Essentials of Econometrics 4th edition Damodar Gujarati, Dawn Porter - Solutions

2.8. State whether the following models are linear regression models: a. Yi = B1 + B2(l / Xi) b. Yi = B1 + B2 In Xi + ui c. In Yi = B1 + B2 Xi + ui d. In Yi = B} + B2In Xi + ui e. Yi = Bi + B2B3Xi + ui f. Yi = B] + B32 Xi + ui
Table 2-8 gives data on weekly family consumption expenditure (Y) (in dollars) and weekly family income (X) (in dollars).HYPOTHETICAL DATA ON WEEKLY CONSUMPTIONEXPENDITURE AND WEEKLY INCOMEa. For each income level, compute the mean consumption expenditure, E(Y | Xi), that is, the conditional
Explain the meaning ofa. Least squares.b. OLS estimators.c. The variance of an estimator.d. Standard error of an estimator.e. Homoscedasticity.f. Heteroscedasticity.g. Autocorrelation.h. Total sum of squares TSS..i. Explained sum of squares ESS.,j. Residual sum of squares RSS..k. r2l. Standard
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 ($, in billions)
Do economic events affect presidential elections? To test this so-called political business cycle theory, Gary Smith20 obtained the following regression results based on the U.S. presidential elections for the four yearly periods from 1928 to 1980 (i.e., the data are for years 1928, 1932,
To study the relationship between capacity utilization in manufacturing and inflation in the United States, we obtained the data shown in Table 3-5 (found on the textbook's Web site). In this table, Y = inflation rate as measured by the percentage change in GDP implicit price deflator and X =
Continue with Problem 3.12, but suppose we now regress X on Y.a. Present the result of this regression and comment.b. If you multiply the slope coefficients in the two regressions, what do you obtain? Is this result surprising to you?c. The regression in Problem 3.12 may be called the direct
Table 3-6 gives data on X (net profits after tax in U.S. manufacturing industries [$, in millions]) and Y (cash dividend paid quarterly in manufacturing industries [$, in millions]) for years 1974 to 1986.CASH DIVIDEND (V) AND AFTER-TAX PROFITS (X)IN U.S. MANUFACTURING INDUSTRIES, 1974-1986a. What
Refer to the S.A.T. data given in Table 2-15 on the textbook's Web site. Suppose you want to predict the male math scores on the basis of the female math scores by running the following regression: Yt = B1 + B2Xt + ut where Y and X denote the male and female math scores, respectively. a. Estimate
Repeat the exercise in Problem 3.15 but let Y and X denote the male and the female critical reading scores, respectively. Assume a female critical reading score for 2008 of 505. Problem 3.15 a. Estimate the preceding regression, obtaining the usual summary statistics. b. Test the hypothesis that
Consider the following regression results: Ŷt= - 0.17 + 5.26Xt 2 = 0.10, Durbin-Watson = 2.01 t = (- 1.73) (2.71) where Y = the real return on the stock price index from January of the current year to January of the following year X = the total dividends in the preceding year divided by the stock
Refer to Example 2.1 on years of schooling and average hourly earnings. The data for this example are given in Table 2-5 and the regression results are presented in Eq. (2.21). For this regressiona. Obtain the standard errors of the intercept and slope coefficients and r2.b. Test the hypothesis
Example 2.2 discusses Okun's law, as shown in Eq. (2.22). This equation can also be written as Xt = B1 + B2Yt, where X = percent growth in real output, as measured by GDP and Y = change in the unemployment rate, measured in percentage points. Using the data given in Table 2-13 on the textbook's Web
State with brief reasons whether the following statements are true, false, or uncertain.a. OLS is an estimating procedure that minimizes the sum of the errors squared, ∑u2i.b. The assumptions made by the classical linear regression model CLRM. are not necessary to compute OLS estimators.c. The
For Example 2.3, relating stock prices to interest rates, are the regression results given in Eq. (2.24) statistically significant? Show the necessary calculations.
Refer to Example 2.5 about antique clocks and their prices. Based on Table 2-14, we obtained the regression results shown in Eqs.(2.27) and (2.28). For each regression obtain the standard errors, the t ratios, and the r2 values. Test for the statistical significance of the estimated coefficients in
Refer to Problem 3.22. Using OLS regressions, answer questions (a), (b), and (c).
Table 3-7 (found on the textbook's Web site) gives data on U.S. expenditure on imported goods (Y) and personal disposable income (X) for the period 1959 to 2006.Based on the data given in this table, estimate an import expenditure function, obtaining the usual regression statistics, and test the
Show that the OLS estimators, b1 and b2, are linear estimators. Also show that these estimators are linear functions of the error term ui.
Prove Eq. (3.35).
a. If B2 = 0, b2 / se(b2) = ... b. l(B2 = 0,t = b2/ ... c. r2 lies between ... and ... d. r lies between ... and ... e. TSS = RSS +... f. d.f. (of TSS) = d.f. (of...) + d.f. (of RSS) g. is called ... h. ∑y2i = 2(Yi - ...)2 i. ∑y2i = b2(...)
Consider the following regression: Ŷi = - 66.1058 + 0.0650 Xi r2 = 0.9460 se = (10.7509) ( ) n = 20 t = ( ) (18.73) Fill in the missing numbers. Would you reject the hypothesis that true B2 is zero at a = 5%? Tell whether you are using a one-tailed or two-tailed test and why.
Show that all the following formulas to compute r2 are equivalent:
Show that ∑ ei = n - nb1 - nb2 = 0
Based on the data for the years 1962 to 1977 for the United States, Dale Bails and Larry Peppers obtained the following demand function for automobiles: Ŷt = 5807 + 3.24Xt r2 = 0.22 se = (1.634) where Y = retail sales of passenger cars (thousands) and X = the real disposable income (billions of
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
You are given the following data based on 10 pairs of observations on Y and X. ∑yi = 1110 ∑Xi = 1680 ∑XiYi = 204,200 ∑X2i = 315,400 ∑Y2i = 133,300 Assuming all the assumptions of CLRM are fulfilled, obtain a. b1[ and b2. b. standard errors of these estimators. c. r2 d. Establish 95%
a. Partial regression coefficient b. Coefficient of multiple determination, R2 c. Perfect collinearity d. Perfect multicollinearity e. Individual hypothesis testing f. Joint hypothesis testing g. Adjusted R2
To explain what determines the price of air conditioners, B. T. Ratchford obtained the following regression results based on a sample of 19 air conditioners: Yi = - 68.236 + 0.023X2i + 19.729X3i + 7.653X4iR2 = 0.84 se = (0.005) (8.992) (3.082) where Y = the price, in dollars X2 = the BTU rating
Based on the U.S. data for 1965-IQ to 1983-IVQ (n = 76), James Doti and Esmael Adibi25 obtained the following regression to explain personal consumption expenditure (PCE) in the United States. Ŷt = - 10.96 + 0.93X2t - 2.09X3t t = (- 3.33) (249.06) (- 3.09) R2 = 0.9996 F = 83,753.7 where Y = the
In the illustrative Example 4.2 given in the text, test the hypothesis that X2 and X3 together have no influence on Y. Which test will you use? What are the assumptions underlying that test?
Table 4-7 (found on the textbook's Web site) gives data on child mortality (CM), female literacy rate (FLR), per capita GNP (PGNP), and total fertility rate (TFR) for a group of 64 countries.a. A priori, what is the expected relationship between CM and each of the other variables?b. Regress CM on
Use formula (4.54) to answer the following question:What conclusion do you draw about the relationship between R2 and 2?
For Example 4.3, compute the F value. If that F value is significant, what does that mean?
Refer to the data given in Table 2-12 (found on the textbook's Web site) to answer the following questions:a. Develop a multiple regression model to explain the average starting pay of MBA graduates, obtaining the usual regression output.b. If you include both GPA and GMAT scores in the model, a
Figure 4-1 gives you the normal probability plot for Example 4.4.a. From this figure, can you tell if the error term in Eq. (4.62) follows the normal distribution? Why or why not?b. Is the observed Anderson-Darling A1value of 0.468 statistically significant? If it is, what does that mean? If it is
Explain step by step the procedure involved ina. Testing the statistical significance of a single multiple regression coefficient.b. Testing the statistical significance of all partial slope coefficients.
Restricted least squares (RLS). If the dependent variables in the restricted and unrestricted regressions are not the same, you can use the following variant of the F test given in Eq. (4.56)where RSSr = residual sum of squares from the restricted regression, RSSur = residual sum of squares from
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
Table 4-8 (found on the textbook's Web site) contains variables from the Los Angeles 2008 Zagat Restaurant Guide. The variables are score values out of 30, with 30 being the best. For each restaurant listed, the table provides data for four categories: food, decor, service, and average price for a
State with brief reasons whether the following statements are true (T), false (F), or uncertain (U).a. The adjusted and unadjusted R2s are identical only when the unadjusted R2 is equal to 1.b. The way to determine whether a group of explanatory variables exerts significant influence on the
You are given the following data:Based on these data, estimate the following regressions a. Yi =A1 + A2X2i+ ui b. Yi = C1 + C3X3i + ui c. Yi = B1 + B2X2i + B3X3i + ui d. Is A2 = B2? Why or why not? e. Is C3 = B3? Why or why not? What general conclusion can you draw from this exercise?
You are given the following data based on 15 observations: = 367.693; 2 = 402.760; 3 = 8.0; ∑y2i = 66,042.269 ∑x22i = 84,855.096; ∑ x23i = 280.0; ∑ yix2i= 74,778.346 ∑yix3i = 4,250.9; ∑x2ix3i = 4,796.0 where lowercase letters, as usual, denote deviations from sample mean values. a.
A three-variable regression gave the following results:a. What is the sample size? b. What is the value of the RSS? c. What are the d.f. of the ESS and RSS? d. What is R2? And 2? e. Test the hypothesis that X2 and X3 have zero influence on Y. Which test do you use and why? f. From the preceding
Explain briefly what is meant by a. Log-log model b. Log-lin model c. Lin-log model d. Elasticity coefficient e. Elasticity at mean value
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
a. Interpret the coefficient of the labor input X2. Is it statistically different from 1? b. Interpret the coefficient of the capital input X3. Is it statistically different from zero? And from 1? c. What is the interpretation of the intercept value of - 1.6524? d. Test the hypothesis that B2 = B3=
In their study of the demand for international reserves (i.e., foreign reserve currency such as the dollar or International Monetary Fund [IMF] drawing rights), Mohsen Bahami-Oskooee and Margaret Malixi obtained the following regression results for a sample of 28 less developed countries
Based on the U.K. data on annual percentage change in wages (Y) and the percent annual unemployment rate (X) for the years 1950 to 1966, the following regression results were obtained: Ŷt = - 1.4282 + 8.7243(1/Xt) se = (2.0675) (2.8478) r2= 0.3849 F(l, 15) = 9.39 a. What is the interpretation of
Table 5-13 gives data on the Consumer Price Index, Y(1980 = 100), and the money supply, X (billions of German marks), for Germany for the years 1971 to 1987.CONSUMER PRICE INDEX (Y)(1980 = 100) AND THE MONEYSUPPLY (X)(MARKS, IN BILLIONS), GERMANY, 1971-1987a. Regress the following: 1. Y on X 2. In
Based on the following data, estimate the model:(1/Yi) = B1 + B2Xi + uia. What is the interpretation of B2? b. What is the rate of change of y with respect to X? c. What is the elasticity of y with respect to X? d. For the same data, run the regression Yi = B1 + B2 (1/Xi) + ui e. Can you compare
Comparing two r2s when dependent variables are different. Suppose you want to compare the r2 values of the growth model (5.19) with the linear trend model (5.23) of the consumer credit outstanding regressions given in the text. Proceed as follows: a. Obtain In Yt, that is, the estimated log value
Based on the GNP/money supply data given in Table 5-14 (found on the textbook's Web site), the following regression results were obtained (y = GNP, X = M2):a. For each model, interpret the slope coefficient. b. For each model, estimate the elasticity of the GNP with respect to money supply and
Refer to the energy demand data given in Table 5-3. Instead of fitting the log-linear model to the data, fit the following linear model:Yt = B1 + B2X2t + B3X3, + uta. Estimate the regression coefficients, their standard errors, and obtain R2 and adjusted R2.b. Interpret the various regression
To explain the behavior of business loan activity at large commercial banks, Bruce J. Summers used the following model:Yt = 1 / A + Bt (A)where Y is commercial and industrial (C&I) loans in millions of dollars, and t is time, measured in months. The data used in the analysis was collected monthly
What is meant by a slope coefficient and an elasticity coefficient? What is the relationship between the two?
Refer to regression (5.31). a. Interpret the slope coefficient. b. Using Table 5-11, compute the elasticity for this model. Is this elasticity constant or variable?
Refer to the data given in Table 5-5 (found on the textbook's Web site). Fit an appropriate Engle curve to the various expenditure categories in relation to total personal consumption expenditure and comment on the statistical results.
Table 5-15 gives data on the annual rate of return Y (%) on A future mutual fund and a return on a market portfolio as represented by the Fisher Index, X (%). Now consider the following model, which is known in the finance literature as the characteristic line.Yt = B1 + B2Xi + uiANNUAL RATES OF
Raw R2 for the regression-through-the-origin model. As noted earlier, for the regression-through-the-origin regression model the conventionally computed R2 may not be meaningful. One suggested alternative for such models is the so-called "raw" R2, which is defined (for the two-variable case) as
For regression (5.39) compute the raw r2 value and compare it with that given in Eq. (5.40).
Consider data on the weekly stock prices of Qualcomm, Inc., a digital wireless telecommunications designer and manufacturer, over the time period of 1995 to 2000. The complete data can be found in Table 5-16 on the textbook's Web site. a. Create a scatter gram of the closing stock price over time.
Table 5-17 on the textbook's Web site contains data about several magazines. The variables are: magazine name, cost of a full-page ad, circulation (projected, in thousands), percent male among the predicted readership, and median household income of readership. The goal is to predict the
Refer to Example 4.5 (Table 4-6) about education, GDP, and population for 38 countries. a. Estimate a linear (LIV) model for the data. What are the resulting equation and relevant output values (i.e., F statistic, t values, and R2)? b. Now attempt to estimate a log-linear model (where both of the
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
Refer to Example 5.6 in the chapter. It was shown that the percentage change in the index of hourly earnings and the unemployment rate from 1958-1969 followed the traditional Phillips curve model. An updated version of the data, from 1965-2007, can be found in Table 5-19 on the textbook's Web
Fill in the blanks in Table 5-12.FUNCTIONAL FORMS OFREGRESSION MODELS
Complete the following sentences: a. In the double-log model the slope coefficient measures ... b. In the lin-log model the slope coefficient measures ... c. In the log-lin model the slope coefficient measures ... d. Elasticity of Y with respect to X is defined as ... e. Price elasticity is defined
State with reason whether the following statements are true (T) or false (F): a. For the double-log model, the slope and elasticity coefficients are the same. b. For the linear-in-variable (LIV) model, the slope coefficient is constant but the elasticity coefficient is variable, whereas for the
The Engel expenditure curve relates a consumer's expenditure on a commodity to his or her total income. Letting Y = the consumption expenditure on a commodity and X = the consumer income, consider the following models: a. Yi = B1 + B2Xi + ui b. Yi = B1 + B2(l/Xi) + ui c. In Yi = B1 + B2 In X, +
The growth model Eq. (5.18) was fitted to several U.S. economic time series and the following results were obtained:a. In each case find out the instantaneous rate of growth. b. What is the compound rate of growth in each case? c. For the S&P data, why is there a difference in the two slope
a. The marginal cost (MC) is the change in the TC for a unit change in output; that is, it is the rate of change of the TC with respect to output. (Technically, it is the derivative of the TC with respect to X, the output.) Derive this function from regression (5.32). b. The average variable cost
Are the following models linear in the parameters? If not, is there any way to make them linear-in-parameter (LIP) models?a.b.
Explain briefly the meaning of: a. Categorical variables. b. Qualitative variables. c. Analysis-of-variance (ANOVA) models. d. Analysis-of-covariance (ANCOVA) models. e. The dummy variable trap. f. Differential intercept dummies. g. Differential slope dummies.
In a regression of weight on height involving 51 students, 36 males and 15 females, the following regression results were obtained:151.2. 3. where weight is in pounds, height is in inches, and where Dum sex = 1 if male = 0 if otherwise Dumht. = the interactive or differential slope dummy a. Which
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 + utwhereD2 = 1 in the second quarter, = 0 if
Use the data of Problem 6.11 but estimate the following model: Salest = B1Dit + B2D2t + B3D3t + B4D4t + ut In this model there is a dummy assigned to each quarter. a. How does this model differ from the one given in Problem 6.11? b. To estimate this model, will you have to use a regression program
How would you modify this equation to allow for the possibility that the coefficient of Tuition also differs from region to region? Present your results. For Information: Refer to Eq. (6.17) in the text.
Re estimate Eq. (6.30) by assigning a dummy for each quarter and compare your results with those given in Eq. (6.30). In estimating such an equation, what precaution must you take?
Consider the following model: Yi = B1 + B2D2i + B3D3i + B4 (D2i D3i) + B5Xi + ui where Y = the annual salary of a college teacher X = years of teaching experience D2 = 1 if male = 0 if otherwise D3 = 1 if white = 0 if otherwise a. The term (D2iD3i) represents the interaction effect. What does this
Suppose in the regression (6.1) we letDi = 1 for female= - 1 for maleUsing the data given in Table 6-2, estimate regression (6.1) with this dummy setup and compare your results with those given in regression (6.4). What general conclusion can you draw?
Continue with the preceding problem but now assume thatDi = 2 for female= 1 for maleWith this dummy scheme re-estimate regression (6.1) using the data of Table 6-2 and compare your results. What general conclusions can you draw from the various dummy schemes?
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
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.
What is the regression equation for an applicant who is an unmarried white male? Is it statistically different for an unmarried white single female? For Information: Refer to Example 6.6.
Continue with Problem 6.20. What would the regression equation be if you were to include interaction dummies for the three qualitative variables in the model?
The impact of product differentiation on rate of return on equity. To find out whether firms selling differentiated products (i.e., brand names) experience higher rates of return on their equity capital, J. A. Dalton and S. L. Levin16 obtained the following regression results based on a sample of
What has happened to the United States Phillips curve? Refer to Example 5.6. Extending the sample to 1977, the following model was estimated:WhereY = the year-to-year percentage change in the index of hourly earningsX = the percent unemployment rateDT = 1 for observations through 1969= 0 if
Count R2. Since the conventional R2 value may not be appropriate for linear probability models, one suggested alternative is the count R2, which is defined as:Since in LPM the dependent variable takes a value of 1 or 0, if the predicted probability is greater than 0.5, we classify that as 1, but if
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
The Phillips curve revisited again. Refer to Example 5.6 and Problem 5.29. It was shown that the percentage change in the index of hourly earnings and the unemployment rate from 1958-1969 followed the traditional Phillips curve model. The updated version of the data, from 1965-2007, can be found in
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 jobManagement= 0 for non managers and 1 for managersEducation= 1 for those whose highest education level is high
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
What problems do you foresee in estimating the following models: a. Yt = B0 + B1D1t + B2D2t + B3D3t + B4D4t + ut where Dit = 1 for observation in quarter i, i = 1, 2,3,4 = 0 otherwise b. GNP, = B1 + B2Mt + B3Mt -1 + B4(Mt - Mt-1) + ut where GNPt = gross national product (GNP) at time t Mt = the
State with reasons whether the following statements are true or false. a. In the model Yi = B1 + B2Di + ui, letting Di take the values of (0, 2) instead of (0, 1) will halve the value of B2 and will also halve the t value. b. When dummy variables are used, ordinary least squares (OLS) estimators
Consider the following model: Yi = B0 + B1Xi + B2D2i + B3D3 + ui where Y = annual earnings of MBA graduates X = years of service D2 = 1 if Harvard MBA = 0 if otherwise D3 = l if Wharton MBA = 0 if otherwise a. What are the expected signs of the various coefficients? b. How would you interpret B2
Continue with Question 6.6 but now consider the following model: Yi = B0 + B1Xi + B2D2i + B3D3i + B4 (D2iXi) + B5 (D3iXi) + ui a. What is the difference between this model and the one given in Question 6.6? b. What is the interpretation of B4 and B5? c. If B4 and B5 are individually statistically
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'tt
In a study of the determinants of direct airfares to Cleveland, Paul W. Bauer and Thomas J. Zlatoper obtained the following regression results (in tabular form) to explain one-way airfare for first class, coach, and discount airfares. (The dependent variable is one-way airfare in dollars). The
What is meant by specification errors?

Showing 200 - 300 of 833

Essentials of Econometrics 4th edition Damodar Gujarati, Dawn Porter - Solutions

Step by Step Answers