Suppose that you are interested in estimating the ceteris paribus relationship between y and x1. For this purpose, you can collect data on two control variables, x2 and x3. (For concreteness, you might think of y as final exam score, x1 as class attendance, x2 as GPA up through the previous semester, and x3 as SAT or ACT score.) Let be the simple regression estimate from y on x1 and let be the multiple regression estimate from y on x1, x2, x3. a. If x1 is highly correlated with x2 and x3 in the sample, and x2 and x3 have large partial effects on y, would you expect and to be similar or very different? Explain. b. If x1 is almost uncorrelated with x2 and x3, but x2 and x3 are highly correlated, will and tend to be similar or very different? Explain. c. If x1 is highly correlated with x2 and x3, and x2 and x3 have small partial effects on y, would you expect se() or se() to be smaller? Explain. d. If x1 is almost uncorrelated with x2 and x3, x2 and x3 have large partial effects on y, and x2 and x3 are highly correlated, would you expect se() or se() to be smaller? Explain.
> The following financial statement was prepared by employees of Walters Corporation. Note 1: New styles and rapidly changing consumer preferences resulted in a $71,500 loss on the disposal of discontinued styles and related accessories. Note 2: The corp
> Simpson Corp. is an entertainment firm that derives approximately 30% of its income from the Casino Knights Division, which manages gambling facilities. As auditor for Simpson Corp., you have recently overheard the following discussion between the contro
> Charlie Brown, controller for the Kelly Corporation, is preparing the company’s income statement at year-end. He notes that the company lost a considerable sum on the sale of some equipment it had decided to replace. Since the company has sold equipment
> Bobek Inc. has recently reported steadily increasing income. The company reported income of $20,000 in 2009, $25,000 in 2010, and $30,000 in 2011. A number of market analysts have recommended that investors buy the stock because they expect the steady gr
> Maher Inc. reported income from continuing operations before taxes during 2012 of $790,000. Additional transactions occurring in 2012 but not considered in the $790,000 are as follows. 1. The corporation experienced an uninsured flood loss (extraordinary
> Presented below is the trial balance of Thompson Corporation at December 31, 2012. A physical count of inventory on December 31 resulted in an inventory amount of $64,000; thus, cost of goods sold for 2012 is $645,000. Instructions Prepare a single-st
> Presented below is information related to Dickinson Company for 2012. Retained earnings balance, January 1, 2012 ………………………………………… $ 980,000 Sales revenue ………………………………………………………………………………….. 25,000,000 Cost of goods sold …………………………………………………………………………… 16,000
> Wade Corp. has 150,000 shares of common stock outstanding. In 2012, the company reports income from continuing operations before income tax of $1,210,000. Additional transactions not considered in the $1,210,000 are as follows. 1. In 2012, Wade Corp. sol
> Below is the Retained Earnings account for the year 2012 for Acadian Corp. Instructions (a) Prepare a corrected retained earnings statement. Acadian Corp. normally sells investments of the type mentioned above. FIFO inventory was used in 2012 to comput
> One of the major groups involved in the standard-setting process is the American Institute of Certified Public Accountants. Initially, it was the primary organization that established accounting principles in the United States. Subsequently, it relinquis
> Presented below is a combined single-step income and retained earnings statement for Nerwin Company for 2012. Additional facts are as follows. 1. “Selling, general, and administrative expenses” for 2012 included a ch
> The following account balances were included in the trial balance of Twain Corporation at June 30, 2012. The Retained Earnings account had a balance of $337,000 at July 1, 2011. There are 80,000 shares of common stock outstanding. Instructions (a) Usi
> Presented below is information related to Brokaw Corp. for the year 2012. Instructions (a) Prepare a multiple-step income statement for 2012. Assume that 60,000 shares of common stock are outstanding. (b) Prepare a retained earnings statement for 2012.
> Presented below are selected amounts from the records of McGraw Corporation as of December 31, 2012. Cash ……………………………………………………………………………… $ 50,000 Administrative expenses ………………………………………………….. 100,000 Selling expenses ……………………………………………………………….. 80,000 Net
> The accountant of Weatherspoon Shoe Co. has compiled the following information from the company’s records as a basis for an income statement for the year ended December 31, 2012. Rent revenue ……………………………………………………………………………………. $ 29,000 Interest expense …
> The following balances were taken from the books of Parnevik Corp. on December 31, 2012. Assume the total effective tax rate on all items is 34%. Instructions Prepare a multiple-step income statement; 100,000 shares of common stock were outstanding du
> Two accountants for the firm of Allen and Wright are arguing about the merits of presenting an income statement in a multiple-step versus a single-step format. The discussion involves the following 2012 information related to Webster Company ($000 omitte
> The financial records of Dunbar Inc. were destroyed by fire at the end of 2012. Fortunately, the controller had kept certain statistical data related to the income statement as presented below. 1. The beginning merchandise inventory was $92,000 and decre
> Presented below are certain account balances of Wade Products Co. Instructions From the foregoing, compute the following: (a) Total net revenue, (b) Net income, (c) Dividends declared during the current year. $ 6,500 12,700 114,400 134,000 71,000 1
> Presented below are changes in all the account balances of Jackson Furniture Co. during the current year, except for retained earnings. Instructions Compute the net income for the current year, assuming that there were no entries in the Retained Earnin
> The financial statements of Marks and Spencer plc (M&S) are available at the book’s companion website or can be accessed at http://corporate.marksandspencer.com/documents/publications/2010/Annual_Report_2010. Instructions Refer to M&S’s financial statem
> On June 5, 2011, Argot Corporation signed a contract with Lopez Associates under which Lopez agreed (1) To construct an office building on land owned by Argot, (2) To accept responsibility for procuring financing for the project and finding tenants, and
> Regression analysis can be used to test whether the market efficiently uses information in valuing stocks. For concreteness, let return be the total return from holding a firm’s stock over the four-year period from the end of 1990 to the end of 1994. The
> As the estimated equation is given below, sleep 5= 3,638.25 - .148 totwrk - 11.13 educ + 2.20 age (112.28) (.017) (5.88) (1.45) n = 706, R2 = .113, where we now report standard errors along with the estimates. (i) Is either educ or age i
> Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6: y = β0 + β1x1 + β2x2 + β3x3 + µ. You would like to test the null hypothesis H0: β1 - 3β2 = 1. (i) Let β 1 and β 2
> (i) The population model estimated in Example 4.7 can be written as Log(scrap) = β0 + β1hrsemp + β2log(sales) + β3log(employ) + u. Using the 43 observations available for 1987, the estimated equation is Log(scrap) = 11.74 - .042 hrsemp - .951 log(sales)
> (i) In the simple regression model price = B0 + B1assess + u, the assessment is rational if B1 = 1 and B0 = 0. The estimated equation is price = - 14.47 + .976 assess (16.27) (.049) n = 88, SSR = 165,644.51, R2 = .820. First, test t
> Are rent rates influenced by the student population in a college town? Let rent be the average monthly rent paid on rental units in a college town in the United States. Let pop denote the total city population, avginc the average city income, and pctstu
> The variable rdintens is expenditures on research and development (R&D) as a percentage of sales. Sales are measured in millions of dollars. The variable profmarg is profits as a percentage of sales. Using the data in RDCHEM for 32 firms in the chemical
> Consider an equation to explain salaries of CEOs in terms of annual firm sales, return on equity (roe, inpercentage form), and return on the firm’s stock (ros, in percentage form): Log(salary) = B0 + B1log(sales) + B2roe + B3ros + u. (i) In terms of the
> Which of the following can cause the usual OLS t statistics to be invalid (that is, not to have t distributions under H0)? (i) Heteroskedasticity. (ii) A sample correlation coefficient of .95 between two independent variables that are in the model. (iii)
> 6 Consider the multiple regression model containing three independent variables, under Assumptions MLR.1 through MLR.4: y = 0 + 1x1 + 2x2 + 3x3 + u. You are interested in estimating the sum of the parameters on x1 and x2; call this u1 5 b0 1 b1.
> Use the data in ECONMATH to answer the following questions. (i) Estimate a model explaining colgpa to hsgpa, actmth, and acteng. Report the results in the usual form. Are all explanatory variables statistically significant? (ii) Consider an increase in h
> (i) Estimate the regression model educ = β0 + β1motheduc + β2fatheduc + β3abil + β4abil2 + µ by OLS and report the results in the usual form. Test the null hypothesis that educ is linearly related to abil against the alternative that the relationship is
> Use the data in ELEM94_95 to answer this question. The findings can be compared with those in Table 4.1. The dependent variable lavgsal is the log of average teacher salary and bs is the ratio of average benefits to average salary (by school). (i) Run
> (i) Use OLS to estimate the model Log(psoda) = β0 + β1prpblck + β2log(income) + β3prppov + µ, and report the results in the usual form. Is
> The data set 401KSUBS contains information on net financial wealth (nettfa), age of the survey respondent (age), annual family income (inc), family size (fsize), and participation in certain pension plans for people in the United States. The wealth and i
> (i) The variable phsrank is the person’s high school percentile. (A higher number is better. For example, 90 means you are ranked better than 90 percent of your graduating class.) Find the smallest, largest, and average phsrank in the sample. (ii) Add ph
> Use the data in WAGE2 for this exercise. (i) Consider the standard wage equation Log(wage) =
> Use the data in MLB1 for this exercise. Use the model estimated in given equation Log(salary) = 11.19 + .0689 years + .0126 gamesyr (0.29) (.0121) (.0026) 1 .00098 bavg + .0144 hrunsyr + .0108 rbisyr (.00110) (.0161) (.0072)
> The restricted version of the model can be estimated using all 1,388 observations in the sample. Compute the R-squared from the regression of bwght on cigs, parity, and faminc using all observations. Compare this to the R-squared reported for the restric
> Refer to Computer Exercise C2 in Chapter 3. Now, use the log of the housing price as the dependent variable: Log(price) = β0 + β1sqrft + β2bdrms + µ. (i) You are interested in estimating and obtaining a confidence interval for the percentage change in pr
> (i) State and test the null hypothesis that the rank of law schools has no ceteris paribus effect on median starting salary. (ii) Are features of the incoming class of students—namely, LSAT and GPA—individually or jointly significant for explaining sala
> The following model can be used to study whether campaign expenditures affect election outcomes: voteA = β0 + β1log(expendA) + β2log(expend) + β3prtystrA + µ, where voteA is the percentage of the vote received by Candidate A, expendA and expendB are cam
> The following estimated equations use the data in MLB1, which contains information on major league baseball salaries. The dependent variable, lsalary, is the log of salary. The two explanatory variables are years in the major leagues (years) and runs bat
> Suppose you have a sample of size n on three variables, y, x1, and z2, and you are primarily interested in the effect of x1 on y. Let
> a. Consider the simple regression model y = b0 + b1x + u under the first four Gauss-Markov assumptions. For some function g(x), for example g(x)= x2 or g(x)= log (1 + x2), define zi = g(xi). Define a slope estimator as Show that b | 1 is linear and unbi
> The following equation represents the effects of tax revenue mix on subsequent employment growth for the population of counties in the United States: growth = 0 + 1shareP + 2shareI + 3shareS + other factors, where growth is the percentage change
> Suppose that the population model determining y is y = 0 +  1x1 +  2x2 +  3x3 + u, and this model satisfies Assumptions MLR.1 through MLR.4. However, we estimate the model that omit
> The following equation describes the median housing price in a community in terms of amount of pollution (nox for nitrous oxide) and the average number of rooms in houses in the community (rooms): Log(price)= 0 + 1log(nox)+ b2rooms + u. a. What are t
> Suppose that average worker productivity at manufacturing firms (avgprod) depends on two factors, average hours of training (avgtrain) and average worker ability (avgabil): avgprod = 0 + 1avgtrain + 2avgabil + u. Assume that this equation satisfies
> Which of the following can cause OLS estimators to be biased? a. Heteroskedasticity. b. Omitting an important variable. c. A sample correlation coefficient of .95 between two independent variables both included in the model.
> In a study relating college grade point average to time spent in various activities, you distribute a survey to several students. The students are asked how many hours they spend each week in four activities: studying, sleeping, working, and leisure. Any
> The median starting salary for new law school graduates is determined by where LSAT is the median LSAT score for the graduating class, GPA is the median college GPA for the class, libvol is the number of volumes in the law school library, cost is the an
> The following model is a simplified version of the multiple regression model used by Biddle and Hamermesh (1990) to study the tradeoff between time spent sleeping and working and to look at other factors affecting where sleep and totwrk (total work) are
> The data in WAGE2 on working men was used to estimate the following equation: where educ is years of schooling, sibs is number of siblings, meduc is mother’s years of schooling, and feduc is father’s years of schooling
> Using the data in GPA2 on 4,137 college students, the following equation was estimated by OLS: colgpa is measured on a four-point scale, hsperc is the percentile in the high school graduating class (defined so that, for example, hsperc = 5 means the top
> The following equations were estimated using the data in LAWSCH85: How can it be that the R-squared is smaller when the variable age is added to the equation? Isalary = 9.90 - .0041 rank + .294 GPA (.24) (.0003) (.069) n = 142, R = .8238 Isalary =
> The data in ECONMATH contain grade point averages and standardized test scores, along with performance in an introductory economics course, for students at a large public university. The variable to be explained is score, the final score in the course me
> Use the data in MEAPSINGLE to study the effects of single-parent households on student math performance. These data are for a subset of schools in southeast Michigan for the year 2000. The socioeconomic variables are obtained at the ZIP code level (where
> Use the data in HTV to answer this question. The data set includes information on wages, education, parents’ education, and several other variables for 1,230 working men in 1991. a. What is the range of the educ variable in the sample? What percentage o
> Use the data in CHARITY to answer the following questions: a. Estimate the equation gift = 1 + 1mailsyear + 2giftlast + 3propresp + u by OLS and report the results in the usual way, including the sample size and R-squared. How does the R-squared
> Use the data in DISCRIM to answer this question. These are ZIP code–level data on prices for various items at fast-food restaurants, along with characteristics of the zip code population, in New Jersey and Pennsylvania. The idea is to see whether fast-fo
> Use the data in MEAP93 to answer this question. a. Estimate the model math10 = 0 + 1log(expend)1 2lnchprg + u, and report the results in the usual form, including the sample size and R-squared. Are the signs of the slope coefficients what you expec
> Use the data set in WAGE2 for this problem. As usual, be sure all of the following regressions contain an intercept. a. Run a simple regression of IQ on educ to obtain the slope coefficient, say, | 1. b. Run the simple regression of log(wage) on educ
> Confirm the partialling out interpretation of the OLS estimates by explicitly doing the partialling out for Example 3.2. This first requires regressing educ on exper and tenure and saving the residuals, . Then, regress log(wage) on . Compare the coeffici
> Use the data in ATTEND for this exercise. a. Obtain the minimum, maximum, and average values for the variables atndrte, priGPA, and ACT. b. Estimate the model atndrte = 0 + 1priGPA + 2ACT+ u, and write the results in equation form. Interpret the
> The file CEOSAL2 contains data on 177 chief executive officers and can be used to examine the effects of firm performance on CEO salary. a. Estimate a model relating annual salary to firm sales and market value. Make the model of the constant elasticity
> Use the data in HPRICE1 to estimate the model price = 0 + 1sqrft + bdrms + u, where price is the house price measured in thousands of dollars. a. Write out the results in equation form. b. What is the estimated increase in price for a house with o
> A problem of interest to health officials (and others) is to determine the effects of smoking during pregnancy on infant health. One measure of infant health is birth weight; a birth weight that is too low can put an infant at risk for contracting variou
> Consider the problem described at the end of Section 2.6: running a regression and only estimating an intercept. a. Given a sample {yi: i = 1, 2, . . . ., n}, let b & 0 be the solution to Show that , that is, the sample average minimizes the sum o
> Suppose you are interested in estimating the effect of hours spent in an SAT preparation course (hours) on total SAT score (sat). The population is all college-bound high school seniors for a particular year. a. Suppose you are given a grant to run a co
> Let and be the OLS intercept and slope estimators, respectively, and let ū be the sample average of the errors (not the residuals!). a. Show that can be written as/, where wi = di/SSTx and di = xi - / b. Use part (a), along with / to show that and
> a. Let and be the intercept and slope from the regression of yi on xi, using n observations. Let c1 and c2, with c2 ≠ 0, be constants. Let and b & 1 be the intercept and slope from the regression of c1yi on c2xi. Show that =(c1/c2)and = c1 , ther
> Consider the standard simple regression model y = ( + (1x + u under the Gauss-Markov Assumptions SLR.1 through SLR.5. The usual OLS estimators and are unbiased for their respective population parameters. Let be the estimator of (1 obtained by assumin
> Consider the savings function sav = + inc + u, u = .e, where e is a random variable with E(e) = 0 and Var(e)= . Assume that e is independent of inc. a. Show that E(u|inc) = 0, so that the key zero conditional mean assumption (Assumption SLR.4) i
> States (and provinces) that have control over taxation sometimes reduce taxes in an attempt to spur economic growth. Suppose that you are hired by a state to estimate the effect of corporate tax rates on, say, the growth in per capita gross state product
> Suppose at your university you are asked to find the relationship between weekly hours spent studying (study) and weekly hours spent working (work). Does it make sense to characterize the problem as inferring whether study “causes” work or work “causes”
> A justification for job training programs is that they improve worker productivity. Suppose that you are asked to evaluate whether more job training makes workers more productive. However, rather than having data on individual workers, you have access to
> Suppose that you are asked to conduct a study to determine whether smaller class sizes lead to improved student performance of fourth graders. a. If you could conduct any experiment you want, what would you do? Be specific. b. More realistically, supp
> The data set in ALCOHOL contains information on a sample of men in the United States. Two key variables are self-reported employment status and alcohol abuse (along with many other variables). The variables employ and abuse are both binary, or indicator,
> Use the data in COUNTYMURDERS to answer this question. Use only the year 1996. The variable murders is the number of murders reported in the county. The variable execs is the number of executions that took place of people sentenced to death in the given
> The data in FERTIL2 were collected on women living in the Republic of Botswana in 1988. The variable children refer to the number of living children. The variable electric is a binary indicator equal to one if the woman’s home has electricity, and zero i
> The data in JTRAIN2 come from a job training experiment conducted for low-income men during 1976–1977; see Lalonde (1986). a. Use the indicator variable train to determine the fraction of men receiving job training. b. The variable re78 is earnings fr
> The data in MEAP01 are for the state of Michigan in the year 2001. Use these data to answer the following questions. a. Find the largest and smallest values of math4. Does the range make sense? Explain. b. How many schools have a perfect pass rate on
> Use the data in BWGHT to answer this question. a. How many women are in the sample, and how many report smoking during pregnancy? b. What is the average number of cigarettes smoked per day? Is the average a good measure of the “typical” woman in this
> Using data from 1988 for houses sold in Andover, Massachusetts, from Kiel and McClain (1995), the following equation relates housing price (price) to the distance from a recently built garbage incinerator (dist): log(price) = 9.40 + 0.312 log (dist)
> In the linear consumption function /= + 1inc, the (estimated) marginal propensity to consume (MPC) out of income is simply the slope, , while the average propensity to consume (APC) is //inc = /inc +. Using observations for 100 families on annual
> The data set BWGHT contains data on births to women in the United States. Two variables of interest are the dependent variable, infant birth weight in ounces (bwght), and an explanatory variable, average number of cigarettes the mother smoked per day dur
> The following table contains the ACT scores and the GPA (grade point average) for eight college students. Grade point average is based on a four-point scale and has been rounded to one digit after the decimal. a. Estimate the relationship between GPA an
> In the simple linear regression model y = (0 + (1x + u, suppose that E(u) =! 0. Letting (0 = E(u), show that the model can always be rewritten with the same slope, but a new intercept and error, where the new error has a zero expected value.
> Let kids denote the number of children ever born to a woman, and let educ denote years of education for the woman. A simple model relating fertility to years of education is kids = 0+ 1 educ + , where is the unobserved error. a. What kinds of fact
> The data set in CATHOLIC includes test score information on over 7,000 students in the United States who were in eighth grade in 1988. The variables math12 and read12 are scores on twelfth grade standardized math and reading tests, respectively. a. How m
> Use the data in COUNTYMURDERS to answer this questions. Use only the data for 1996. a. How many counties had zero murders in 1996? How many counties had at least one execution? What is the largest number of executions? b. Estimate the equation murders =
> To complete this exercise, you need a software package that allows you to generate data from the uniform and normal distributions. a. Start by generating 500 observations on xi—the explanatory variable—from the unifor
> Use the data in CHARITY [obtained from Franses and Paap (2001)] to answer the following questions: a. What is the average gift in the sample of 4,268 people (in Dutch guilders)? What percentage of people gave no gift? b. What is the average mailings per
> We used the data in MEAP93 for Example 2.12. Now we want to explore the relationship between the math pass rate (math10) and spending per student (expend). a. Do you think each additional dollar spent has the same effect on the pass rate, or does a dimi
> For the population of firms in the chemical industry, let rd denote annual expenditures on research and development, and let sales denote annual sales (both are in millions of dollars). a. Write down a model (not an estimated equation) that implies a con
> Use the data in WAGE2 to estimate a simple regression explaining monthly salary (wage) in terms of IQ score (IQ). a. Find the average salary and average IQ in the sample. What is the sample standard deviation of IQ? (IQ scores are standardized so that t
> Use the data in SLEEP75 from Biddle and Hamermesh (1990) to study whether there is a tradeoff between the time spent sleeping per week and the time spent in paid work. We could use either variable as the dependent variable. For concreteness, estimate the
