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About 833 results. 1294 free access solutions
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| m71385 | Table 5-18 on the textbook s Web site contains data on average life expectancy for 40 countries. It comes from the World Almanac and Book of Facts, 1993, by Pharos Books. The independent variables are the ratio of the number of people per television set and the ratio of number of people per physician.
a. Try fitting a linear (LIV) model to the data. Does this model seem to fit well?
b. Create two scatter grams, one of the natural log of life expectancy versus the natural log of people per television, and one of the natural log of life expectancy versus the natural log of people per physician. Do the graphs appear linear?
c. Estimate the equation for a log-linear model. Does this model fit well?
d. What do the coefficients of the log-linear model indicate about the relationships of the variables to life expectancy? Does this seem reasonable? |
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| m71386 | Table 6-12 on the textbook s Web site gives non seasonally adjusted quarterly data on the retail sales of hobby, toy, and game stores (in millions) for the period 1992:1 to 2008: II.
Consider the following model:
Salest = B1 + B2D2t + B3D3t + B4D4t + ut
where
D2 = 1 in the second quarter, = 0 if otherwise
D3 = 1 in the third quarter, = 0 if otherwise
D4 = 1 in the fourth quarter, = 0 if otherwise
a. Estimate the preceding regression.
b. What is the interpretation of the various coefficients?
c. Give a logical reason for why the results are this way.
*d. How would you use the estimated regression to depersonalize the data? |
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| m71387 | Table 6-13, found on the textbook s Web site, gives data on after-tax corporate profits and net corporate dividend payments ($, in billions) for the United States for the quarterly period of 1997:1 to 2008:2.
a. Regress dividend payments (V) on after-tax corporate profits (X) to find out if there is a relationship between the two.
b. To see if the dividend payments exhibit any seasonal pattern, develop a suitable dummy variable regression model and estimate it. In developing the model, how would you take into account that the intercept as well as the slope coefficient may vary from quarter to quarter?
c. When would you regress Y on X, disregarding seasonal variation?
d. Based on your results, what can you say about the seasonal pattern, if any, in the dividend payment policies of U.S. private corporations? Is this what you expected a priori? |
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| m71388 | Table 6-14, found on the textbook s Web site, gives quarterly data on real personal expenditure (PCE), real expenditure on durable goods (EXPDUR), real expenditure on nondurable goods (EXPNONDUR), and real expenditure on services (EXPSER), for the United States for the period 2000-1 to 2008-3. All data are in billions of (2000) dollars, and the quarterly data are at seasonally adjusted annual rates.
a. Plot the data on EXPDUR, EXPNONDUR, and EXPSER against PCE.
b. Suppose you regress each category of expenditure on PCE and the three dummies shown in Table 6-14. Would you expect the dummy variable coefficients to be statistically significant? Why or why not? Present your calculations.
c. If you do not expect the dummy variables to be statistically significant but you still include them in your model, what are the consequences of your action? |
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| m71389 | Table 6-15 on the textbook s Web site contains data on 46 mid-level employees and their salaries. The available independent variables are:
Experience = years of experience at the current job
Management = 0 for non managers and 1 for managers
Education = 1 for those whose highest education level is high school
2 for those whose highest education level is college
3 for those whose highest education level is graduate school
a. Does it make sense to utilize Education as it is listed in the data? What are the issues with leaving it this way?
b. After addressing the issues in part (a), run a linear regression using Experience, Management, and the changed Education variables. What is the new model? Are all the variables significant?
c. Now create a model to allow for the possibility that the increase in Salary may be different between managers and non managers, with respect to their years of experience. What are the results?
*d. Finally, create a model that incorporates the idea that Salary might increase, with respect to years of experience, at a different rate between employees with different education levels. |
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| m71390 | Table 7-10 on the textbook s Web site contains data about the manufacturing sector of all 50 states and the District of Columbia. The dependent variable is output, measured as "value added" in thousands of U.S. dollars, and the independent variables are worker hours and capital expenditures.
a. Predict output using a standard linear model. What is the function?
b. Create a log-linear model using the data as well. What is this function?
c. Use the MWD test to decide which model is more appropriate. |
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| m71391 | Table 7-5, found on the textbook s Web site, gives data on the real gross product, labor input, and real capital input in the Taiwanese manufacturing sector for the years 1958 to 1972. Suppose the theoretically correct production function is of the Cobb-Douglas type, as follows:
In Yt = B1 + B2 In X2t + B3 In X3t + ut
where In = the natural log.
a. Given the data shown in Table 7-5, estimate the Cobb-Douglas production function for Taiwan for the sample period and interpret the results.
b. Suppose capital data were not initially available and therefore someone estimated the following production function:
In Yt = C1 + C2 In X2t + vt
where v = an error term. What kind of specification error is incurred in this case? What are the consequences? Illustrate with the data in Table 7-5.
c. Now pretend that the data on labor input were not available initially and suppose you estimated the following model:
In Yt = C1 + C2 In X3t + wt
where w = an error term. What are the consequences of this type of specification error? Illustrate with the data given in Table 7-5. Consider the following models: |
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| m71392 | Table 7-6 (found on the textbook s Web site) gives data on the real rate of return (Y) on common stocks, the output growth (X2), and inflation (X3), all in percent for the United States for 1954 to 1981.
a. Regress Y on X3.
b. Regress Y on X2 and X3.
c. Comment on the two regression results in view of Professor Eugene Fama s observation that "the negative simple correlation between real stock returns and inflation is spurious (or false) because it is the result of two structural relationships: a positive relation between current real stock returns and expected output growth and a negative relationship between expected output growth and current inflation."
d. Do the regression in part (b) for the period 1956 to 1976, omitting the data for 1954 and 1955 due to unusual stock return behavior in those years, and compare this regression with the one obtained in part (b). Comment on the difference, if any, between the two.
e. Suppose you want to run the regression for the period 1956 to 1981 but want to distinguish between the periods 1956 to 1976 and 1977 to 1981. How would you run this regression? |
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| m71393 | Table 7-7 (found on the textbook s Web site) gives data on indexes of aggregate final energy demand (Y), the real gross domestic product, the GDP (X2), and the real energy price (X3) for the OECD countries-the United States, Canada, Germany, France, the United Kingdom, Italy, and Japan-for the period 1960 to 1982. (All indexes with base 1973 = 100.)
a. Estimate the following models:
Model A: In Yt = B1 + B2 In X2t + B3 In X3t + u1t
Model B: In Yt = A1 + A2 In X2t + A3 In X2(t - 1) + A4 In X3t + u2t
Model C: In Yt = C1 + C2 In X2t + C3 In X3t + C4 In X3(t - 1) + u3t
Model D: In Yt = D1 + D2 In X2t + D3 In X3t + D4 In Y(t - 1) + u4t
where the u s are the error terms.
Models B and C are called dynamic models-models that explicitly take into account the changes of a variable over time. Models B and C are called distributed lag models because the impact of an explanatory variable on the dependent variable is spread over time, here over two time periods. Model D is called an autoregressive model because one of the explanatory variables is a lagged value of the dependent variable.
b. If you estimate Model A only, whereas the true model is either B, C, or D, what kind of specification bias is involved?
c. Since all the preceding models are log-linear, the slope coefficients represent elasticity coefficients. What are the income (i.e., with respect to GDP) and price elasticities for Model A? How would you go about estimating these elasticities for the other three mod |
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| m71394 | Table 7-8 on the textbook s Web site gives data on variables that might affect the demand for chickens in the United States. The dependent variable here is the per capita consumption of chickens, and the explanatory variables are per capita real disposable income and the prices of chicken and chicken substitutes (pork and beef).
a. Estimate a log-linear model using these data.
b. Estimate a linear model using these data.
c. How would you choose between the two models? What test will you use? Show the necessary computations. |
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| m71395 | Table 8-10 on the textbook s Web site gives data on the average salary of top managers (in thousands of Dutch guilders), profit (in millions of Dutch guilders), and turnover (in millions of Dutch guilders) for 84 of the largest firms in the Netherlands. Let V = salary, X2 = profit, and X3 = turnover.
a. Estimate the following regression:
In Yi = B1 + B2In X2 + B3In X3 + ui
where In = natural logarithm.
b. Are all the slope coefficients individually statistically significant at the 5% level?
c. Are the slope coefficients together statistically significant at the 5% level? Which test would you use and why?
d. If the answer to (b) is yes, and the answer to (a) is no, what may be the reason(s)?
e. If you suspect multicollinearity, how would you find that out? Which test(s) would you use? |
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| m71396 | Table 8-7 on the textbook s Web site gives data on imports, GDP, and the Consumer Price Index (CPI) for the United States over the period 1975-2005.
You are asked to consider the following model:
In Imports t = β1 + β2 In GDP t + β3 In CPI t + ut
a. Estimate the parameters of this model using the data given in the table.
b. Do you suspect that there is multicollinearity in the data?
c. Regress:
(1) In Importst = A1 + A2 In GDPt
(2) In Importst = B1 + B2 In CPIt
(3) In GDPt = C1 + C2 In CPIt
On the basis of these regressions, what can you say about the nature of multicollinearity in the data?
d. Suppose there is multicollinearity in the data but (2 and 3 are individually significant at the 5% level and the overall F test is also significant. In this case, should we worry about the collinearity problem? |
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| m71397 | Table 8-8 on the textbook s Web site gives data on new passenger cars sold in the United States as a function of several variables.
a. Develop a suitable linear or log-linear model to estimate a demand function for automobiles in the United States.
b. If you decide to include all the regressors given in the table as explanatory variables, do you expect to face the multicollinearity problem? Why?
c. If you do expect to face the multicollinearity problem, how will you go about resolving the problem? State your assumptions clearly and show all calculations. |
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| m71398 | Table 9-5, on the textbook s Web site, gives data on five socioeconomic indicators for a sample of 20 countries, divided into four per-capita income categories: low-income (up to $500 per year), lower-middle income (annual income between $500 and $2200), upper-middle income (annual income between $2300 and $5500), and higher-income (over $5500 a year). The first five countries in the table belong to the first income category, the second five countries to the second income category, and so on.
a. Create a regression using all five independent variables. A priori, what do you expect the impact of the population growth rate (X4) and daily calorie intake (X5) will be on infant mortality rate (Y)?
b. Estimate the preceding regression and see if your expectations were correct.
c. If you encounter multicollinearity in the preceding regression, what can you do about it? You may undertake any corrective measures that you deem necessary. |
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| m71399 | Table 9-8 (found on the textbook s Web site) gives data on salary and related data on 447 executives of Fortune 500 companies. Salary = 1999 salary and bonuses; tot-comp = 1999 CEO total compensation; tenure = number of years as CEO (0 if less than 6 months); age = age of CEO; sales = total 1998 sales revenue of the firm; profits = 1998 profits for the firm; and assets = total assets of the firm in 1998.
a. Estimate the following regression from these data and obtain the Breusch-Pagan statistic to check for heteroscedasticity:
Salaryi = B1 + B2tenurei + B3agei + B4salesi + B5profitsi + B6pssetsi + ui
Does there seem to be a problem with heteroscedasticity?
b. Now create a second model using In(Salary) as the dependent variable. Is there any improvement in the heteroscedasticity?
c. Create scatter grams of Salary versus each of the independent variables. Can you discern which variable(s) is (are) contributing to the issue? What suggestions would you make now to address this? What is your final model?
d. Now obtain (White s) robust standard errors. Are there any noticeable differences? |
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| m71400 | Table 9-9 (on the textbook s Web site) gives data on 81 cars regarding MPG (average miles per gallon), HP (engine horsepower), VOL (cubic feet of cab space), SP (top speed, miles per hour), and WT (vehicle weight in 100 lbs.).
a. Consider the following model:
MPGi = B1 + B2SPi + B3HPi + B4WTi + ui
Estimate the parameters of this model and interpret the results. Do they make economic sense?
b. Would you expect the error variance in the preceding model to be heteroscedastic? Why?
c. Use the White test to find out if the error variance is heteroscedastic.
d. Obtain White s heteroscedasticity-consistent standard errors and t values and compare your results with those obtained from OLS.
e. If heteroscedasticity is established, how would you transform the data so that in the transformed data the error variance is homoscedastic? Show the necessary calculations. |
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| m71402 | Table B-6 gives data on the number of new business incorporations (Y) and the number of business failures (X) for the United States from 1984 to 1995.
a. What is the average value of new business incorporations? And the variance?
b. What is the average value of business failures? And the variance?
c. What is the covariance between Y and X? And the correlation coefficient?
NUMBER OF NEW BUSINESS INCORPORATIONS (Y) AND NUMBER
OF BUSINESS FAILURES (X), UNITED STATES, 1984-1995
d. Are the two variables independent?
e. If there is correlation between the two variables, does this mean that one variable causes the other variable? That is, do new incorporations cause business failures, or vice versa? |
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| m71433 | The 10 economic forecasters of a random sample were asked to forecast the rate of growth of the real gross national product (GNP) for the coming year. Suppose the probability distribution of the r.v.-forecast-is normal.
a. The probability is 0.10 that the sample variance of the forecast is more than X percent of the population variance. What is the value of X?
b. If the probability is 0.95 so that the sample variance is between X and y per-cent of the population variance, what will be the values of X and Y? |
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| m71476 | The amount of toothpaste in a tube is normally distributed with a mean of 6.5 ounces and an s.d. of 0.8 ounces. The cost of producing each tube is 50 cents. If in a quality control examination a tube is found to weigh less than 6 ounces, it is to be refilled to the mean value at a cost of 20 cents per tube. On the other hand, if the tube weighs more than 7 ounces, the company loses a profit of 5 cents per tube.
If 1000 tubes are examined,
a. How many tubes will be found to contain less than 6 ounces?
b. In that case, what will be the total cost of the refill?
c. How many tubes will be found to contain more than 7 ounces? In that case, what will be the amount of profits lost? |
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| m71543 | The characteristic line of modern investment analysis involves running the following regression:
r1 = B1 + B2r mt + ut
where r = the rate of return on a stock or security
rm = the rate of return on the market portfolio represented by a broad market index such as S&P 500, and
t = time
In investment analysis, B2 is known as the beta coefficient of the security and is used as a measure of market risk, that is, how developments in the market affect the fortunes of a given company.
Based on 240 monthly rates of return for the period 1956 to 1976, Fogler and Ganapathy obtained the following results for IBM stock. The market index used by the authors is the market portfolio index developed at the University of Chicago:
rt = 0.7264 + 1.0598rmt
se = (0.3001) (0.0728) r2 = 0.4710
a. Interpret the estimated intercept and slope.
b. How would you interpret r2?
c. A security whose beta coefficient is greater than 1 is called a volatile or aggressive security. Set up the appropriate null and alternative hypotheses and test them using the t test. Use a = 5%. |
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