The term regression was originally used in 1885 by Sir Francis Galton in his analysis of the relationship between the heights of children and parents.He formulated the “law of universal regression,”which specifies that “each peculiarity in a man isshared by his kinsmen, but on average in a lessdegree.” (Evidently, people spoke this way in 1885.) In1903, two statisticians, K. Pearson and A. Lee, took arandom sample of 1,078 father–son pairs to examineGalton’s law (“On the Laws of Inheritance in Man,I. Inheritance of Physical Characteristics,” Biometrika2:457–462). Their sample regression line wasSon’s height = 33.73 + .516 × Father’s height a. Interpret the coefficients. b. What does the regression line tell you about the heights of sons of tall fathers? c. What does the regression line tell you about the heights of sons of short fathers?
> Refer to Exercise A15.5. Suppose that in addition to varying the marketing strategy, the manufacturer also decided to advertise in one of the two media that are available: television and newspapers. As a consequence, the experiment was repeated in the fo
> Do more educated people spend more time watching or news on the Internet? To help answer the question, a statistics practitioner undertook a survey that asked a random sample of people how many years of education they had and the amount of time they spe
> Refer to Exercise 16.10. Use the t-test of the coefficient of correlation to determine whether there is evidence of a positive linear relationship between number of cigarettes smoked and the number of sick days. Data from Exercise 16.10: Besides their k
> Are food budget and household income in Exercise 16.15 linearly related? Employ the t-test of the coefficient of correlation to answer the question.
> Repeat Exercise 16.6 using the t-test of the coefficient of correlation. Is this result identical to the one you produced in Exercise 16.6?
> Repeat Exercise 16.13 using the t-test of the coefficient of correlation to determine whether there is a negative linear relationship between the number of hours of engine use and the selling price of the used boats. Data from Exercise 16.13: Millions o
> Refer to Exercise 16.18. a. Compute the coefficient of determination and describe what it tells you. b. Can we infer that aptitude test scores and percentages of nondefectives are linearly related? Data from Exercise 16.18: Although a large number of ta
> Are height and income in Exercise 16.17 positively linearly related?
> Can we infer that office rents and vacancy rates are linearly related in Exercise 16.16?
> Refer to Exercise 16.15. a. Determine the coefficient of determination and describe what it tells you. b. Conduct a test to determine whether there is evidence of a linear relationship between household income and food budget. Data from Exercise 16.15:
> Assess fit of the regression line in Exercise 16.14.
> According to the latest census, the number of households in a large metropolitan area is 425,000. The home-delivery department of the local newspaper reports that 104,320 households receive daily home delivery. To increase home-delivery sales, the market
> Is there enough evidence to infer that as the number of hours of engine use increases, the price decreases in Exercise 16.13?
> Refer to Exercise 16.12. a. Determine the standard error of estimate, and describe what this statistic tells you about the regression line. b. Can we conclude that the size and price of the apartment building are linearly related? c. Determine the coeffi
> Refer to Exercise 16.11. a. Test to determine whether there is evidence of a linear relationship between distance to the nearest fire station and percentage of damage. b. Estimate the slope coefficient with 95% confidence. c. Determine the coefficient of
> Is there evidence of a linear relationship between number of cigarettes smoked and number of sick days in Exercise 16.10?
> Refer to Exercise 16.9. Use two statistics to measure the strength of the linear association. What do these statistics tell you? Data from Exercise 16.9: The human resource manager of a telemarketing firm is concerned about the rapid turnover of the fir
> Is there enough evidence to infer that age and theamount of time needed to complete the questionnaire are linearly related in Exercise 16.8?
> Refer to Exercise 16.7. Apply the three methods of assessing the model to determine how well the linear model fits. Data from Exercise 16.7: Florida condominiums are popular winter retreats for many North Americans. In recent years, the prices have stea
> Refer to Exercise 16.6. a. What is the standard error of estimate? Interpret its value. b. Describe how well the memory test scores and length of television commercial are linearly related. c. Are the memory test scores and length of commercial linearly
> Determine whether there is evidence of a negative linear relationship between temperature and the number of beers sold at Yankee Stadium in Exercise 16.5.
> Is there evidence of a linear relationship between the number of hours of television viewing and how overweight the child is in Exercise 16.4?
> Throughout the day, many exercise shows appear on television. These usually feature attractive and fit men and women performing various exercises and urging viewers to duplicate the activity at home. Some viewers are exercisers. However, some people like
> Calculate the coefficient of determination and conducta test to determine whether a linear relationship exists between housing starts and mortgage interest in Exercise 16.3.
> Refer to Exercise 16.2. a. Determine the standard error of estimate. b. Is there evidence of a linear relationship between advertising and sales? c. Estimate 1 with 95% confidence. d. Compute the coefficient of determination and interpret this value. e.
> Suppose that you have the following data: a. Draw the scatter diagram. Does it appear that x and y are related? If so, how? b. Test to determine whether there is evidence of a linear relationship. x 3 5 2 6 1 4 y 25 110 9 250 3 71
> You have been given the following data: a. Draw the scatter diagram. Does it appear that x and y are related? If so, how? b. Test to determine whether there is evidence of a linear relationship. x 1 3 4 6 9 8 10 y 1 8 15 33 75 70 95
> Assuming that the required conditions are satisfied in Exercise 16.13, what does this tell you about the distribution of used boat prices?
> What are the required conditions for Exercise 16.8? Do these seem reasonable?
> Describe what the required conditions mean in Exercise 16.6. If the conditions are satisfied, what can you say about the distribution of memory test scores?
> Although a large number of tasks in the computer industry are robotic, many operations require human workers. Some jobs require a great deal of dexterity to properly position components into place. A large North American computer maker routinely tests ap
> (Exercise 3.64 revisited) One general belief held by observers of the business world is that taller men earn more money than shorter men. In a University of Pittsburgh study, 250 MBA graduates, all about 30 years old, were polled and asked to report thei
> An economist wanted to investigate the relationship between office rents (the dependent variable) and vacancy rates. Accordingly, he took a random sample of monthly office rents and the percentage of vacant office space in 30 different cities. a. Determi
> Managers are frequently called on to negotiate in a variety of settings. This calls for an ability to think logically, which requires an ability to concentrate and ignore distractions. In a study of the effect of distractions, a random sample of 208 stud
> An economist for the federal government is attempting to produce a better measure of poverty than is currently in use. To help acquire information, she recorded the annual household income (in $1,000s) and the amount of money spent on food during one wee
> (Exercise 3.62 revisited) In an attempt to determine the factors that affect the amount of energy used, 200 households were analyzed. In each, the number of occupants and the amount of electricity used were measured. Determine the regression line and int
> 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 bank financing, and, as a result, it is important for financial institutions to be capable of
> A real estate agent specializing in commercial real estate wanted a more precise method of judging the likely selling price (in $1,000s) of apartment buildings. As a first effort, she recorded the price of a number of apartment buildings sold recently an
> Fire damage in the United States amounts to billions of dollars, much of it insured. The time taken to arrive at the fire is critical. This raises the question, Should insurance companies lower premiums if the home to be insured is close to a fire statio
> 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. Each person was asked to report the average number of cigarettes smoked per day and the numbe
> The human resource manager of a telemarketing firm is concerned about the rapid turnover of the firm’s telemarketers. It appears that many telemarketers do not work very long before quitting. There may be a number of reasons, including relatively low pay
> In 2010, the United States conducted a census of the entire country. The census is completed by mail. To help ensure that the questions are understood, a random sample of Americans take the questionnaire before it is sent out. As part of their analysis,
> Florida condominiums are popular winter retreats for many North Americans. In recent years, the prices have steadily increased. A real estate agent wanted to know why prices of similar-sized apartments in the same building vary. A possible answer lies in
> In television’s early years, most commercials were 60 seconds long. Now, however, commercials can be any length. The objective of commercials remains the same—to have as many viewers as possible remember the product in a favorable way and eventually buy
> Golf-equipment manufacturers compete against one another by offering a bewildering array of new products and innovations. Oversized clubs, square grooves, and graphite shafts are examples of such innovations. The effect of these new products on the avera
> To help determine how many beers to stock the concession manager at Yankee Stadium wanted to know how the temperature affected beer sales. Accordingly, she took a sample of 10 games and recorded the number of beers sold and the temperature in the middle
> Critics of television often refer to the detrimental effects that all the violence shown on television has on children. However, there may be another problem. It may be that watching televisionalso reduces the amount of physical exercise, causing weight
> To determine how the number of housing starts is affected by mortgage rates an economist recorded the average mortgage rate and the number of housing starts in a large county for the past 10 years. These data are listed here. a. Determine the regression
> Attempting to analyze the relationship between advertising and sales, the owner of a furniture store recorded the monthly advertising budget ($ thousands) and the sales ($ millions) for a sample of 12 months. The data are listed here. a. Draw a scatter
> Does one’s occupation affect whether the household has been turned down for credit in the previous 5 years (TURNDOWN: 1 = Yes, 2 = No)? Is there enough evidence to conclude that there are differences between the three working categories (OCCAT2: 1 = Mana
> One of the questions asked respondents whether their household had been late with any debt payment in the previous year (LATE: 0 = No, 1 = Yes). Is there enough evidence to conclude that male heads of households are less likely than female heads (HHSEX:
> Do banks and financial institutions turn down female heads (HHSEX: 1 = Male, 2 = Female) of households more frequently than male heads of households’ application for credit (TURNDOWN: 1 = Turned down)? Use an appropriate statistical method to determine w
> Between student loans, credit card balances, vehicle loans, and mortgages almost all household have some debt. Estimate the number of Americans with no household debt (HDEBT: 0).
> One survey question asked in which industry was the head of the household employed in. One of the categories was mining, construction, or manufacturing, all of which may be in decline. Estimate the number of people employed in one of these industries (IN
> Most people who quit smoking cigarettes do so for health reasons. However, some quitters find that they gain weight after quitting, and scientists estimate that the health risks of smoking two packs of cigarettes per day or carrying 65 extra pounds of we
> The nuclear family is defined as a pair of adults and their children. Is this going out of style? Estimate the proportion of nuclear family households (FAMSTRUCT: 4 = Married or living with partner + children).
> Do more educated heads of households have less debt? Conduct a test to determine whether there are differences in household debt (DEBT) between the four categories of education (EDCL 1 = No high school diploma, 2 = High school diploma, 3 = Some college,
> One way to judge how well upperclass households are doing this year as opposed to other years is to determine what their normal income is. Estimate the normal income for upper-class households (NORMINC).
> Who goes deeper into debt (DEBT) among heads of middle-class households, men or women (HHSEX: 1 = Male, 2 = Female)? Conduct a test to determine whether there is enough evidence to conclude that male heads of households go deeper into debt.
> The upper class in the 2010 survey had household net worth between $1,345,975 and $7,402,095. In 2010, the interest paid by money market deposit and money market mutual funds paid very low interest. Estimate the mean invested in these accounts by househo
> Does home ownership (HOUSECL: 1 = Own, 2 = Not) affect how much is spent on food away from home (FOODAWAY)? Perform a statistical analysis to determine whether there is enough evidence to infer that middle-class home owners spend less on food away than d
> Is the number of years of education of individuals affected by the educational attainment of their fathers? To answer this question, is there enough evidence to conclude that years of education (EDUC) is positively related to the years of education of fa
> Is there sufficient evidence to conclude that as income (RINCOME) increases Americans are less likely to believe that government should reduce income inequality (EQWLTH: 1 = Government should reduce differences; 2, 3, 4, 5, 6, 7 = No government action)?
> One of the questions in the survey was “Does the Earth go around the Sun or does the Sun go around the Earth?” (EARTHSUN: 1 = Earth around Sun, 2 = Sun around Earth, 8 = Don’t know, 9 = No answer). Estimate the number of Americans who knew the answer is
> Many aspects of life, including jobs, become routine and perhaps boring. The General Social Survey asked respondents: “In general, do you find life... Is there enough evidence to infer that the majority find life exciting (LIFE: 1 = Exciting)?”
> A fast-food franchiser is considering building a restaurant at a downtown location. Based on a financial analysis, a site is acceptable only if the number of pedestrians passing the location during the work day averages more than 200 per hour. To help de
> Are Americans more educated? Conduct a test to determine whether there is enough evidence to conclude that the average American has completed at least a high school education (12 years of school) (EDUC).
> Do most people love their jobs? The survey asked respondents: “On the whole, how satisfied are you with the work you do?” Estimate the number of American workers who are very satisfied (SATJOB: 1 = Very satisfied).
> Do people have an overconfidence attitude about their financial situation compared to others? Estimate the number of American adults who say that they belong in the upper class (CLASS: 4 = Upper class).
> Do married men and women have different perceptions of their marriage? The survey asked the following question: “Taking all things together, how would you describe your marriage (HAPMAR: 1= Very happy, 2 = Pretty happy, 3 = Not too happy)?” Is there enou
> Do men and women differ in their belief that they pay too much income tax? Conduct a test to determine whether there is enough evidence to conclude that men and women (SEX: 1 = Male, 2 = Female) differ in their responses to the tax question (TAX: = Too h
> Does being unemployed for any period of time affect an individual’s political persuasion? Determine whether there is enough evidence to infer that Americans who have been unemployed in the last 10 years (UNEMP: 1 = Yes, 2 = No) have different party affil
> Is there a relationship between years of education (EDUC) of people and the years of education of their mothers (MAEDUC)? Use a statistical procedure to answer the question.
> The survey asked respondents :If you were to get enough money to live as comfortably as you would like for the rest of your life, would you continue to work or would you stop working?” Can we infer from the data that more than half would continue working
> Can we infer from the data that the majority of Americans support capital punishment for murderers (CAPPUN: 1 = Favor, 2 = Oppose)?
> Since there are no employers that one needs to impress to get a job we would expect self-employed (WRKSLF: 1 = self-employed, 2 = someone else) people to have less formal education than other workers (EDUC). Is there enough statistical evidence to draw t
> Cardizem CD is a prescription drug that is used to treat high blood pressure and angina. One common side effect of such drugs is the occurrence of headaches and dizziness. To determine whether its drug has the same side effects, the drug’s manufacturer,
> Home ownership was always part of the American dream. Estimate the number of Americans who own their own home (DWELOWN: 1 = Own).
> Do liberals like paying tax and conservative hate it? Or they all the same. Use an appropriate statistical technique to determine whether liberals, moderates, and conservatives (POLVIEWS3) differ in their response to the question, “Federal income tax you
> The survey asked the question, “Do you favor requiring a police permit to buy a gun?” Is there enough evidence to infer that liberals, moderates, and conservatives (POLVIEWS3) differ in their responses to the question (GUNLAW: 1 = Support, 2 = Oppose)?
> Does the amount of education one has affect the number of children (CHILDS)? Conduct a test of the five categories of educational attainment (DEGREE: 0 = Left high school, 1 = High school, 2 = Junior college, 3 = Bachelor’s degree, 4 = Graduate) to answe
> The following question was asked. “Is it government’s responsibility to help pay for doctor and hospital bills?” (The responses were HELPSICK: 1 = Government should help; 2, 3, 4, 5 = People should help themselves). Can we infer from the data that the re
> The survey asked this question. A doctor tells a couple that there is one chance in four that their child will have an inherited disease. Does this mean that if the first child has the illness, the next three will not? (ODDS1: 1 = Yes, 2 = No, 8 = Don’t
> Who is most educated among the liberals, moderates, and conservatives) (POLVIEWS3: 1 = Liberal, 2 = Moderate, 3 = Conservative)? Conduct a test to determine whether differences in education (EDUC) exist among the three political philosophies.
> One way of judging the state of the economy is to determine how many hours is the average person working per week. Estimate with 95% confidence the number of hours of work per week for the average person (HRS1).
> Do Americans who want government to improve the standard of living of poor people also want government to help sick people pay doctor and hospital bills? Answer the question by determining whether there is enough evidence to infer that these two variable
> As people age do they believe that government should take no action to reduce income inequality? Conduct a test to determine whether there is enough evidence to infer that older Americans (AGE) are less likely to want government to act (EQWLTH: 1 = Gover
> Many North American cities encourage the use of bicycles as a way to reduce pollution and traffic congestion. So many people now regularly use bicycles to get to work and for exercise that some jurisdictions have enacted bicycle helmet laws that specify
> There are some jobs people have for life (university professor comes immediately to mind). But do most people go from one job to another sometimes experiencing unemployment? The General Social survey may have an answer. It asked respondents have they eve
> Use an inferential technique to determine whether there is enough evidence to infer that women (SEX: 1 = Male, 2 = Female) are more likely to work for the government (WRKGOVT: 1 = Government, 2 = Private enterprise) than men?
> Does political philosophy affect support for capital punishment? Is there enough evidence to conclude that support for capital punishment (CAPPUN: 1 = Favor, 2 = Oppose) differs between the three political points of view (POLVIEWS3: 1 = Liberal, 2 = Mode
> There are many advantages to selfemployment (WRKSLF: 1 = self-employed; 2 = someone else) including the ability to decide how hard and how often to work. Does that mean that self-employed individuals work less than other workers (HRS1)? Conduct a test to
> Are there differences between Democrats, Independents, and Republicans (PARTYID3) in their answers to the following question: “Should government do more or less to solve country’s problems (HELPNOT: 1 = Government should do more; 2, 3, 4, 5 = Government
> Who is more likely to have completed a graduate degree, men or women? Conduct a test to determine whether there is enough evidence to infer that men and women (SEX: 1 = Male, 2 = Female) differ in their completion of graduate degrees (DEGREE: 4 = Graduat
> Do conservatives oppose gun control while liberals support it? Conduct a test to determine whether there is sufficient evidence to conclude that the three political parties (PARTYID3: 1 = Democrat, 2 = Independent, 3 = Republican) differ in their support
> Is it true that as we age we become more conservative? If this is true we would expect that conservatives would be older than liberals and independents. Analyze the data to determine whether there is enough evidence to conclude that differences in age (A
> Are American women more liberal than American men? If so we should see evidence from the General Social Survey. Is there enough evidence to conclude that there are differences in political philosophies (POLVIEWS3: 1 = Liberal, 2 = Moderate, 3 = Conservat
> The survey asked the following question: “I’m going to show you a seven-point scale on which political views that people might hold arranged from extremely liberal to extremely conservative. Where would you place yourself on this scale?” Estimate the num
> The proliferation of self-serve pumps at gas stations has generally resulted in poorer automobile maintenance. One feature of poor maintenance is low tire pressure, which results in shorter tire life and higher gasoline consumption. To examine this probl
> The survey asked the following question: “Is it government’s responsibility to help pay for doctor and hospital bills?” The responses were HELPSICK: 1 = Government should help; 2, 3, 4, 5 = People should help themselves). Is there enough statistical evid
