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Introductory Econometrics A Modern Approach 6th Edition Jeffrey M. Wooldridge - Solutions

2.7 Table 2.19 on the companion website gives fertility and other related data for 64 countries.33 Develop suitable model(s) to explain child mortality, considering the various function forms and the measures of goodness of fi t discussed in the chapter.
2.6 Table 2.18 on the companion website gives cross-country data for 83 countries on per worker GDP for 1997 and the Corruption Perceptions Index for 1998.32 (a) Plot the index of corruption perceptions against per worker GDP. (b) Based on this plot what might be an appropriate model relating the
2.5 Show that the coeffi cient of determination, R2, can also be obtained as the squared correlation between actual Y values and the Y values estimated from the regression model (= Yi), where Y is the dependent variable. Note that the coeffi cient of correlation between variables Y and X is defi
2.3 For the food expenditure data given in Table 2.8, see if the following model fi ts the data well: SFDHOi = B1 + B2 Expendi + B3 Expendi 2 and compare your results with those discussed in the text.
2.1 Consider the following production function, known in the literature as the transcendental production function (TPF). Q BL K e i i B i B BL BK i i 1 2 3 4 5 where Q, L, and K represent output, labor, and capital, respectively. (a) How would you linearize this function? (Hint: logarithms.) (b)
1.5 Interaction among regressors. Consider the wage regression model given in Table 1.3. Suppose you decide to add the variable education.experience, the product of the two regressors, to the model. What is the logic behind introducing such a variable, called the interaction variable, to the
1.4 Consider the following regression model: yi = B1 + B2xi + ui where xi and yi are as defi ned in Exercise 1.3. Show that in this model b1 = 0. What is the advantage of this model over the model in Exercise 1.3?
1.3 Consider the bivariate regression model: Yi = B1 + B2Xi + ui Verify that the OLS estimators for this model are as follows: 2 2 1 2 2 2ˆ 2 i i i i x y b x b Y bX e n V ¦ ¦ ¦ where 1 2 ( ), ( ), ( ) i i ii ii i x X X y Y Y e Y b bX .
1.2 Table 1.5 (available on the companion website) gives data on 654 youths, aged 3 to 19, in the areas of East Boston in the late 1970s on the following variables:21 fev = continuous measure (in liters) smoke = smoker coded as 1, non-smoker coded as 0 age = in years ht = height in inches sex =
1.1 Consider the regression results given in Table 1.2. (a) Suppose you want to test the hypothesis that the true or population regression coeffi cient of the education variable is 1. How would you test this hypothesis? Show the necessary calculations. (b) Would you reject or not reject the
Use the data in BEAUTY for this question.(i) Using the data pooled for men and women, estimate the equation lwage 5 b0 1 b1belavg 1 b2abvavg 1 b3female 1 b4educ 1 b5exper 1 b5exper2 1 u, and report the results using heteroskedasticity-robust standard errors below coefficients. Are any of the
Use the data in FERTIL2 to answer this question.(i) Estimate the model children 5 b0 1 b1age 1 b2age2 1 b3educ 1 b4electric 1 b5urban 1 u and report the usual and heteroskedasticity-robust standard errors. Are the robust standard errors always bigger than the nonrobust ones?(ii) Add the three
Use the data in MEAP00 to answer this question.(i) Estimate the model math4 5 b0 1 b1lunch 1 b2log1enroll2 1 b3log1exppp2 1 u by OLS and obtain the usual standard errors and the fully robust standard errors. How do they generally compare?(ii) Apply the special case of the White test for
Use the data in 401KSUBS for this question, restricting the sample to fsize 5 1.(i) To the model estimated in Table 8.1, add the interaction term, e401k · inc. Estimate the equation by OLS and obtain the usual and robust standard errors. What do you conclude about the statistical significance of
Use the data set 401KSUBS for this exercise.(i) Using OLS, estimate a linear probability model for e401k, using as explanatory variables inc, inc2, age, age2, and male. Obtain both the usual OLS standard errors and the heteroskedasticityrobust versions. Are there any important differences?(ii) In
In Example 8.7, we computed the OLS and a set of WLS estimates in a cigarette demand equation.(i) Obtain the OLS estimates in equation (8.35).(ii) Obtain the h^i used in the WLS estimation of equation (8.36) and reproduce equation (8.36).From this equation, obtain the unweighted residuals and
Use the data set GPA1 for this exercise.(i) Use OLS to estimate a model relating colGPA to hsGPA, ACT, skipped, and PC. Obtain the OLS residuals.(ii) Compute the special case of the White test for heteroskedasticity. In the regression of u^2 i on colGPAi, colGPA2 i , obtain the fitted values, say
Use the data in LOANAPP for this exercise.(i) Estimate the equation in part (iii) of Computer Exercise C8 in Chapter 7, computing the heteroskedasticity-robust standard errors. Compare the 95% confidence interval on bwhite with the nonrobust confidence interval.(ii) Obtain the fitted values from
In Example 7.12, we estimated a linear probability model for whether a young man was arrested during 1986:arr86 5 b0 1 b1pcnv 1 b2avgsen 1 b3tottime 1 b4ptime86 1 b5qemp86 1 u.(i) Using the data in CRIME1, estimate this model by OLS and verify that all fitted values are strictly between zero and
Use the data in PNTSPRD for this exercise.(i) The variable sprdcvr is a binary variable equal to one if the Las Vegas point spread for a college basketball game was covered. The expected value of sprdcvr, say m, is the probability that the spread is covered in a randomly selected game. Test H0: m 5
Use VOTE1 for this exercise.(i) Estimate a model with voteA as the dependent variable and prtystrA, democA, log(expendA), and log(expendB) as independent variables. Obtain the OLS residuals, u^i, and regress these on all of the independent variables. Explain why you obtain R2 5 0.(ii) Now, compute
(i) Use the data in HPRICE1 to obtain the heteroskedasticity-robust standard errors for equation(8.17). Discuss any important differences with the usual standard errors.(ii) Repeat part (i) for equation (8.18).(iii) What does this example suggest about heteroskedasticity and the transformation used
The following equations were estimated using the data in ECONMATH. The first equation is for men and the second is for women. The third and fourth equations combine men and women.score 5 20.52 1 13 .60 colgpa 1 0 .670 act 13.722 10.942 10.1502 n 5 406. R2 5 .4025, SSR 5 38,781.38.score 5 13 .79 1
Consider a model at the employee level, yi,e 5 b0 1 b1xi,e,1 1 b2xi,e,2 1 p 1 bkxi,e,k 1 fi 1 vi,e, where the unobserved variable fi is a “firm effect” to each employee at a given firm i. The error term vi,e is specific to employee e at firm i. The composite error is ui,e 5 fi 1 vi,e, such as
There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedasticity. One possibility not covered in the text is to run the regression u^2 i on xi1, xi2, p, xik, y^2 i , i 5 1, p, n, where the u^i are the OLS residuals and the y^i are the OLS fitted values. Then,
Using the data in GPA3, the following equation was estimated for the fall and second semester students:trmgpa 5 22.12 1 .900 crsgpa 1 .193 cumgpa 1 .0014 tothrs 1.552 1.1752 1.0642 1.00122 3.554 3.1664 3.0744 3.00124 1 .0018 sat 2 .0039 hsperc 1 .351 female 2 .157 season 1.00022 1.00182 1.0852
Use the data in FERTIL2 to answer this question.(i) Find the smallest and largest values of children in the sample. What is the average of children?Does any woman have exactly the average number of children?(ii) What percentage of women have electricity in the home?(iii) Compute the average of
Use the data in CHARITY to answer this question. The variable respond is a dummy variable equal to one if a person responded with a contribution on the most recent mailing sent by a charitable organization. The variable resplast is a dummy variable equal to one if the person responded to the
Use the data in APPLE to answer this question.(i) Define a binary variable as ecobuy 5 1 if ecolbs . 0 and ecobuy 5 0 if ecolbs 5 0. In other words, ecobuy indicates whether, at the prices given, a family would buy any ecologically friendly apples. What fraction of families claim they would buy
Use the data set in BEAUTY, which contains a subset of the variables (but more usable observations than in the regressions) reported by Hamermesh and Biddle (1994).(i) Find the separate fractions of men and women that are classified as having above average looks.Are more people rated as having
Use the data in 401KSUBS for this exercise.(i) Compute the average, standard deviation, minimum, and maximum values of nettfa in the sample.(ii) Test the hypothesis that average nettfa does not differ by 401(k) eligibility status; use a twosided alternative. What is the dollar amount of the
Use the data in NBASAL for this exercise.(i) Estimate a linear regression model relating points per game to experience in the league and position (guard, forward, or center). Include experience in quadratic form and use centers as the base group. Report the results in the usual form.(ii) Why do you
There has been much interest in whether the presence of 401(k) pension plans, available to many U.S.workers, increases net savings. The data set 401KSUBS contains information on net financial assets(nettfa), family income (inc), a binary variable for eligibility in a 401(k) plan (e401k), and
Use the data in LOANAPP for this exercise. The binary variable to be explained is approve, which is equal to one if a mortgage loan to an individual was approved. The key explanatory variable is white, a dummy variable equal to one if the applicant was white. The other applicants in the data set
Use the data in WAGE1 for this exercise.(i) Use equation (7.18) to estimate the gender differential when educ 5 12.5.Compare this with the estimated differential when educ 5 0.
Use the data in SLEEP75 for this exercise. The equation of interest is sleep 5 b0 1 b1totwrk 1 b2educ 1 b3age 1 b4age2 1 b5yngkid 1 u.(i) Estimate this equation separately for men and women and report the results in the usual form.Are there notable differences in the two estimated equations?(ii)
In Problem 2 in Chapter 4, we added the return on the firm’s stock, ros, to a model explaining CEO salary; ros turned out to be insignificant. Now, define a dummy variable, rosneg, which is equal to one if ros , 0 and equal to zero if ros $ 0. Use CEOSAL1 to estimate the model log1salary2 5 b0 1
Use the data in GPA2 for this exercise.(i) Consider the equation colgpa 5 b0 1 b1hsize 1 b2hsize2 1 b3hsperc 1 b4sat 1 b5female 1 b6athlete 1 u, where colgpa is cumulative college grade point average; hsize is size of high school graduating class, in hundreds; hsperc is academic percentile in
The following equations were estimated using the data in ECONMATH, with standard errors reported under coefficients. The average class score, measured as a percentage, is about 72.2; exactly 50% of the students are male; and the average of colgpa (grade point average at the start of the term) is
For a child i living in a particular school district, let voucheri be a dummy variable equal to one if a child is selected to participate in a school voucher program, and let scorei be that child’s score on a subsequent standardized exam. Suppose that the participation variable, voucheri, is
Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the model y 5 b0 1 d0d 1 b1z 1 d1d # z 1 u;this is a general version of a model with an interaction between a dummy variable and a quantitative variable. [An example is in equation (7.17). ](i) Since it changes
In the example in equation (7.29), suppose that we define outlf to be one if the woman is out of the labor force, and zero otherwise.(i) If we regress outlf on all of the independent variables in equation (7.29), what will happen to the intercept and slope estimates? (Hint: inlf 5 1 2 outlf . Plug
To test the effectiveness of a job training program on the subsequent wages of workers, we specify the model log1wage2 5 b0 1 b1train 1 b2educ 1 b3exper 1 u, where train is a binary variable equal to unity if a worker participated in the program. Think of the error term u as containing unobserved
In Example 7.2, let noPC be a dummy variable equal to one if the student does not own a PC, and zero otherwise.(i) If noPC is used in place of PC in equation (7.6), what happens to the intercept in the estimated equation? What will be the coefficient on noPC? (Hint: Write PC 5 1 2 noPC and plug
An equation explaining chief executive officer salary is log1salary2 5 4.59 1 .257 log1sales2 1 .011 roe 1 .158 finance 1.302 1.0322 1.0042 1.0892 1 .181 consprod 2 .283 utility 1.0852 1.0992 n 5 209, R2 5 .357.The data used are in CEOSAL1, where finance, consprod, and utility are binary variables
Using the data in GPA2, the following equation was estimated:sat 5 1,028.10 1 19.30 hsize 2 2.19 hsize2 2 45.09 female 16.292 13.832 1.532 14.292 2 169.81 black 1 62.31 female#black 112.712 118.152 n 5 4,137, R2 5 .0858.The variable sat is the combined SAT score; hsize is size of the student’s
The following equations were estimated using the data in BWGHT:log1bwght2 5 4.66 2 .0044 cigs 1 .0093 log1faminc2 1 .016 parity 1.222 1.00092 1.00592 1.0062 1 .027 male 1 .055 white 1.0102 1.0132 n 5 1,388, R2 5 .0472
Using the data in SLEEP75 (see also Problem 3 in Chapter 3), we obtain the estimated equation sleep 5 3,840.83 2 .163 totwrk 2 11.71 educ 2 8.70 age 1235.112 1.0182 15.862 111.212 1 .128 age2 1 87.75 male 1.1342 134.332 n 5 706, R2 5 .123, R2 5 .117.The variable sleep is total minutes per week
Use the data in BENEFITS to answer this question. It is a school-level data set at the K–5 level on average teacher salary and benefits. See Example 4.10 for background.(i) Regress lavgsal on bs and report the results in the usual form. Can you reject H0: bbs 5 0 against a two-sided alternative?
Use the data in MEAP00 to answer this question.(i) Estimate the model math4 5 b0 1 b2lexppp 1 b2lenroll 1 b3lunch 1 u by OLS, and report the results in the usual form. Is each explanatory variable statistically significant at the 5% level?(ii) Obtain the fitted values from the regression in part
Use the subset of 401KSUBS with fsize 5 1; this restricts the analysis to single-person households;see also Computer Exercise C8 in Chapter 4.(i) What is the youngest age of people in this sample? How many people are at that age?(ii) In the model nettfa 5 b0 1 b1inc 1 b2age 1 b3age2 1 u, what is
Use APPLE to verify some of the claims made in Section 6-3.(i) Run the regression ecolbs on ecoprc, regprc and report the results in the usual form, including the R-squared and adjusted R-squared. Interpret the coefficients on the price variables and comment on their signs and magnitudes.(ii) Are
Use the data in BWGHT2 for this exercise.(i) Estimate the equation log1bwght2 5 b0 1 b1npvis 1 b2npvis2 1 u by OLS, and report the results in the usual way. Is the quadratic term significant?(ii) Show that, based on the equation from part (i), the number of prenatal visits that maximizes log(bwght)
The data set NBASAL contains salary information and career statistics for 269 players in the National Basketball Association (NBA).(i) Estimate a model relating points-per-game (points) to years in the league (exper), age, and years played in college (coll). Include a quadratic in exper; the other
Use the data in HPRICE1 for this exercise.(i) Estimate the model price 5 b0 1 b1lotsize 1 b2sqrft 1 b3bdrms 1 u and report the results in the usual form, including the standard error of the regression. Obtain predicted price, when we plug in lotsize 5 10,000, sqrft 5 2,300, and bdrms 5 4; round
Use the data in ATTEND for this exercise.(i) In the model of Example 6.3, argue that Dstndfnl/DpriGPA < b2 1 2b4 priGPA 1 b6atndrte.Use equation (6.19) to estimate the partial effect when priGPA 5 2.59 and atndrte 5 82.Interpret your estimate.
Use the data in VOTE1 for this exercise.(i) Consider a model with an interaction between expenditures:voteA 5 b0 1 b1prtystrA 1 b2expendA 1 b3expendB 1 b4expendA#expendB 1 u.What is the partial effect of expendB on voteA, holding prtystrA and expendA fixed? What is the partial effect of expendA on
Use the housing price data in HPRICE1 for this exercise.(i) Estimate the model log1price2 5 b0 1 b1log1lotsize2 1 b2log1sqrft2 1 b3bdrms 1 u and report the results in the usual OLS format.(ii) Find the predicted value of log(price), when lotsize 5 20,000, sqrft 5 2,500, and bdrms 5 4.Using the
Use the data in GPA2 for this exercise.(i) Estimate the model sat 5 b0 1 b1hsize 1 b2hsize2 1 u, where hsize is the size of the graduating class (in hundreds), and write the results in the usual form. Is the quadratic term statistically significant?(ii) Using the estimated equation from part (i),
Consider a model where the return to education depends upon the amount of work experience (and vice versa):log1wage2 5 b0 1 b1educ 1 b2exper 1 b3educ # exper 1 u.(i) Show that the return to another year of education (in decimal form), holding exper fixed, is b1 1 b3exper.(ii) State the null
Use the data in WAGE1 for this exercise.(i) Use OLS to estimate the equation log1wage2 5 b0 1 b1educ 1 b2exper 1 b3exper2 1 u and report the results using the usual format.(ii) Is exper2 statistically significant at the 1% level?(iii) Using the approximation%Dwage < 1001b^2 1 2b^3exper2Dexper, find
Use the data in KIELMC, only for the year 1981, to answer the following questions. The data are for houses that sold during 1981 in North Andover, Massachusetts; 1981 was the year construction began on a local garbage incinerator.(i) To study the effects of the incinerator location on housing
The following two equations were estimated using the data in MEAPSINGLE. The key explanatory variable is lexppp, the log of expenditures per student at the school level.math4 5 24.49 1 9 .01 lexppp 2 .422 free 2 .752 lmedinc 2 .274 pctsgle 159.242 14.042 1.0712 15.3582 1.1612 n 5 229, R2 5 .472, R2
If we start with (6.38) under the CLM assumptions, assume large n, and ignore the estimation error in the b^j, a 95% prediction interval for y0 is 3exp121.96s^ 2 exp1logy0 2 , exp11.96s^ 2 exp1logy0 2 4.The point prediction for y0 is y^0 5 exp1s^ 2 2exp1logy0 2.(i) For what values of s^ will the
Suppose we want to estimate the effects of alcohol consumption (alcohol) on college grade point average (colGPA). In addition to collecting information on grade point averages and alcohol usage, we also obtain attendance information (say, percentage of lectures attended, called attend). A
The following three equations were estimated using the 1,534 observations in 401K:prate 5 80.29 1 5 .44 mrate 1 .269 age 2 .00013 totemp 1.782 1.522 1.0452 1.000042 R2 5 .100, R2 5 .098.
In Example 4.2, where the percentage of students receiving a passing score on a tenth-grade math exam (math10) is the dependent variable, does it make sense to include sci11—the percentage of eleventh graders passing a science exam—as an additional explanatory variable?
The following model allows the return to education to depend upon the total amount of both parents’education, called pareduc:log1wage2 5 b0 1 b1educ 1 b2educ#pareduc 1 b3exper 1 b4tenure 1 u.(i) Show that, in decimal form, the return to another year of education in this model is Dlog1wage2/Deduc
Using the data in RDCHEM, the following equation was obtained by OLS:rdintens 5 2.613 1 .00030 sales 2 .0000000070 sales2 1.4292 1.000142 1.00000000372 n 5 32, R2 5 .1484.(i) At what point does the marginal effect of sales on rdintens become negative?(ii) Would you keep the quadratic term in the
Let b^0, b^ 1, p, b^k be the OLS estimates from the regression of yi on xi1, p, xik, i 5 1, 2, p, n. For nonzero constants c1, p, ck, argue that the OLS intercept and slopes from the regression of c0yi on c1xi1, p, ckxik, i 5 1, 2, p, n, are given by b|0 5 c0b^0, b|1 5 1c0/c1 2b^1, p, b^k 5 1c0/ck
The following equation was estimated using the data in CEOSAL1:log1salary2 5 4.322 1 .276 log1sales2 1 .0215 roe 2 .00008 roe2 1.3242 1.0332 1.01292 1.000262 n 5 209, R2 5 .282.This equation allows roe to have a diminishing effect on log(salary). Is this generality necessary?Explain why or why not.
Use the data in ECONMATH to answer this question.(i) 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?(ii) Consider the linear model score 5 b0 1 b1colgpa 1 b2actmth 1 b3acteng 1 u.Why cannot
Consider the analysis in Computer Exercise C11 in Chapter 4 using the data in HTV, where educ is the dependent variable in a regression.(i) How many different values are taken on by educ in the sample? Does educ have a continuous distribution?(ii) Plot a histogram of educ with a normal distribution
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 its mean; therefore, if we standardize a
In equation (4.42) of Chapter 4, 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 observations for which all
Use the data in GPA2 for this exercise.(i) Using all 4,137 observations, estimate the equation colgpa 5 b0 1 b1hsperc 1 b2sat 1 u and report the results in standard form.(ii) Reestimate the equation in part (i), using the first 2,070 observations.(iii) Find the ratio of the standard errors on
Use the data in WAGE1 for this exercise.(i) Estimate the equation wage 5 b0 1 b1educ 1 b2exper 1 b3tenure 1 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 Assumption MLR.6 is closer to being satisfied for the
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-fitting normal distribution—that is, using the
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 b0 by b|0 5 y 2 b|1x. Show that plim b|0 5 b0.
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 distribution in the U.S. adult population? Explain.
Suppose that the model pctstck 5 b0 1 b1funds 1 b2risktol 1 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 can choose from, and risktol is some measure of
In the simple regression model under MLR.1 through MLR.4, we argued that the slope estimator, b^1, is consistent for b1. Using b^0 5 y 2 b^1x1, show that plim b^0 5 b0. [You need to use the consistency of b^1 and the law of large numbers, along with the fact that b0 5 E1y2 2 b1E1x1 2.]
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 hsgpa of one standard deviation, about .343. By
Use the data in HTV to answer this question. See also Computer Exercise C10 in Chapter 3.(i) Estimate the regression model educ 5 b0 1 b1motheduc 1 b2fatheduc 1 b3abil 1 b4abil2 1 u by OLS and report the results in the usual form. Test the null hypothesis that educ is linearly related to abil
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 the simple regression of lavgsal on bs. Is the
Use the data in DISCRIM to answer this question. (See also Computer Exercise C8 in Chapter 3.)(i) Use OLS to estimate the model log1psoda2 5 b0 1 b1prpblck 1 b2log1income2 1 b3prppov 1 u, and report the results in the usual form. Is b^1 statistically different from zero at the 5% level against a
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 income variables are both recorded in
Refer to the example used in Section 4-4. You will use the data set TWOYEAR.(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
Use the data in WAGE2 for this exercise.(i) Consider the standard wage equation log1wage2 5 b0 1 b1educ 1 b2exper 1 b3tenure 1 u.State the null hypothesis that another year of general workforce experience has the same effect on log(wage) as another year of tenure with the current employer.(ii) Test
Use the data in MLB1 for this exercise.(i) Use the model estimated in equation (4.31) and drop the variable rbisyr. What happens to the statistical significance of hrunsyr? What about the size of the coefficient on hrunsyr?(ii) Add the variables runsyr (runs per year), fldperc (fielding
In Example 4.9, 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 restricted model in Example 4.9.
Refer to Computer Exercise C2 in Chapter 3. Now, use the log of the housing price as the dependent variable:log1price2 5 b0 1 b1sqrft 1 b2bdrms 1 u.(i) You are interested in estimating and obtaining a confidence interval for the percentage change in price when a 150-square-foot bedroom is added to
Use the data in LAWSCH85 for this exercise.(i) Using the same model as in Problem 4 in Chapter 3, 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
The following model can be used to study whether campaign expenditures affect election outcomes:voteA 5 b0 1 b1log1expendA2 1 b2log1expendB2 1 b3prtystrA 1 u, where voteA is the percentage of the vote received by Candidate A, expendA and expendB are campaign expenditures by Candidates A and B, and
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 percentage of students eligible for the federal
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 following simple regression relates math10 to
The following table was created using the data in CEOSAL2, where standard errors are in parentheses below the coefficients: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
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 efficient markets hypothesis says that
In Problem 3 in Chapter 3, we estimated the equation sleep 5 3,638.25 2 .148 totwrk 2 11.13 educ 1 2.20 age 1112.282 1.0172 15.882 11.452 n 5 706, R2 5 .113, where we now report standard errors along with the estimates.(i) Is either educ or age individually significant at the 5% level against a
Consider the multiple regression model with three independent variables, under the classical linear model assumptions MLR.1 through MLR.6:y 5 b0 1 b1x1 1 b2x2 1 b3x3 1 u.You would like to test the null hypothesis H0: b1 2 3b2 5 1.(i) Let b^1 and b^2 denote the OLS estimators of b1 and b2. Find

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