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Statistics For Business And Economics 8th Edition Paul Newbold, William Carlson, Betty Thorne - Solutions

Consider a regression analysis with n = 34 and four potential independent variables. Suppose that one of the independent variables has a correlation of 0.23 with the dependent variable. Does this imply that this independent variable will have a very small Student's t statistic in the regression
Consider a regression analysis with n = 47 and three potential independent variables. Suppose that one of the independent variables has a correlation of 0.95 with the dependent variable. Does this imply that this independent variable will have a very large Student's t statistic in the regression
Consider a regression analysis with n = 49 and two potential independent variables. Suppose that one of the independent variables has a correlation of 0.56 with the dependent variable. Does this imply that this independent variable will have a very small Student's t statistic in the regression
In order to assess the effect in one state of a casualty insurance company€™s economic power on its political power, the following model was hypothesized and fitted to data from all 50 states:Y = Î²0 + Î²1X1 + Î²2X2 + Î²3X3 + Î²4x4 +
A random sample of 93 freshmen at the University of Illinois was asked to rate, on a scale of 1 (low) to 10 (high), their overall opinion of residence hall life. They were also asked to rate their levels of satisfaction with roommates, with the floor, with the hall, and with the resident advisor.
The following model was fitted to 47 monthly observations in an attempt to explain the difference between certificate of deposit rates and commercial paper rates:Y = Î²0 + Î²1X1 + Î²2X2 + ÎµwhereY = commercial paper certificate of deposit rateless
The following model was fitted to a sample of 30 families in order to explain household milk consumption: yi = b0 + b1x1i + b2x2i + ei where yi = milk consumption, in quarts per week x1i = weekly income, in hundreds of dollars x2i = family size The least squares estimates of the regression
You have been asked to develop a multiple regression model to predict the traffic fatality rate per 100 million miles in 2007. The data file Vehicle Travel State contains traffic data by state for the year 2007; the variables are described in the Chapter 11 appendix.Consider the following possible
The data file Economic Activity contains data for the 50 states in the United States; the variables are described in the Chapter 11 appendix. You are asked to develop a model to predict the percentage of females that are in the labor force. The possible predictor variables are per capita disposable
The United Nations has hired you as a consultant to help identify factors that predict manufacturing growth in developing countries. You have decided to use multiple regression to develop a model and identify important variables that predict growth. You have collected the data in the data file
The method of least squares is used far more often than any alternative procedure to estimate the parameters of a multiple regression model. Explain the basis for this method of estimation, and discuss why its use is so widespread.
It is common practice to compute an analysis of variance table in conjunction with an estimated multiple regression. Carefully explain what can be learned from such a table.
State whether each of the following statements is true or false. a. The error sum of squares must be smaller than the regression sum of squares. b. Instead of carrying out a multiple regression, we can get the same information from simple linear regressions of the dependent variable on each
If an additional independent variable, however irrelevant, is added to a multiple regression model, a smaller sum-of-squared errors will result. Explain why this is so, and discuss the consequences for the interpretation of the coefficient of determination.
A dependent variable is regressed on two independent variables. It is possible that the hypotheses H0: β1 = 0 and H0: β2 = 0 cannot be rejected at low significance levels, yet the hypothesis H0: β1 = β2 = 0 can be rejected at a very low significance level. In what circumstances might this
Suppose that the regression model y = β0 + β1x1 + β2x2 + ε is estimated by least squares. Show that the residuals, ei, from the fitted model sum to 0.
A study was conducted to assess the influence of various factors on the start of new firms in the computer chip industry. For a sample of 70 countries the following model was estimated:R2 = 0.766wherey` = new business starts in the industryx1 = population in millionsx2 = industry sizex3 = measure
The following model was fitted to a sample of 25 students using data obtained at the end of their freshman year in college. The aim was to explain students’ weight gains: yi = β0 + β1x1i + β2x2i + β3x3iεi where yi = weight gained, in pounds, during freshman year x1i = average number of meals
A survey research group conducts regular studies of households through mail questionnaires and is concerned about the factors influencing the response rate. In an experiment, 30 sets of questionnaires were mailed to potential respondents. The regression model fitted to the resulting data set was as
A consulting group offers courses in financial management for executives. At the end of these courses, participants are asked to provide overall ratings of the value of the course. To assess the impact of various factors on ratings, the modelY = Î²0 + Î²1X1 + Î²2X2 + Î²3X3 + Îµwas fitted
At the end of classes professors are rated by their students on a scale of 1 (poor) to 5 (excellent). Students are also asked what course grades they expect, and these are coded as A = 4, B = 3, and so on. The data file Teacher Rating contains, for a random sample of 20 classes, ratings of
Flyer Computer, Inc., wishes to know the effect of various variables on labor efficiency. Based on a sample of 64 observations, the following model was estimated by least squares:wherey` = index of direct labor efficiency in production plantx1 = ratio of overtime hours to straight-time hours worked
Based on 107 students€™ scores on the first examination in a course on business statistics, the following model was estimated by least squares:wherey` = student€™s actual score on the examinationx1 = student€™s expected score on the examinationx2 = hours per week spent working on the
Based on 25 years of annual data, an attempt was made to explain savings in India. The model fitted was as follows:y = β0 + β1x1 + β2x2 + εwherey = change in real deposit ratex1 = change in real per capita incomex2 = change in real interest rateThe least squares parameter estimates (with
Based on data on 2,679 high school basketball players, the following model was fitted:y = b0 + b1x1 + b2x2 + g + b9x9 + ewherey = minutes played in seasonx1 = field@goal percentagex2 = free@throw percentagex3 = rebounds per minutex4 = points per minutex5 = fouls per minutex6 = steals per minutex7 =
Based on data from 63 counties, the following model was estimated by least squares:wherey` = growth rate in real gross domestic productx1 = real income per capitax2 = average tax rate, as a proportion of gross national productThe numbers in parentheses under the coefficients are the estimated
The following regression model was fitted to data on 60 U.S. female amateur golfers:where y` = winnings per tournament in dollars x1 = average length of drive in yards x2 = percentage times drive ends in fairway x3 = percentage times green reached in regulation x4 = percentage times par saved after
The Economics Department wishes to develop a multiple regression model to predict student GPA for economics courses. Department faculty have collected data for 112 graduates, which include the variables economics GPA, SAT verbal, SAT mathematics, ACT English, ACT social science, and high school
Write the model specification and define the variables for a multiple regression model to predict college GPA as a function of entering SAT scores and the year in college: freshman, sophomore, junior, and senior.
You have been asked to serve as a consultant and expert witness for a wage-discrimination lawsuit. A group of Latino and black women have filed the suit against their company, Amalgamated Distributors, Inc. The women, who have between 5 and 25 years of service with the company, allege that the
Consider the following models estimated using regression analysis applied to time-series data. What is the long-term effect of a 1-unit increase in x in period t?a. yt = 10 + 2xt + 0.34yt-1b. yt = 10 + 2.5xt + 0.24yt-1c. yt = 10 + 2xt + 0.64yt-1d. yt = 10 + 4.3xt + 0.34yt-1
A market researcher is interested in the average amount of money spent per year by college students on clothing. From 25 years of annual data, the following estimated regression was obtained through least squares:wherey = expenditure per student, in dollars, on clothesx1 = disposable income per
Use the data from the Retail Sales file to estimate the regression modelyt = β0 + β1xt + γyt-1 + εtand test the null hypothesis that g = 0, whereyt = retail sales per householdxt = disposable income per household
The data file Money UK contains observations from the United Kingdom on the quantity of money in millions of pounds (Y); income, in millions of pounds (X1); and the local authority interest rate (X1). Estimate the model (Mills 1978)yt = β0 + β1x1t + β2x2t + γyt-1 + εtand write a report on your
The data file Pension Funds contains data on the market return (X) of stocks and the percentage (Y) of portfolios in common stocks at market value at the end of the year for private pension funds. Estimate the modelyt = β0 + β1xt + γyt-1 + εtand write a report on your findings.
The data file Income Canada shows quarterly observations on income (Y) and money supply (X) in Canada. Estimate the model (Hsiao 1979)yt = β0 + β1xt + γyt-1 + εtand write a report on your findings.
The data file Births Australia shows annual observations on the first confinement resulting in a live birth of the current marriage (Y) and the number of first marriages (for females) in the previous year (X) in Australia. Estimate the model (McDonald 1981)yt = β0 + β1xt + γyt-1 + εtand write a
The data file Thailand Consumption shows 29 annual observations on private consumption (Y) and disposable income (X) in Thailand. Fit the regression modellog yt = β0 + β1log x1t + γlog yt-1 + εtand write a report on your findings.
Write the model specification and define the variables for a multiple regression model to predict wages in U.S. dollars as a function of years of experience and country of employment, indicated as Germany, Great Britain, Japan, United States, and Turkey.
Suppose that a regression relationship is given by the following:Y = β0 + β1X1 + β2X2 + εIf the simple linear regression of Y on X1 is estimated from a sample of n observations, the resulting slope estimate is generally biased for β1. However, in the special case where the sample correlation
Transportation Research, Inc., has asked you to prepare some multiple regression equations to estimate the effect of variables on fuel economy. The data for this study are contained in the data file Motors, and the dependent variable is miles per gallon-milpgal-as established by the Department of
Use the data in the file Citydatr to estimate a regression equation that can be used to determine the marginal effect of the percent commercial property on the market value per owner-occupied residence (Hseval). Include the percent of owneroccupied residences (Homper), percent of industrial
In the regression model Y = β0 + β1X1 + β2X2 + ε the extent of any multicollinearity can be evaluated by finding the correlation between X1 and X2 in the sample. Explain why this is so.
An economist estimates the following regression model: y = β0 + β1x1 + β2x2 + ε The estimates of the parameters β1 and β2 are not very large compared with their respective standard errors. But the size of the coefficient of determination indicates quite a strong relationship between the
Based on data from 63 counties, the following model was estimated by least squares:where y` = growth rate in real gross domestic product x1 = real income per capita x2 = average tax rate, as a proportion of gross national product The numbers below the coefficients are the coefficient standard
In Chapter 11, the regression of retail sales per household on disposable income per household was estimated by least squares. The data are given in Table 11.1, and Table 11.2 shows the residuals and the predicted values of the dependent variable. Use the data file Retail Sales.a. Graphically check
Consider a regression model that uses 48 observations. Let ei denote the residuals from the fitted regression and y`i be the in-sample predicted values of the dependent variable. The least squares regression of e2i on y`i has coefficient of determination 0.032. What can you conclude from this
The data file Economic Activity contains data for 50 states in the United States. Develop a multiple regression model to predict total retail sales for auto parts and dealers. Find two or three of the best predictor variables from those in the data file using the variable descriptions from the
You have been asked by East Anglica Realty, Ltd., to provide a linear model that will estimate the selling price of homes as a function of family. There is particular concern for obtaining the most efficient estimate of the relationship between income and house price. East Anglica has collected
Write the model specification and define the variables for a multiple regression model to predict the cost per unit produced as a function of factory type (indicated as classic technology, computer-controlled machines, and computer-controlled material handling), and as a function of country
Consider the following regression model:yt = β0 + β1x1t + β2x2t + .. + βKxKt + εtShow that ifVar(ε) = Kx2i(K > 0)thenVar [εi/xi] = KDiscuss the possible relevance of this result in treating a form of heteroscedasticity.
Refer to Exercise 13.14 and data file Money UK. Let ei denote the residuals from the fitted regression and y`i be the in-sample predicted values. The least squares regression of e2 on y`i has coefficient of determination of 0.087. What can you conclude from this finding? Let ei denote the residuals
Suppose that a regression was run with three independent variables and 30 observations. The Durbin Watson statistic was 0.50. Test the hypothesis that there was no autocorrelation. Compute an estimate of the autocorrelation coefficient if the evidence indicates that there was autocorrelation.a.
Suppose that a regression was run with two independent variables and 28 observations. The Durbin-Watson statistic was 0.50. Test the hypothesis that there was no autocorrelation. Compute an estimate of the autocorrelation coefficient if the evidence indicates that there was autocorrelation.a.
In a regression based on 30 annual observations, U.S. farm income was related to four independent variables-grain exports, federal government subsidies, population, and a dummy variable for bad weather years. The model was fitted by least squares, resulting in a Durbin-Watson statistic of 1.29. The
The data file Money UK contains observations from the United Kingdom on the quantity of money in millions of pounds (Y); income, in millions of pounds 1X12; and the local authority interest rate (X2). Estimate the model (Mills 1978)yt = β0 + β`x1t + β2x2t + γgyt-1 + εtand write a report on
The data file Thailand Consumption shows 29 annual observations on private consumption (Y) and disposable income (X) in Thailand. Fit the regression modellog yt = β0 + β1log x1t + γglog yt-1 + εtand write a report on your findings. Test the null hypothesis of no autocorrelated errors against
A factory operator hypothesized that his unit output costs (y) depend on wage rate (x1), other input costs (x2), overhead costs (x3), and advertising expenditures (x4). A series of 24 monthly observations was obtained, and a least squares estimate of the model yielded the following results:The
The data file Advertising Retail shows, for a consumer goods corporation, 22 consecutive years of data on sales (y) and advertising (x).a. Estimate the regression:yt = β0 + β1xt + εtb. Check for autocorrelated errors in this model.c. If necessary, re-estimate the model, allowing for
The omission of an important independent variable from a time-series regression model can result in the appearance of auto correlated errors. In Example 13.7 we estimated the modelyt = β0 + β1x1t + εtrelating profit margin to net revenue per dollar for our savings and loan data. Carry out a
An economist wants to estimate a regression equation relating demand for a product (Y) to its price (X1) and income (X2). It is to be based on 12 years of quarterly data. However, it is known that demand for this product is seasonal; that is, it is higher at certain times of the year than
Write brief reports, including examples, explaining the use of each of the following in specifying regression models:a. Dummy variablesb. Lagged dependent variablesc. The logarithmic transformation
Consider the fitting of the following model: Y = β0 + β1X1 + β2X2 + β3X3 + ε where Y = tax revenues as a percentage of gross national product in a country X1 = exports as a percentage of gross national product in the country X2 = income per capita in the country X3 = dummy variable taking the
Discuss the following statement: In many practical regression problems, multicollinearity is so severe that it would be best to run separate simple linear regressions of the dependent variable on each independent variable.
Explain the nature of and the difficulties caused by each of the following:a. Heteroscedasticityb. Autocorrelated errors
The following model was fitted to data on 90 German chemical companies:where the numbers in parentheses are estimated coefficient standard errors andy = share pricex1 = earnings per sharex2 = funds flow per sharex3 = dividends per sharex4 = book value per sharex5 = a measure of growtha. Test at the
The following model was fitted to data from 28 countries in 1989 in order to explain the market value of their debt at that time:y = secondary market price, in dollars, in 1989 of $100 of the country€™s debtx1 = 1 if U.S. bank regulators have mandated write-down for the country€™s assets on
An attempt was made to construct a regression model explaining student scores in intermediate economics courses (Waldauer, Duggal, and Williams 1992). The population regression model assumed that Y = total student score in intermediate economics courses X1 = mathematics score on Scholastic Aptitude
The following regression was fitted by least squares to 32 annual observations on time-series data:whereyt = quantity of U.S. wheat exportedx1t = price of U.S. wheat on world marketx2t = quantity of U.S. wheat harvestedx3t = measure of income in countries importing U.S. wheatx4t = price of barley
The following regression was fitted by least squares to 30 annual observations on time-series data:whereyt = number of business failuresx1t = rate of unemploymentx2t = short-term interest ratex3t = value of new business orders placed The numbers below the coefficients are the coefficient standard
A stockbroker is interested in the factors influencing the rate of return on the common stock of banks. For a sample of 30 banks, the following regression was estimated by least squares:wherey = percentage rate of return on common stock of bankx1 = percentage rate of growth of bank€™s
Sharon Parsons, president of Gourmet Box Mini Pizza, has asked for your assistance in developing a model that predicts the demand for the new snack lunch pizza named Pizza1. This product competes in a market with three other brands that are named B2, B3, and B4 for identification. At present the
A market researcher is interested in the average amount of money per year spent by students on entertainment. From 30 years of annual data, the following regression was estimated by least squares:whereyt = expenditure per student, in dollars, on entertainmentxt = disposable income per student, in
A local public utility would like to be able to predict a dwelling unit's average monthly electricity bill. The company statistician estimated by least squares the following regression model:yt = Î²0 + Î²1x1t + Î²2x2t + Îµtwhereyt = average monthly electricity bill, in dollarsx1t = average
The data file Indonesia Revenue show 15 annual observations from Indonesia on total government tax revenues other than from oil (y), national income 1x12, and the value added by oil as a percentage of gross domestic product 1x22. Estimate by least squares the following regression:log yt = β0 + β1
The data file German Income shows 22 annual observations from the Federal Republic of Germany on percentage change in wages and salaries (y), productivity growth (x1), and the rate of inflation (x2), as measured by the gross national product price deflator. Estimate by least squares the following
The data file Japan Imports shows 35 quarterly observations from Japan on quantity of imports (y), ratio of import prices to domestic prices (x1), and real gross national product (x2). Estimate by least squares the following regression:log yt = β0 + β1 log x1t + β2 log x2t + γ log yt-1 +
A study was conducted on the labor-hour costs of Federal Deposit Insurance Corporation (FDIC) audits of banks. Data were obtained on 91 such audits. Some of these were conducted by the FDIC alone and some jointly with state auditors. Auditors rated banks' management as good, satisfactory, fair, or
The data file Britain Sick Leave shows data from Great Britain on the days of sick leave per person (Y), unemployment rate (X1), ratio of benefits to earnings (X2), and the real wage rate (X3). Estimate the modellog yt = β0 + β1 log x1t + β2 log x2t + β3 log x3t + εtand write a report on your
The U.S. Department of Commerce has asked you to develop a regression model to predict quarterly investment in production and durable equipment. The suggested predictor variables include GDP, prime interest rate, per capita income lagged, federal government spending, and state and local government
An economist has asked you to develop a regression model to predict consumption of service goods as a function of disposable personal income and other important variables. The data for your analysis are found in the data file Macro2010, which is described in the data dictionary in the chapter
Jack Wong, a Tokyo investor, is considering plans to develop a primary steel plant in Japan. After reviewing the initial design proposal, he is concerned about the proposed mix of capital and labor. He has asked you to prepare several production functions using some historical data from the United
John Ramapujan is the plant manager for Kitchen Products, Inc. He has asked you to help identify worker factors that influence productivity. In particular, he is interested in gender differences, the effect of working on different shifts, and employee attitudes toward the present benefits plan
The administrator of a small city has asked you to identify variables that influence the mean market value of houses in small midwestern cities. You have obtained data from a number of small cities, which are stored in the data file Citydatr, with variables described in the Chapter 12 appendix. The
The chief financial officer of a major service company has asked you to develop a regression model to predict consumption of service goods as a function of GDP and other important variables. The data for your analysis are found in the data fileMacro2010, which is stored on your data disk and
The marketing vice president of Consolidated Appliances has asked you to develop a regression model to predict consumption of durable goods as a function of disposable personal income and other important variables. The data for your analysis are found in the data file Macro2010, which is described
You have been asked to develop a model using multiple regression that predicts the retail sale of beef using time-series data. The data file Beef Veal Consumption contains a number of variables related to the beef retail markets beginning in 1935 and extending through the present. The variables are
You have been asked to develop a model using multiple regression that predicts the retail sale of veal using time series data. The data file Beef Veal Consumption contains a number of variables related to the veal retail markets beginning in 1935 and extending through the present.a. Prepare a model
You have been asked to develop a model using multiple regression that predicts the retail sale of beef and veal combined using time series data. The data file Beef Veal Consumption contains a number of variables related to the beef and veal retail markets beginning in 1935 and extending through the
Health care cost is an increasingly important part of the United States economy. In this exercise you are to identify variables that are predictors for the cost of physician and clinical services, either individually or in combination. Use the data file Health Care Cost Analysis, which contains
Health care cost is an increasingly important part of the U.S. economy. In this exercise you are to identify variables that are predictors for hospital cost, either individually or in combination. Use the data file Health Care Cost Analysis, which contains annual health care costs for the period
Health care cost is an increasingly important part of the U.S. economy. In this exercise you are to identify variables that are predictors for drug cost, either individually or in combination. Use the data file Health Care Cost Analysis, which contains annual health care costs for the period
You have been asked to develop a multiple regression model to predict per capita sales of cold cereal in cities with populations over 100,000. As a first step you hold a meeting with the key marketing managers that have experience with cereal sales. From this meeting you discover that per capita
Maxine Makitright, president of Good Parts, Ltd., has asked you to develop a model that predicts the number of defective parts per 8-hour work shift in her factory. She believes that there are differences among the three daily shifts and among the four raw-material suppliers. In addition, higher
Custom Woodworking, Inc., has been in business for 40 years. The company produces high-quality custommade wooden furniture and very high quality interior cabinet and interior woodwork for expensive homes and offices. It has been very successful in large part because of the highly skilled
A random sample of 150 residents in one community was asked to indicate their first preference for one of three television stations that air the 5 p.m. news. The results obtained are shown in the following table. Test the null hypothesis that for this population their first preferences are evenly
A random sample of statistics professors was asked to complete a survey including questions on curriculum content, computer integration, and software preferences. Of the 250 responses, 100 professors indicated that they preferred software package M and 80 preferred software package E, whereas the
The number of times a machine broke down each week was observed over a period of 100 weeks and recorded in the accompanying table. It was found that the average number of breakdowns per week over this period was 2.1. Test the null hypothesis that the population distribution of breakdown is Poisson.
In a period of 100 minutes there were a total of 190 arrivals at a highway toll booth. The accompanying table shows the frequency of arrivals per minute over this period. Test the null hypothesis that the population distribution is Poisson.
A random sample of 50 students was asked to estimate how much money they spent on textbooks in a year. The sample skewness of these amounts was found to be 0.83 and the sample kurtosis was 3.98. Test at the 10% level the null hypothesis that the population distribution of amounts spent is normal.

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