Question: Use the data in COUNTYMURDERS to answer

> 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

> 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 attendan

> 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

> 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

> The data set in CEOSAL2 contains information on chief executive officers for U.S. corporations. The variable salary is annual compensation, in thousands of dollars, and ceoten is prior number of years as company CEO. a. Find the average salary and the a

> The data in 401K are a subset of data analyzed by Papke (1995) to study the relationship between participation in a 401(k) pension plan and the generosity of the plan. The variable prate is the percentage of eligible workers with an active account; this

> Consider the estimated equation from Example 4.3, which can be used to study the effects of skipping class on college GPA: colGPA = 1.39 + .412 hsGPA + .015 ACT - .083 skipped (.33) (.094) (.011) (.026) n = 1

> The following histogram was created using the variable score in the data file ECONMATH. Thirty bins were used to create the histogram, and the height of each cell is the proportion of observations falling within the corresponding interval. The best-fitti

> In the simple regression model (5.16), under the first four Gauss-Markov assumptions, we showed that estimators of the form (5.17) are consistent for the slope, B1. Given such an estimator, define an estimator of

> The data set SMOKE contains information on smoking behavior and other variables for a random sample of single adults from the United States. The variable cigs is the (average) number of cigarettes smoked per day. Do you think cigs has a normal distributi

> Suppose that the model pctstck = B0+ B1funds + B2risktol + u satisfies the first four Gauss-Markov assumptions, where pctstck is the percentage of a worker’s pension invested in the stock market, funds is the number of mutual funds that the worker c

> In the simple regression model under MLR.1 through MLR.4, we argued that the slope estimator,

> Use the data in ECONMATH to answer this question. Logically, what are the smallest and largest values that can be taken on by the variable score? What are the smallest and largest values in the sample? Consider the linear model score = B0 + B1colgp

> educ is the dependent variable in a regression. (a) How many different values are taken on by educ in the sample? Does educ have a continuous distribution? (b) Plot a histogram of educ with a normal distribution overlay. Does the distribution of educ a

> Several statistics are commonly used to detect nonnormality in underlying population distributions. Here we will study one that measures the amount of skewness in a distribution. Recall that any normally distributed random variable is symmetric about

> In given equation, using the data set BWGHT, compute the LM statistic for testing whether motheduc and fatheduc are jointly significant. In obtaining the residuals for the restricted model, be sure that the restricted model is estimated using only those

> Use the data in GPA2 for this exercise. (1) Using all 4,137 observations, estimate the equation colgpa = B0 + B1hsperc + B2sat + u and report the results in standard form. (2) Reestimate the equation in part (1), using the first 2,070 observations.

> Use the data in WAGE1 for this exercise. (i) Estimate the equation wage = B0 + B1educ + B2exper + B3tenure + u. Save the residuals and plot a histogram. (ii) Repeat part (i), but with log(wage) as the dependent variable. (iii) Would you say that Assumpt

> The data in MEAPSINGLE were used to estimate the following equations relating school-level performance on a fourth-grade math test to socioeconomic characteristics of students attending school. The variable free, measured at the school level, is the perc

> The following analysis was obtained using data in MEAP93, which contains school-level pass rates (as a percent) on a tenth-grade math test. (i) The variable expend is expenditures per student, in dollars, and math10 is the pass rate on the exam. The foll

> The variable mktval is market value of the firm, profmarg is profit as a percentage of sales, ceoten is years as CEO with the current company, and comten is total years with the company. (i) Comment on the effect of profmarg on CEO salary. (ii) Does mark

> Use the data in WAGE1 for this exercise. a. Find the average education level in the sample. What are the lowest and highest years of education? b. Find the average hourly wage in the sample. Does it seem high or low? c. The wage data are reported in

> The Pinkerton Publishing Company is considering two mutually exclusive expansion plans. Plan A calls for the expenditure of $50 million on a largescale, integrated plant that will provide an expected cash flow stream of $8 million per year for 20 years.

> Your company is considering two mutually exclusive projects, X and Y, whose costs and cash flows are shown below: The projects are equally risky, and their cost of capital is 12%. You must make a recommendation, and you must base it on the modified IRR (

> Project S has a cost of $10,000 and is expected to produce benefits (cash flows) of $3,000 per year for 5 years. Project L costs $25,000 and is expected to produce cash flows of $7,400 per year for 5 years. Calculate the two projects’ NPVs, IRRs, MIRRs,

> The Scampini Supplies Company recently purchased a new delivery truck. The new truck cost $22,500, and it is expected to generate net after-tax operating cash flows, including depreciation, of $6,250 per year. The truck has a 5-year expected life. The ex

> Your division is considering two investment projects, each of which requires an up-front expenditure of $25 million. You estimate that the cost of capital is 10% and that the investments will produce the following after-tax cash flows (in millions of dol

> The Aubey Coffee Company is evaluating the within-plant distribution system for its new roasting, grinding, and packing plant. The two alternatives are: (1) a conveyor system with a high initial cost but low annual operating costs, and (2) several fork

> The Ulmer Uranium Company is deciding whether or not to open a strip mine whose net cost is $4.4 million. Net cash inflows are expected to be $27.7 million, all coming at the end of Year 1. The land must be returned to its natural state at a cost of $25

> Filkins Fabric Company is considering the replacement of its old, fully depreciated knitting machine. Two new models are available: Machine 190-3, which has a cost of $190,000, a 3-year expected life, and after-tax cash flows (labor savings and depreciat

> The table below gives the balance sheet for Travelers’ Inn Inc. (TII), a company that was formed by merging a number of regional motel chains. The following facts also apply to TII. (1) Short-term debt consists of bank loans that curre

> Suppose the Schoof Company has this book value balance sheet: The notes payable are to banks, and the interest rate on this debt is 10%, the same as the rate on new bank loans. These bank loans are not used for seasonal financing but instead are part of

> Distinguish between beta (i.e., market) risk, within-firm (i.e., corporate) risk, and stand-alone risk for a potential project. Of the three measures, which is theoretically the most relevant, and why?

> On January 1, the total market value of the Tysseland Company was $60 million. During the year, the company plans to raise and invest $30 million in new projects. The firm’s present market value capital structure, shown below, is consid

> The Ewert Exploration Company is considering two mutually exclusive plans for extracting oil on property for which it has mineral rights. Both plans call for the expenditure of $10 million to drill development wells. Under Plan A, all the oil will be ext

> Cummings Products is considering two mutually exclusive investments whose expected net cash flows are as follows: a. Construct NPV profiles for Projects A and B. b. What is each project’s IRR? c. If each project’s cost

> Spencer Supplies’ stock is currently selling for $60 a share. The firm is expected to earn $5.40 per share this year and to pay a year-end dividend of $3.60. a. If investors require a 9% return, what rate of growth must be expected for Spencer? b. If S

> Radon Homes’ current EPS is $6.50. It was $4.42 5 years ago. The company pays out 40% of its earnings as dividends, and the stock sells for $36. a. Calculate the historical growth rate in earnings. (Hint: This is a 5-year growth period.) b. Calculate t

> The earnings, dividends, and stock price of Shelby Inc. are expected to grow at 7% per year in the future. Shelby’s common stock sells for $23 per share, its last dividend was $2.00, and the company will pay a dividend of $2.14 at the end of the current

> Garlington Technologies Inc.’s 2015 financial statements are shown below: Suppose that in 2016 sales increase by 10% over 2015 sales and that 2016 dividends will increase to $112,000. Forecast the financial statements using the forecast

> Stevens Textiles’ 2015 financial statements are shown below: Balance Sheet as of December 31, 2015 (Thousands of Dollars) Income Statement for December 31, 2015 (Thousands of Dollars) a. Suppose 2016 sales are projected to increase by

> Upton Computers makes bulk purchases of small computers, stocks them in conveniently located warehouses, ships them to its chain of retail stores, and has a staff to advise customers and help them set up their new computers. Upton’s bal

> The Booth Company’s sales are forecasted to double from $1,000 in 2015 to $2,000 in 2016.Here is the December 31, 2015, balance sheet: Booth’s fixed assets were used to only 50% of capacity during 2015, but its current

> How would each of the factors in the following table affect a firm’s cost of debt, rd(1 2 T); its cost of equity, rs; and its weighted average cost of capital, WACC? Indicate by a plus (1), a minus (2), or a zero (0) if the factor would

> At year-end 2015, Wallace Landscaping’s total assets were $2.17 million and its accounts payable were $560,000. Sales, which in 2015 were $3.5 million, are expected to increase by 35% in 2016. Total assets and accounts payable are proportional to sales,

> Maggie’s Muffins Inc. generated $5,000,000 in sales during 2015, and its year-end total assets were $2,500,000. Also, at year-end 2015, current liabilities were $1,000,000, consisting of $300,000 of notes payable, $500,000 of accounts payable, and $200,0

> Refer to Problem 12-1. What is the project’s MIRR? Problem 12-1: A project has an initial cost of $40,000, expected net cash inflows of $9,000 per year for 7 years, and a cost of capital of 11%.

> The financial staff of Cairn Communications has identified the following information for the first year of the roll-out of its new proposed service: The Company faces a 40% tax rate. What is the project’s operating cash flow for the fir

> Broussard Skateboard’s sales are expected to increase by 15% from $8 million in 2015 to $9.2 million in 2016. Its assets totaled $5 million at the end of 2015. Broussard is already at full capacity, so its assets must grow at the same rate as projected s