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business
statistics for business and economics

Questions and Answers of Statistics For Business And Economics

Consider the hypothesis that poverty is a function of race and sex. Sample data on the subject are collected and coded using the three dummy variables P, R, and S.The P dummy represents poverty (P =
The relationship between drug abuse and crime has been described by the regression(a) Interpret the multiple regression equation.(b) What problems may be associated with the interpretation of this
Protski, Inc., an audit firm, wants to develop a multiple regression model that can explain the value of a house Y, measured in thousands of dollars, by the age of the house X1, its square footage
(a) Define autocorrelation. State which assumptions of the regression model are violated when autocorrelation exists.(b) What is the difference between positive and negative autocorrelation?(c)
A firm with a nationwide system of bus facilities wants to develop a regression model that can explain its profit Y,measured in thousands of dollars per year, by its annual sales of bus repair and
Dividends per share (DPS), price per share (PPS), and retained earnings (RE)for the 30 Dow Jones industrials for 1984 give us the following multiple regression model:(a) Interpret the multiple
From Table 16.1, we can define the empirical relationship among PPSi, DPSi, and REi asTable 16.1 PPS; = 11.336 + 12.434DPS; +3.0875RE; () (B) (B) We also have Cov(PPS,DPS) = 20.174 Cov(RE,DPS) =
What is multicollinearity? What problems does it cause? How can we detect multicollinearity? When we detect multicollinearity, what should we do?
What is autocorrelation? What problems does autocorrelation cause? How can we detect autocorrelation?
What is heteroscedasticity? What problems does it cause? How can we detect heteroscedasticity?
What is specification bias? What problems does specification bias lead to? How can we avoid specification bias?
What is a nonlinear regression model? Why do we sometimes choose to estimate a nonlinear model?
What is a lagged dependent variable? Why do we use lagged dependent variables in a regression?
What is a dummy variable? What does the coefficient on the dummy variable measure? Give some examples drawn from economics, finance, and accounting of times when we would want to use a dummy variable
Suppose we are interested in measuring the differences in earnings among whites, blacks, Hispanics, and Asians. How many dummy variables should we use in our regression?
What are interaction variables? When would we choose to use interaction variables? What does the coefficient of the interaction variable tell us?
Suppose you have a sample of 40 observations and 3 explanatory variables and you want to test for autocorrelation. What can you say about autocorrelation if you have the following Durbin–Watson
When we use a lagged dependent variable in our regression, R2 is generally much higher than when such a variable is not included. Can you think of any reasons why?
Suppose you are interested in how stock returns differ in different months of the year. You decide to use dummy variables to examine this difference. If you choose to use 12 dummy variables, what
Look at the following scatter diagrams and explain whether heteroscedasticity appears to be a problem in either of them. a y by X
When heteroscedasticity is detected, we sometimes use a weighted regression in which the dependent and independent variables are weighted by the variances of their error terms. Thus, the estimated
What assumptions concerning the slope coefficient b must we make when we use dummy variables in a regression?
You are interested in the relationship between y and three possible explanatory variables x1, x2, and x3. You are given the following correlation matrix:Given this information, do you think
Suppose you have been hired by a lawyer who is interested in showing that a company discriminates against women in the wages it pays. You estimate the regression(a) Interpret the coefficients for
In order to forecast the value of a variable, we sometimes use a nonlinear trend regression such aswhere t = time. Briefly explain why this model may be better than a model such as = a + Bit + B + e
Suppose you are given the following data for Abbott Laboratories sales.Use MINITAB to do the following:(a) Use model A from question 26 to estimate the relationship between sales and time (t).(b) Use
Use MINITAB and the data given in question 27 and the equations given in question 26.(a) Draw a graph showing the actual amount of sales and the estimate of sales based on equation A.(b) Draw a graph
Redo question 28, this time using only data from 1978 to 1987. Does your answer to part (c) change? If so, account for this result.Question 28Use MINITAB and the data given in question 27 and the
The following are error terms from a regression, where n = 23 and k = 2.Compute the Durbin–Watson d statistic. Does autocorrelation appear to be a problem? Year 1970 1971 1972 1973 1974 1975 1976
A biologist is interested in the effect of temperature and humidity on cell growth. She collects the following information from 8 samples:Use the MINITAB program to estimate the relationship among
Use a t test to test the significance of the coefficient on the interaction variable in question 31. Construct a 90 % confidence interval for this coefficient.Question 31A biologist is interested in
A popular belief in some financial circles is that most of the movement of the stock market takes place in January. Suppose you are interested in testing this“January effect” on General Motors
A college admissions officer is interested in knowing whether there is a difference between males’ and females’ math SAT scores. She collects the following information on the math SAT score, high
The batting instructor of the Toronto Blue Jays would like to see whether playing ball in the winter (winter ball) has any effect on a player’s season batting average. He collects the following
Suppose you estimate a multiple regression and find the t statistics on the coefficients to be insignificant, whereas the F-statistic indicates that the coefficients are jointly significant. What
Suppose a labor economist is interested in seeing whether there is a difference in earnings and education between people in the northeast and people in other parts of the country. He estimates the
A financial analyst is interested in the relationship between dividend per share(DPS) and earnings per share (EPS). He collects information on these two variables and estimates the regressionFromthis
You are interested in examining the relationship between consumption and income (the consumption function) during two different periods: the period before the Vietnam War and the period during and
The following scatter diagram shows the relationship between average total cost and quantity of output. Suggest a multiple regression model to describe this relationship. Average Total Cost ..
You are given the following error terms, which are the result of a regression of sales versus advertising expenditures for the Huessy Corporation over a 20-year period:(a) Compute the Durbin–Watson
Redo question 42 using the data for the auto industry.Question 42Estimate the regression of Chrysler’s return on assets against its debt/equity ratio. Compute the Durbin–Watson statistic. Does
Using Chrysler’s data, compute r1, the correlation coefficient between et and et-1, for the error terms computed in Chrysler’s regression model.Use MINITAB and the following information to answer
Redo question 46 using the data for Ford.Question 46Using Chrysler’s data, compute r1, the correlation coefficient between et and et-1, for the error terms computed in Chrysler’s regression
Redo question 46 using the data for GM.Question 46Using Chrysler’s data, compute r1, the correlation coefficient between et and et-1, for the error terms computed in Chrysler’s regression
Redo question 46 using the data for the auto industry.Question 46Using Chrysler’s data, compute r1, the correlation coefficient between et and et-1, for the error terms computed in Chrysler’s
Use MINITAB and the following information to answer question. To find out whether there is a relationship between the amount of financial leverage a firm uses and the return on the firm’s assets,
Use MINITAB and the following information to answer question. To find out whether there is a relationship between the amount of financial leverage a firm uses and the return on the firm’s assets,
Use MINITAB and the following information to answer question. To find out whether there is a relationship between the amount of financial leverage a firm uses and the return on the firm’s assets,
Use MINITAB and the following information to answer question. To find out whether there is a relationship between the amount of financial leverage a firm uses and the return on the firm’s assets,
Suppose you have a sample of 50 observations and 4 explanatory variables and you want to test for autocorrelation. What can you say about autocorrelation if you have the following Durbin–Watson
A financial analyst is interested in the relationship between earnings per share(EPS) and sales. She collects information on these two variables. Then she estimates the regressionand, from it,
Suppose we have the following two versions of the market model, which shows the relationship between the rate of return on a stock and the rate of return on some market index:(a) Suppose the
An economist estimates the equation: , 1,000+.75Y, +.10C-1 where = C, consumption in time period t Y, income in time period t C-1= consumption in time period t - 1 Interpret the coefficients of the
A farmer is interested in measuring the relationship among the number of bushels of corn grown, the amount of rainfall, and the amount of fertilizer used. Give two different equations that he could
Suppose the farmer in question 59 collects the following data:(a) Estimate the models you suggested in question 59.(b) Compare the results of the two models. Which model do you believe is better?
A marketing manager believes that advertising expenditures are effective in increasing sales only to a certain extent. He discovers that when the advertising expenditures exceed a certain level,
An economist wants to study the factors that determine the hourly wage rate.He comes up with the regressionWhat problem might the economist encounter in estimating this model? y = a +bx + cx + dx3+e
An economist conducts research on the relationship between household spending and income. She collects data on 60 households’ spending and income during 1986. After using regression analysis, she
Which of the following models is nonlinear in parameters where y and x are variables anda, b, and c are parameters? (a) y = axx (b) y = a + bx (c) y = a + bx + cx (d) y = a + b(1/x)
Use the following information to answer question. What determines the voting behavior in a presidential election? An economist believes that people “vote their pockets.” He argues that economic
Use the following information to answer question. What determines the voting behavior in a presidential election? An economist believes that people “vote their pockets.” He argues that economic
Use the following information to answer question. What determines the voting behavior in a presidential election? An economist believes that people “vote their pockets.” He argues that economic
Use the following information to answer question. What determines the voting behavior in a presidential election? An economist believes that people “vote their pockets.” He argues that economic
Use the following information to answer question. What determines the voting behavior in a presidential election? An economist believes that people “vote their pockets.” He argues that economic
Use the following information to answer question. What determines the voting behavior in a presidential election? An economist believes that people “vote their pockets.” He argues that economic
A financial analyst is interested in the relationship between earnings per share(EPS) and sales for Addison Company. He collects information on these two variables for a 10-year period. He estimates
Based on the correlations among the returns for T-Bill, Chrysler, Ford, GM, and NYSE Index in the following output, is there a problem about multicollinearity? Chrysler Ford GM NYSE Index T-Bill
The Durbin–Watson statistic computed from fitting a regression on Ford using NYSI Index and Chrysler as predictors is 1.9904. Is there a problem of autocorrelation?
From the following result, is there a “January effect”on returns of Ford even if NYSI Index and Chrysler are included as predictors? Predictor Constant NYSE index Chrysler Jan Coef 0.009900
(Problem 74 continued.) Write down the estimated regression equations for January and non-January, respectively.Problem 74From the following result, is there a “January effect”on returns of Ford
(Problem 75 continued.) Since the January effect is significant, do we need to consider the interaction between the January effect and the returns of NYSE Index and Chrysler?Write down the estimated
Add an interaction term (GNP) (Dummy) to Eq. 16.26. The MINITAB outputs are presented as follows. Please compare these results with those presented in Table 16.10.Eq. 16.26Table 16.10 MTB > MTB >
Add an interaction term (GNP) (Dummy) to Eq. 16.29. The MINITAB output is presented as follows. Please compare these results with those presented in Fig. 16.22.Eq. 16.29Fig. 16.22 MTB > BRIEF 3 MTB >
Mr. John is a central New Jersey real estate salesman. He claims that the median selling price of houses in the area is about $ 100,000. To check this claim, you randomly select 10 houses that were
Use the sign test to test, at the 5 percent level, whether the following data come from a population with median 10. Use H1: median ≠ 10. 13.7 12.0 9.4 8.1 25.9 11.2 15.9 17.5 12.7 12.3 12.9 10.8
Use the number-of-runs test to determine at the 5 percent level of significance whether it can be concluded that these binary sequences are not random:(a) 0 0 1 1 1 0 1 0 1 1 1 0 0 1 0 0 1 1 0 1 1 1
The following sequence indicates whether a manufacturer’s daily production of videocassette recorders (VCRs) was above (X) or below (Y) the long-term median number of defective
The following sequence indicates whether an accident occurred at a given intersection during the rush “hour” (7:00 A.M. to 9:30 A.M). (Y indicates an accident, N no accident.)N Y N N Y Y N N N Y
At the 5 percent level of significance, can we conclude that this sequence of symbols is a random series? ++++-++-+-+ +++++ + -
Find the Spearman rank correlation for the scores for friendliness and response time given to brand Y computers by 7 users. Test for significance, assuming that the critical value for rs when n = 7
In a rank correlation problem with n = 50 observations, the sum of the squared differences between the rank observations is Σd2 = 12,500. Calculate r.
The ratings assigned by a personnel manager and his assistant to several job applicants are given in the accompanying table. Use Spearman rank correlation measure r to show whether the personnel
A company wishes to compare typing accuracy on two kinds of computer keyboards. Fifteen experienced typists type the same 600 words. Keyboard X1 is used 7 times and keyboard X2 is used 8 times, with
The owner of a convenience store has noticed that the register shortages are higher at the eastside store than at the westside store. The following dollar shortages were reported for 10 randomly
The manufacturer of a new shaving cream tests 3 new advertising campaigns in a total of 21 markets. Sales in the third week after introduction are given in the accompanying table.Use the
Compare parametric tests to nonparametric tests. What are the assumptions of each type of test? Give some examples of each type of test.
The “weak form” of the efficient market hypothesis says that historical stock prices cannot be used to earn abnormal profits—that is, stock prices move randomly. Go to the library, collect 30
Toss a coin 50 times and use a number-of-runs test to see whether the outcome of tossing a coin is random at a 5 percent level of significance.Use the following information to answer questions
Use the following information to answer questions 16–19. A psychologist conducting research on the differences in aptitude between males and females found 10 pairs of twins wherein one of the twins
Use the following information to answer questions 16–19. A psychologist conducting research on the differences in aptitude between males and females found 10 pairs of twins wherein one of the twins
Use the following information to answer questions 16–19. A psychologist conducting research on the differences in aptitude between males and females found 10 pairs of twins wherein one of the twins
Use the following information to answer questions 16–19. A psychologist conducting research on the differences in aptitude between males and females found 10 pairs of twins wherein one of the twins
A statistics professor is interested in whether there is any difference between the scores in the first-period statistics class and those in her third-period statistics class. She collects the
The prices for ABC Company’s stock over a 12-day period follow. Test, at theα = .05 level, whether changes in the stock price are random. 83.20 81.15 79.32 80.10 79.21 78.30 79.65 80.27 89.82
The following array shows price changes for silver. A + denotes an increase in price from the previous day; a – denotes a decrease in price from the previous day.Test, at the 10 percent level of
Suppose we want to test whether the number of times black or red comes up on a roulette wheel is random. In 100 spins of the wheel, we find that black comes up 48 times and red comes up 52 times. The
Suppose you toss a coin 50 times and receive 22 heads and 28 tails with 25 runs.Is the tossing of a head or tail random? Test this hypothesis at the 5 percent level of significance.
You are given the following 4 samples of price changes for a stock. Count the number of runs in each sample. + (c) + + (d) ++ + 1 I I
Suppose you collect the following information on salaries for two groups of college professors: professors in the sciences and professors in the humanities.(a) Compute the ranks for each group.(b) Do
In a TV newsroom, 30 economists were asked one by one whether each was optimistic about the future of the economy. The answers (in order) wereThe alert TV audience suspects that when the economists

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