A computer dating service typically asks for various pieces of information such as height, weight, income, and so on. One such service requested the length of index fingers. The only plausible reason for this request is to act as a proxy on height. Women have often complained that men lie about their heights. If there is a strong relationship between heights and index fingers, the information can be used to “correct” false claims about heights. To test the relationship between the two variables researchers gathered the heights and lengths of index fingers (in centimeters) of 121 students. a. Graph the relationship between the two variables. b. Is there sufficient evidence to infer that height and length of index fingers are linearly related? c. Predict with 95% confidence the height of someone whose index finger is 6.5 cm long. Is this prediction likely to be useful? Explain. (The authors would like to thank Howard Waner for supplying the problem and data.)
> After analyzing whether the number of ads is related to the number of customers, the manager in Exercise 16.99 decided to determine whether the advertising made any difference. As a result, he reorganized the experiment. Each week he advertised several t
> Refer to Exercise 18.44. a. Estimate a second-order model with interaction. b. Is this model valid in predicting the number of accidents? Test at the 10% significance level. Data from Exercise 18.44: The number of car accidents on a particular stretch o
> The number of car accidents on a particular stretch of highway seems to be related to the number of vehicles that travel over it and the speed at which they are traveling. A city alderman has decided to ask the county sheriff to provide him with statisti
> Car designers have been experimenting with ways to improve gas mileage for many years. An important element in this research is the way in which a car’s speed affects how quickly fuel is burned. Competitions whose objective is to drive the farthest on th
> A fast-food restaurant chain whose menu features hamburgers and chicken sandwiches is about to add a fish sandwich to its menu. There was considerable debate among the executives about the likely demand and what the appropriate price should be. A recentl
> Refer to Exercise 17.17 a. Use stepwise regression to compute the regression equation. b. Compare the output with that produced in Exercise 17.17. Data from Exercise 17.17: La Quinta Motor Inns is a moderately priced chain of motor inns located across t
> Refer to Exercise 17.16. a. Use stepwise regression to compute the regression equation. b. Compare the output with that produced in Exercise 17.16. Data from Exercise 17.16: The pollster also recorded the following variables in addition to the variable
> Discuss how the factor values and weights affect the final result. Explain the strengths and weaknesses of the statistical analysis.
> The cost of workplace injuries is high for the individual worker, for the company, and for society. It is in everyone’s interest to rehabilitate the injured worker as quickly as possible. A statistician working for an insurance company has investigated t
> Re-do Example 18.4 by assigning your own values to each factor and to the weights. What conclusion did you reach?
> Re-do Example 18.4. Change the weights for knowledge and training to 15% and for working conditions to 25%. What effect does this have on the conclusion? Briefly explain why the result was predictable.
> Pay equity for men and women has been an ongoing source of conflict for a number of years in North America. Suppose that a statistics practitioner is investigating the factors that affect salary differences between male and female university professors.
> The general manager of a supermarket chain believes that sales of a product are influenced by the amount of space the product is allotted on shelves. If true, this would have great significance, because the more profitable items could be given more shelf
> Absenteeism is a serious employment problem in most countries. It is estimated that absenteeism reduces potential output by more than 10%. Two economists launched a research project to learn more about the problem. They randomly selected 100 organization
> Refer to Exercise 16.139. The gender of the student was recorded where 1 = male and 0 = female. a. Does the inclusion of gender improve the model? b. Predict with 95% confidence the height of a female whose index finger is 6.5 cm long. c. Predict with 95
> Refer to Exercise 16.132, where a simple linear regression model was used to analyze the relationship between welding machine breakdowns and the age of the machine. The analysis proved to be so useful to company management that it decided to expand the m
> Profitable banks are ones that make good decisions on loan applications. Credit scoring is the statistical technique that helps banks make that decision. However, many branches overturn credit scoring recommendations, whereas other banks do not use the t
> Graph y versus x1 for x2 = 2, 4, and 5 for each of the following equations. a. y = 0.5 + 1x1 − 0.7x2 − 1.2x21 + 1.5x22 b. y = 0.5 + 1x1 − 0.7x2 − 1.2x21 + 1.5x22 + 2x1x2
> Refer to Exercise 17.12 where the amount of time to unload a truck was analyzed. The manager realized that another variable, the time of day, may affect unloading time. He recorded the following codes: 1 = morning, 2 = early afternoon, and 3 = late after
> In the door-to-door selling of vacuum cleaners, various factors influence sales. The Birk Vacuum Cleaner Company considers its sales pitch and overall package to be extremely important. As a result, it often thinks of new ways to sell its product. Becaus
> Recall Exercise 16.6 where a statistics practitioner analyzed the relationship between the length of a commercial and viewers’ memory of the commercial’s product. However, in the experiment not only was the length varied but also the type of commercial.
> The manager of an amusement park would like to be able to predict daily attendance in order to develop more accurate plans about how much food to order and how many ride operators to hire. After some consideration, he decided that the following three fac
> Refer to Exercise 17.10, where a multiple regression analysis was performed to predict men’s longevity based on the parents’ and grandparents’ longevity. In addition to these data, suppose that the actuary also recorded whether the man was a smoker (1 =
> Refer to Exercise 17.14. a. Predict with 95% confidence the MBA program GPA of a BEng whose undergraduate GPA was 9.0, whose GMAT score as 700, and who has had 10 years of work experience. b. Repeat part (a) for a BA student. Data from Exercise 17.14: T
> Refer to Exercise 17.14. After considering the results of the initial study, the dean realized that she may have omitted an important variable— the type of undergraduate degree. She returned to her sample of students and recorded the type of undergraduat
> In a study of computer applications, a survey asked which microcomputer a number of companies used. The following indicator variables were created. Which computer is being referred to by each of the following pairs of values? a. I1 = 0; I2 = 1 b. I1 = 1
> Create and identify indicator variables to represent the following nominal variables. a. Religious affiliation (Catholic, Protestant, and others) b. Working shift (8 a.m. to 4 p.m., 4 p.m. to 12 midnight, and 12 midnight to 8 a.m.) c. Supervisor (Jack Jo
> How many indicator variables must be created to represent a nominal independent variable that has five categories?
> The production manager of a chemical plant wants to determine the roles that temperature and pressure play in the yield of a particular chemical produced at the plant. From past experience, she believes that when pressure is held constant, lower and high
> Graph y versus x1 for x2 = 1, 2, and 3 for each of the following equations. a. y = 1 + 2x1 + 4x2 b. y = 1 + 2x1 + 4x2 − x1x2
> the value of television commercials is by telephone surveys conducted shortly after commercials are aired. Respondents who watched a certain television station at a given time period, during which the commercial appeared, are asked whether they can recal
> The administrator of a school board in a large county was analyzing the average mathematics test scores in the schools under her control. She noticed that there were dramatic differences in scores among the schools. In an attempt to improve the scores of
> For many cities around the world, garbage is an increasing problem. Many North American cities have virtually run out of space to dump the garbage. A consultant for a large American city decided to gather data about the problem. She took a random sample
> The marketing manager for a chain of hardware stores needed more information about the effectiveness of the three types of advertising that the chain used. These are localized direct mailing (in which flyers describing sales and featured products are dis
> The admissions officer of a university is trying to develop a formal system to decide which students to admit to the university. She believes that determinants of success include the standard variables—high school grades and SAT scores. However, she also
> The manager of a tire store in Minneapolis has been concerned with the high cost of inventory. The current policy is to stock all the snow tires that are predicted to sell over the entire winter at the beginning of the season (end of October). The manage
> Refer to Exercise 16.131. Determine whether there is evidence of first-order autocorrelation. Data from Exercise 16.131: The manager of Colonial Furniture has been reviewing weekly advertising expenditures. During the past 6 months, all advertisements f
> Refer to Exercise 17.3. Is there evidence of positive first-order autocorrelation? Data from Exercise 17.3: The president of a company that manufactures drywall wants to analyze the variables that affect demand for his product. Drywall is used to constr
> Weekly sales of a company’s product (y) and those of its main competitor (x) were recorded for one year. a. Conduct a regression analysis of these data. b. Plot the residuals versus the time periods. Does there appear to be autocorrelation? c. Perform th
> Observations of variables y, x1, and x2 were taken over 100 consecutive time periods. a. Conduct a regression analysis of these data. b. Plot the residuals versus the time periods. Describe the graph. c. Perform the Durbin-Watson test. Is there evidence
> Test the following hypotheses with = .05. H0: There is no first-order autocorrelation. H1: There is negative first-order autocorrelation. n = 33, k = 4, d = 2.25
> The widespread use of salt on roads in Canada and the northern United States during the winter and acid precipitation throughout the year combine to cause rust on cars. Car manufacturers and other companies offer rustproofing services to help purchasers
> After a recent study, researchers reported on the effects of folic acid on the occurrence of spina bifida—a birth defect in which there is incomplete formation of the spine. A sample of 2,000 women who gave birth to children with spina bifida and who wer
> Test the following hypotheses with = .02. H0: There is no first-order autocorrelation. H1: There is first-order autocorrelation. n = 90, k = 5, d = 1.60
> Test the following hypotheses with = .05. H0: There is no first-order autocorrelation. H1: There is positive first-order autocorrelation. n = 50, k = 2, d = 1.38
> When one company buys another company, it is not unusual that some workers are terminated. The severance benefits offered to the laid-off workers are often the subject of dispute. Suppose that the Laurier Company recently bought the Western Company and s
> Given the following information, perform the Durbin-Watson test to determine whether first order autocorrelation exists: n = 25, k = 5,= .10, d = .90
> Exercise 13.19 described a survey that asked people between 18 and 34 years of age and 35 to 50 years of age how much time they spent listening to FM radio each day. Also recorded were the amounts spent on music throughout the year. Can we infer that a l
> In addition to the data recorded for Exercises 12.31 and 13.227, we recorded the grade point average of the students who held down parttime jobs. Determine whether there is evidence of a linear relationship between the hours spent at parttime jobs and th
> (Exercise 3.67 revisited) A very large contribution to profits for a movie theater is the sale of popcorn, soft drinks, and candy. A movie theater manager speculated that the longer the time between showings of a movie, the greater the sales of concessio
> Mutual funds minimize risks by diversifying the investments they make. There are mutual funds that specialize in particular types of investments. For example, the TD Precious Metal Mutual Fund buys shares in gold mining companies. The value of this mutua
> The analysis that the human resources manager performed in Exercise 16.18 indicated that the dexterity test is not a predictor of job performance. However, before discontinuing the test, he decided that the problem is that the statistical analysis was fl
> Automobile insurance appraisers examine cars that have been involved in accidental collisions and estimate the cost of repairs. An insurance executive claims that there are significant differences in the estimates from different appraisers. To support hi
> Some critics of television complain that the amount of violence shown on television contributes to violence in our society. Others point out that television also contributes to the high level of obesity among children. We may have to add financial proble
> Every year, the U.S. Federal Trade Commission rates cigarette brands according to their levels of tar and nicotine, substances that are hazardous to smokers’ health. Additionally, the commission includes the amount of carbon monoxide, which is a by-produ
> An agronomist wanted to investigate the factors that determine crop yield. Accordingly, she undertook an experiment wherein a farm was divided into 30 one-acre plots. The amount of fertilizer applied to each plot was varied. Corn was then planted, and th
> The president of a company that manufactures car seats has been concerned about the number and cost of machine breakdowns. The problem is that the machines are old and becoming quite unreliable. However, the cost of replacing them is quite high, and the
> The manager of Colonial Furniture has been reviewing weekly advertising expenditures. During the past 6 months, all advertisements for the store have appeared in the local newspaper. The number of ads per week has varied from one to seven. The store’s sa
> Perform a complete diagnostic analysis for Exercise 16.18 to determine whether the required conditions are satisfied.
> Are the required conditions satisfied for Exercise 16.17?
> Check to ensure that the required conditions for Exercise 16.16 are satisfied.
> Are the required conditions satisfied for Exercise 16.15?
> Refer to Exercise 16.14. a. Determine the residuals and the standardized residuals. b. Draw the histogram of the residuals. Does it appear that the errors are normally distributed? Explain. c. Identify possible outliers. d. Plot the residuals versus the
> Most automobile repair shops now charge according to a schedule that is claimed to be based on average times. This means that instead of determining the actual time to make a repair and multiplying this value by their hourly rate, repair shops determine
> Refer to Exercise 16.13. Are the required conditions satisfied? Data from Exercise 16.13: Millions of boats are registered in the United States. As is the case with automobiles, there is an active used-boat market. Many of the boats purchased require ba
> Check the required conditions for Exercise 16.12.
> Refer to Exercise 16.11. a. Determine the residuals and the standardized residuals. b. Draw the histogram of the residuals. Does it appear that the errors are normally distributed? Explain. c. Identify possible outliers. d. Plot the residuals versus the
> Refer to Exercise 16.10. Are the required conditions satisfied? Data from Exercise 16.10: Besides their known long-term effects, do cigarettes also cause short-term illnesses such as colds? To help answer this question, a sample of smokers was drawn. Ea
> Determine whether negative first-order autocorrelation exists when d = 2.85, n = 50, and k = 5. (Use a 1% significance level.)
> Are the required conditions satisfied in Exercise 16.8?
> Perform the Durbin-Watson test at the 5% significance level to determine whether positive first-order autocorrelation exists when d = 1.10, n = 25, and k = 3.
> Refer to Exercise 17.16. Are the required conditions satisfied? Data from Exercise 17.16: The pollster also recorded the following variables in addition to the variable DEFINITE. Number of days in previous week watching national news on television (DAYS
> Calculate and plot the residuals and predicted values of y for Exercise 16.5.
> Refer to Exercise 16.4. a. Calculate the residuals. b. Calculate the predicted values of y. c. Plot the residuals (on the vertical axis) and the predicted values of y. Data from Exercise 16.4: Critics of television often refer to the detrimental effects
> Discrimination in hiring has been illegal for many years. It is illegal to discriminate against any person on the basis of race, gender, or religion. It is also illegal to discriminate because of a person’s handicap if it in no way prevents that person f
> Calculate the residuals and predicted values of y in Exercise 16.3.
> Refer to Exercise 16.2. Calculate the residuals and the predicted values of y. Data from Exercise 16.2: Attempting to analyze the relationship between advertising and sales, the owner of a furniture store recorded the monthly advertising budget ($ thous
> You are given the following six points: a. Determine the regression equation. b. Use the regression equation to determine the predicted values of y. c. Use the predicted and actual values of y to calculate the residuals. d. Compute the standardized resi
> Refer to Exercise 17.15. Determine whether the required conditions are satisfied. Data from Exercise 17.15: With voter turnout during presidential elections around 50%, a vital task for politicians is to try to predict who will actually vote. A variable
> Refer to Exercise 17.15. Check the required conditions. Data from Exercise 17.15: With voter turnout during presidential elections around 50%, a vital task for politicians is to try to predict who will actually vote. A variable used to determine who is
> The general manager of the Cleveland Indians baseball team is in the process of determining which minor-league players to draft. He is aware that his team needs home-run hitters and would like to find a way to predict the number of home runs a player wil
> Refer to Exercise 17.14. Are the required conditions satisfied? Data from Exercise 17.14: The MBA program at a large university is facing a pleasant problem—too many applicants. The current admissions policy requires students to have completed at least
> Refer to Exercise 17.13. a. Are the required conditions satisfied? b. Is multicollinearity a problem? If so, explain the consequences. Data from Exercise 17.13: Lotteries have become important sources of revenue for governments. Many people have critici
> Determine whether there are violations of the required conditions in the regression model used in Exercise 17.11.
> Refer to Exercise 17.10. Calculate the residuals and predicted values. a. Is the normality requirement satisfied? b. Is the variance of the error variable constant? c. Is multicollinearity a problem? Data from Exercise 17.10: Life insurance companies ar
> Health-care costs in the United States and Canada are concerns for citizens and politicians. The question is, How can we devise a system wherein people’s medical bills are covered but individuals attempt to reduce costs? An American company has come up w
> Determine whether the required conditions are satisfied in Exercise 17.9
> Are the required conditions satisfied for the regression analysis in Exercise 17.8?
> Refer to Exercise 17.7. a. Conduct an analysis of the residuals to determine whether any of the required conditions are violated. b. Does it appear that multicollinearity is a problem? c. Identify any observations that should be checked for accuracy. Da
> Are the required conditions satisfied in Exercise 17.6?
> Calculate the residuals and predicted values for the regression analysis in Exercise 17.5. a. Does the error variable appear to be normally distributed? b. Is the variance of the error variable constant? c. Is multicollinearity a problem?
> Pick any one of the previous five exercises and briefly describe why the intervals are so wide.
> Refer to Exercise 16.49. The temperature is 80 degrees. Predict with 95% confidence how far the golfer’s next drive will travel. Data from Exercise 16.49: Refer to Exercise 3.71 wherein we looked at the relationship between temperature and distance that
> Refer to Exercise 16.48. Predict with 90% confidence how definite is the intention to vote for one 50-year-old. Data from Exercise 16.48: In most presidential elections in the United States, the voter turnout is quite low, often in the neighborhood of 5
> Refer to Exercise 16.47. Estimate with 90% confidence the mean number of days watching the national news on television for the population of 70-year-olds. Data from Exercise 16.47: National news on television features commercials describing pharmaceutic
> Refer to Exercise 16.46. Use a prediction interval with 90% confidence to predict the auction selling price of one Canada 1925 nickel with a grade of 40. Data from Exercise 16.46: Refer to Exercise 3.70 where we looked at the relationship between the gr
> A study was undertaken to determine whether a drug commonly used to treat epilepsy could help alcoholics to overcome their addiction. The researchers took a sample of 103 hardcore alcoholics. Fifty-five drinkers were given topiramate and the remaining
> Refer to Exercise 16.45. Estimate with 95% confidence the mean time spent watching or reading news on the Internet for the population of people who have completed 12 years of education. Data from Exercise 16.45: Do more educated people spend more time w
> Refer to Exercise 16.18. Estimate with 95% confidence the mean percentage of defectives for workers who score 80 on the dexterity test. Data from Exercise 16.18: Although a large number of tasks in the computer industry are robotic, many operations requ
> Refer to Exercise 16.17. a. Estimate with 95% confidence the mean annual income of 6’2” (74 inches)-tall men. b. Suppose that an individual is 5’8” (68 inches). Predict with 95% confidence his annual income. Data from Exercise 16.17: One general belief
