security recipients. |
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| m67195 | As cheese ages, several chemical processes take place that determine the taste of the final product. Table 8-9 on the textbook s Web site contains data on the concentrations of various chemicals in 30 samples of mature cheddar cheese and a subjective measure of taste for each sample. The variables Acetic and H2S are the natural logarithm of the concentration of acetic acid and hydrogen sulfide, respectively. The variable lactic has not been log-transformed.
a. Draw a scatter plot of the four variables.
b. Do a bivariate regression of taste on acetic and H2S and interpret your results.
c. Do a bivariate regression of taste on lactic and H2S. How do interpret the results?
d. Do a multiple regression of taste on acetic, H2S, and lactic. Interpret your results.
e. Knowing what you know about multicollinearity, how would you decide among these regressions?
f. What overall conclusions can you draw from your analysis? |
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| m67272 | Assume that the per capita income of residents in a country is normally distributed with mean µ = $1000 and variance σ2 = 10,000 ($ squared).
a. What is the probability that the per capita income lies between $800 and $1200?
b. What is the probability that it exceeds $1200?
c. What is the probability that it is less than $800?
d. Is it true that the probability of per capita income exceeding $5000 is practically zero? |
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| m67310 | Assuming the AR(1) scheme, what are the consequences of the CLRM assumption that the error terms in the PRF are uncorrelated? |
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| m67339 | Based on 11 annual observations, the following regressions were obtained:
Model A: Ŷt = 2.6911 - 0.4795Xt
se = (0.1216) (0.1140) r2 = 0.6628
Model B: InŶt = 0.7774 - 0.2530 In Xt
se = (0.0152) (0.0494) r2= 0.7448
where Y = the cups of coffee consumed per person per day and X = the price of coffee in dollars per pound.
a. Interpret the slope coefficients in the two models.
b. You are told that = 2.43 and = 1.11. At these mean values, estimate the price elasticity for Model A.
c. What is the price elasticity for Model B?
d. From the estimated elasticities, can you say that the demand for coffee is price inelastic?
e. How would you interpret the intercept in Model B?
f. Since the r2 of Model B is larger than that of Model A, Model B is preferable to Model A. Comment on this statement. |
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| m67340 | Based on a random sample of 10 values from a normal population with mean µ and standard deviation σ, you calculated that = 8 and the sample standard deviation = 4. Estimate a 95% confidence interval for the population mean. Which probability distribution did you use? Why? |
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| m67341 | Based on a random sample of 500 married women, the following table gives the joint PMF of their work status in relation to the presence or absence of children in the household.10
CHILDREN AND WORK STATUS OF WOMEN IN THE UNITED STATES
a. Are children and working outside of the home mutually exclusive?
b. Are working outside of the home and presence of children independent events? |
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| m67343 | Based on a sample of 20 couples, Barbara Bund lackson26 obtained the following regression.
where P = the probability of restaurant usage, = 1 if went to a restaurant,
0 otherwise
Income = the income in thousands of dollars
Babysitter = 1 if needed a babysitter
0 if otherwise
Of the 20 couples, 11 regularly went to a restaurant, 6 regularly used a babysitter, and the income ranged from a low of $17,000 to a high of $44,000.
a. Interpret the preceding logit regression.
b. Find out the logit value of a couple with an income of $44,000 who needed a babysitter.
c. For the same couple, find out the probability of going to a restaurant. |
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| m67347 | Based on data for the United States for the period 1965 to 2006 (found in Table 3-4 on the textbook s Web site), the following regression results were obtained:
GNPt = - 995.5183 + 8.7503 M1t r2 = 0.9488
se = ( ) (0.3214)
t = (- 3.8258) ( )
where GNP is the gross national product ($, in billions) and M1 is the money supply ($, in billions).
M1 includes currency, demand deposits, traveler s checks, and other checkable deposits.
a. Fill in the blank parentheses.
b. The monetarists maintain that money supply has a significant positive impact on GNP. How would you test this hypothesis?
c. What is the meaning of the negative intercept?
d. Suppose M1 for 2007 is $750 billion. What is the mean forecast value of GNP for that year? |
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| m67354 | Based on quarterly observations for the United States for the period 1961-1 through 1977-11, H. C. Huang, J. J. Siegfried, and F. Zardoshty14 estimated the following demand function for coffee. (The figures in parentheses are t values.)
In Qt = 1.2789 - 0.1647 In Pt + 0.5115 In It + 0.1483 In P t
t = (-2.14) (1.23) (0.55)
- 0.0089T - 0.0961 D1t - 0.1570D2t - 0.0097D3t R2 = 0.80
t = (- 3.36) (- 3.74) (- 6.03) (- 0.37)
where Q = pounds of coffee consumed per capita
P = the relative price of coffee per pound at 1967 prices
I = per capita PDI, in thousands of 1967 dollars
P = the relative price of tea per quarter pound at 1967 prices
t = the time trend with t = 1 for 1961-I, to t = 66 for 1977-II
D1 = 1 for the first quarter
D2 = 1 for the second quarter
D3 = 1 for the third quarter
In = the natural log
a. How would you interpret the coefficients of P, I, and P ?
b. Is the demand for coffee price elastic?
c. Are coffee and tea substitute or complementary products?
d. How would you interpret the coefficient of t?
e. What is the trend rate of growth or decline in coffee consumption in the United States? If there is a decline in coffee consumption, what accounts for it?
f. What is the income elasticity of demand for coffee?
g. How would you test the hypothesis that the income elasticity of demand for coffee is not significantly different from 1?
h. What do the dummy variables represent in this case?
i. How do you interpret the dummies i |
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| m67358 | Based on the Current Population Survey (CPS) of March 1995, Paul Rudd extracted a sample of 1289 workers, aged 18 to 65, and obtained the following information on each worker:
Wage = hourly wage in $
Age = age in years
Female = 1 if female worker
Nonwhite = 1 if a nonwhite worker
Union = 1 if a union member
Education = years of schooling
Experience = potential labor market experience in years.
The full data set can be found as Table 6-16 on the textbook s Web site.
a. Based on these data, estimate the following model, obtaining the usual regression statistics.
In Wagei = B1 + B2 Age + B3 Female + B4 Nonwhite + B5 Union + B6 Education
+ B7 Experience + ui
where In Wage = (natural logarithm of Wage)
b. How do you interpret each regression coefficient?
c. Which of these coefficients are statistically significant at the 5% level? Also obtain the p value of each estimated t value.
d. Do union workers, on average, earn a higher hourly wage?
e. Do female workers, on average, earn less than their male counterparts?
f. Is the average hourly wage of female nonwhite workers lower than the average hourly wage of female white workers? How do you know? (Hint: interaction dummy.)
g. Is the average hourly wage of female union workers higher than the average hourly wage of female non-union workers? How do you know?
h. Using the data, develop alternative specifications of the wage function, taking into account possible interactions between dummy variables |
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