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Statistics 13th Global Edition James T. McClave And Terry T Sincich - Solutions

Entry-level job preferences. Benefits Quarterly periodical publishes a study of entry-level job preferences.A number of independent variables are used to model the job preferences (measured on a 10-point scale) of business school graduates. Suppose stepwise regression is used to build a model for
RNA analysis of wheat genes. Engineers from the Department of Crop and Soil Sciences at Washington State University used regression to estimate the number of copies of a gene transcript in an aliquot of ribonucleic acid (RNA) extracted from a wheat plant (Electronic Journal of Biotechnology, Apr.
Sale prices of apartments. A Minneapolis, Minnesota, real-estate appraiser used regression analysis to explore the relationship between the sale prices of apartment buildings sold in Minneapolis and various character istics of the properties. Twenty-five apartment buildings were randomly sampled
Habitats of grizzly bears. Do grizzly bears segregate on the basis of sex? One hypothesis is that female grizzlies avoid male-occupied habitats because of competition for food and cannibalism. A competing theory is that females do not avoid males, but simply have different habitats available to
Revenues of popular movies. The Internet Movie Database(www.imdb.com) monitors the gross revenues of all major motion pictures. The table on p. 791 gives both the domestic (United States and Canada) and international gross revenues for a sample of 22 popular movies.a. Write a first-order model for
“Sun safety” study. Excessive exposure to solar radiation is known to increase the risk of developing skin cancer, yet many people do not practice “sun safety.” A group of University of Arizona researchers examined the feasibility of educating preschool (four- to five-year-old)children
Rating funny cartoons. Newspaper cartoons, although designed to be funny, often invoke hostility, pain, or aggression in readers, especially when those cartoons Repellent Type Cost/Use ($)Maximum Protection (hours)1 Aerosol 0.61 6.5 2 Aerosol 0.72 3.5 3 Aerosol 0.69 6.0 4 Aerosol 0.74 7.0 5 Aerosol
Comparing mosquito repellents. Which insect repellents protect best against mosquitoes? Periodically, consumer groups conduct tests to compare insect repellents(e.g., Consumer Reports, June 2000). Consider a similar study of 14 popular mosquito repellents. Each product was classified as either an
Optimizing semiconductor material processing. Fluorocarbon plasmas are used in the production of semiconductor materials. In the Journal of Applied Physics(Dec. 1, 2000), electrical engineers at Nagoya University(Japan) studied the kinetics of fluorocarbon plasmas in order to optimize material
Snow geese feeding trial. Refer to the Journal of Applied Ecology (Vol. 32, 1995) study of the feeding habits of baby snow geese, presented in Exercise 11.150 (p. 676).Data on gosling weight change, digestion efficiency, acid-detergent fiber (all measured as percentages), and diet(plants or duck
Deferred tax allowance study. A study was conducted to identify accounting choice variables that influence a manager’s decision to change the level of the deferred tax asset allowance at a firm (The Engineering Economist, Jan./Feb. 2004). Data were collected on a sample of 329 firms that reported
Growth of Japanese beetles. In the Journal of Insect Behavior (Nov. 2001), biologists at Eastern Illinois University published the results of their study on Japanese beetles. The biologists collected beetles over a period of n = 13 summer days in a soybean field. For one portion of the study, the
Improving SAT scores. Refer to the Chance (Winter 2001) study of students who paid a private tutor (or coach) to help them improve their SAT scores, presented in Exercise 2.197 (p. 136). Multiple regression was used to estimate the effect of coaching on SAT-Mathematics scores. Data on 3,492
Violent behavior in children. Refer to the Development Psychology (Mar. 2003) study of the behavior of elementary school children, presented in Exercise 8.149 (p. 454).The researchers used a quadratic equation to model the level (y) of aggressive fantasies experienced by a child as a function of
Defects in nuclear missile housing parts. The technique of multivariable testing was discussed in The Journal of the Reliability Analysis Center (First Quarter, 2004).Multivariable testing was shown to improve the quality of carbon-foam rings used in nuclear missile housings.The rings are produced
Listen-and-look study. Where do you look when you are listening to someone speak? Researchers have discovered that listeners tend to gaze at the eyes or mouth of the speaker. In a study published in Perception &Psychophysics (Aug. 1998), subjects watched a videotape of a speaker giving a series of
Distress in EMS workers. The Journal of Consulting and Clinical Psychology (June 1995) reported on a study of emergency service (EMS) rescue workers who responded to the I-880 freeway collapse during a San Francisco earthquake. The goal of the study was to identify the predictors of symptomatic
Students’ ability in science. An article published in the American Educational Research Journal (Fall 1998) used multiple regression to model the students’ perceptions of their ability in science classes. The sample consisted of 165 Grade 5–8 students. The dependent variable of interest, the
Global warming and foreign investments. Scientists believe that a major cause of global warming is higher levels of carbon dioxide 1CO22 in the atmosphere.In the Journal of World-Systems Research (Summer 2003), sociologists examined the impact of a dependence on foreign investment on CO2 emissions
Suppose you fit the regression model E1y2 = b0 + b1 x1 + b2 x2 + b3 x2 2 + b4 x1 x2 + b5 x1 x2 2 to n = 30 data points and wish to test the null hypothesis H0: b4 = b5 = 0.a. State the alternative hypothesis.b. Explain in detail how to compute the F-statistic needed to test the null hypothesis.c.
To model the relationship between y (a dependent variable)and x (an independent variable), a researcher has taken one measurement of y at each of three different x values. Drawing on his mathematical expertise, the researcher realizes that he can fit the second-order model E1y2 = b0 + b1 x + b2 x2
Suppose you have developed a regression model to explain the relationship between y and x1, x2, and x3. The ranges of the variables you observed were as follows: 50 … y … 100, 10 … x1 … 75, .25 … x2 … .75, and 2,000 … x3 … 2,500. Will the error of prediction be smaller when you use
Suppose you fit the model y = b0 + b1 x1 + b2 x21+ b3 x2 + b4 x1 x2 + e to n = 25 data points and find that b n 0 = 1.24 b n 1 = -2.43 b n 2 = .03 b n 3 = .65 b n 4 = 1.75 sbn 1= 1.15, sbn 2= .18, sbn 3= .30, sbn 4= 1.49 SSE = .47, R2= .85a. Is there sufficient evidence to conclude that at least
Bubble behavior in subcooled flow boiling. Refer to the Heat Transfer Engineering (Vol. 34, 2013) study of bubble behavior in subcooled flow boiling, Exercise 12.59(p. 716). You fit an interaction model for bubble density(y) as a function of x1 = mass flux and x2 = heat flux.Conduct a complete
Emotional intelligence and team performance. Refer to the Engineering Project Organizational Journal (Vol. 3, 2013)study of the relationship between emotional intelligence of individual team members and their performance during an engineering project, Exercise 12.39 (p. 708). Using data on n = 23
Cooling method for gas turbines. Refer to the Journal of Engineering for Gas Turbines and Power (Jan. 2005) study of a high-pressure inlet fogging method for a gas turbine engine, presented in Exercise 12.27 (p. 701). Now consider the interaction model E1y2 = b0 + b1 x1 + b2 x2 + b3 x1 x2 for heat
Reality TV and cosmetic surgery. Refer to the Body Image: An International Journal of Research (Mar.2010) study of the influence of reality TV shows on one’s desire to undergo cosmetic surgery, Exercise 12.25 (p. 700). In Exercise 12.25, you fit the first-order model, E1y2 = b0 + b1x1 + b2x2 +
A rubber additive made from cashew nut shells. Refer to the Industrial & Engineering Chemistry Research(May 2013) study of the use of cardanol as an additive for natural rubber, Exercise 12.24 (p. 700). You analyzed a first-order model for y = grafting efficiency as a function of x1 = initiator
Arsenic in groundwater. Refer to the Environmental Science& Technology (Jan. 2005) study of the reliability of a commercial kit to test for arsenic in groundwater, Exercise 12.23(p. 700). Recall that you fit a first-order model for arsenic level (y) as a function of latitude (x1), longitude (x2),
Failure times of silicon wafer microchips. Refer to the National Semiconductor study of manufactured silicon wafer integrated circuit chips, Exercise 12.78 (p. 725). Recall that the failure times of the microchips (in hours) were determined at different solder temperatures (degrees Celsius).The
Accuracy of software effort estimates. Refer to the Journal of Empirical Software Engineering (Vol. 9, 2004)study of the accuracy of new software effort estimates, Exercise 12.140 (p. 758). Recall that stepwise regression was used to develop a model for the relative error in estimating effort (y)
Yield strength of steel alloy. Refer to Exercise 12.142(p. 759) and the Modelling and Simulation in Materials Science and Engineering (Vol. 13, 2005) study in which engineers built a regression model for the tensile yield strength (y) of a new steel alloy. The engineers discovered that the
Personality and aggressive behavior. Psychological Bulletin (Vol. 132, 2006) reported on a study linking personality and aggressive behavior. Four of the variables measured in the study were aggressive behavior, irritability, trait anger, and narcissism. Pairwise correlations for these four
Personality traits and job performance. Refer to the Journal of Applied Psychology (Jan. 2011) study of the determinants of task performance, Exercise 12.111(p. 742). In addition to x1 = conscientiousness score and x2 = 51 if highly complex job, 0 if not6, the researchers also used x3 = emotional
Dating and disclosure. Refer to the Journal of Adolescence (Apr. 2010) study of adolescents’ disclosure of their dating and romantic relationships, Exercise 12.16(p. 698). Recall that multiple regression was used to model y = level of an adolescent’s disclosure of a date’s identity to his/her
Identify the problem(s) in each of the residual plots shown on page 752.
Consider fitting the multiple regression model E1y2 = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x4 + b5 x5 A matrix of correlations for all pairs of independent variables is given on the right. Do you detect a multicollinearity problem? Explain.x1 x2 x3 x4 x5 x1 — .94 .87 -.24 .01 x2 — -.04 .22 .46 x3
True or False. Regression models fit to time-series data typically result in uncorrelated errors.
The Federal Trade Commission (FTC) annually ranks varieties of domestic cigarettes according to their tar, nicotine, and carbon monoxide content. The U.S.surgeon general considers each of these three substances hazardous to a smoker’s health.Past studies have shown that increases in the tar and
Refer to Example 12.16. Analyze the distribution of the residuals in the grandfather clock example, both before and after the outlier residual is removed.Determine whether the assumption of a normally distributed error term is reasonable.
Refer to Example 12.6 (p. 710), in which we modeled the auction price y of a grandfather clock as a function of age x1 and number of bidders, x2. The data for this example are repeated in Table 12.9, with one important difference: The auction price of the clock at the top of the sixth column has
The data in Table 12.8 are the salaries, y, and years of experience, x, for a sample of 50 social workers. The first-order model E1y2 = b0 + b1 x was fitted to the data using by SPSS. The SPSS printout is shown in Figure 12.37, followed by a plot of the residuals versus yn in Figure 12.38.
Refer to the problem of modeling the relationship between home size (x) and electrical usage (y) in Example 12.7 (p. 717). The data for n = 15 homes are repeated in Table 12.7. MINITAB printouts for a straight-line model and a quadratic model fitted to the data are shown in Figures 12.34a and
Using corn in a duck diet. Corn is high in starch content;consequently, it is considered excellent feed for domestic chickens. Does corn possess the same potential in feeding ducks bred for broiling? This was the subject of research published in Animal Feed Science and Technology (Apr. 2010). The
Bus rapid-transit study. The Center for Urban Transportation Research (CUTR) at the University of South Florida conducted a survey of Bus rapid transit(BRT) customers in Miami (Transportation Research Board Annual Meeting, Jan. 2003). Data on the following variables (all measured on a five-point
Yield strength of steel alloy. Industrial engineers at the University of Florida used regression modeling as a tool to reduce the time and cost associated with developing new metallic alloys (Modelling and Simulation in Materials Science and Engineering, Vol. 13, 2005). To illustrate, the engineers
An analysis of footprints in sand. Fossilized human footprints provide a direct source of information on the gait dynamics of extinct species. To gain insight into this phenomenon, a group of scientists used human subjects (16 young adults) to generate footprints in sand (American Journal of
Accuracy of software effort estimates. Periodically, software engineers must provide estimates of their effort in developing new software. In the Journal of Empirical Software Engineering (Vol. 9, 2004), multiple regression was used to predict the accuracy of these effort estimates.The dependent
Study of sex offenders. A study of sex offenders in the Canadian Federal Prison System was published in the British Journal of Criminology (May 2014). The following data were collected for each of 59 male sex offenders: race, type of crime (violent or nonviolent), age at first conviction, and total
Distribution of yellowhammer birds. An article in the Journal of Animal Ecology (July 2006) discussed some of the caveats of using stepwise regression. An example presented used stepwise regression to find the best predictors of the number of yellowhammers inhabiting lowland farms in the United
Suppose there are six independent variables x1, x2, x3, x4, x5, and x6 that might be useful in predicting a response y.A total of n = 50 observations is available, and it is decided to employ stepwise regression to help in selecting the independent variables that appear to be useful. The computer
Explain the difference between a stepwise model and a standard regression model.
An international management consulting company develops multiple-regression models for executive salaries of its client firms. The consulting company has found that models that use the natural logarithm of salary as the dependent variable have better predictive power than those using salary as the
Emotional distress in firefighters. The Journal of Human Stress (Summer 1987) reported on a study of the “psychological response of firefighters to chemical fire.” It is thought that the complete second-order model E1y2 = b0 + b1 x1 + b2 x21+ b3 x2 + b4 x1 x2 + b5 x21 x2 where y = Emotional
Predicting thrust force of a metal drill. In Frontiers in Automobile and Mechanical Engineering (Nov. 2010), a model was developed to predict the thrust force when drilling into a hybrid metal composite. Three variables related to thrust force are spindle speed (revolutions per minute), feed rate
Agreeableness, gender, and wages. Refer to the Journal of Personality and Social Psychology (Feb. 2012) study of on-the-job agreeableness and wages, Exercise 12.112(p. 742). The researchers modeled mean income, E(y), as a function of both agreeableness score (x1) and a dummy variable for gender (x2
Whales entangled in fishing gear. Refer to the Marine Mammal Science (Apr. 2010) study of whales entangled in fishing gear, Exercise 12.109 (p. 741). A first-order model for the length (y) of an entangled whale that is a function of water depth of the entanglement (x1) and gear type (set nets,
Glass as a waste encapsulant. The encapsulation of waste in glass is considered to be a promising solution to the problem of low-level nuclear waste. A study was undertaken jointly by the Department of Materials Science and Engineering at the University of Florida and the U.S. Department of Energy
Personality traits and job performance. Refer to the Journal of Applied Psychology (Jan. 2011) study of the relationship between task performance and conscientiousness, Exercise 12.111 (p. 742). Recall that y = task performance score (measured on a 30-point scale) was modeled as a function of x1 =
Reality TV and cosmetic surgery. Refer to the Body Image:An International Journal of Research (Mar. 2010) study of the influence of reality TV shows on one’s desire to undergo cosmetic surgery, Exercise 12.25 (p. 700). Recall that psychologists modeled desire to have cosmetic surgery (y) as a
Study of supervisor-targeted aggression. “Moonlighters”are workers who hold two jobs at the same time. What are the factors that affect the likelihood of a moonlighting worker becoming aggressive toward his or her supervisor?This was the research question of interest in the Journal of Applied
Workplace bullying and intention to leave. Refer to the Human Resource Management Journal (Oct. 2008) study of workplace bullying, Exercise 12.113 (p. 743). Recall that multiple regression was used to model an employee’s intention to leave (y) as a function of bullying (x1, measured on a
Mental health of a community. An article in the Community Mental Health Journal (Aug. 2000) used multiple-regression analysis to model the level of community adjustment of clients of the Department of Mental Health and Addiction Services in Connecticut.The dependent variable, community adjustment
Shared leadership in airplane crews. Refer to the Human Factors (Mar. 2014) study of shared leadership by the cockpit and cabin crews of a commercial airplane, Exercise 9.13 (p. 476). Recall that simulated flights were taken by 84 six-person crews, where each crew consisted of a two-person cockpit
Willingness to donate organs. How willing are you to donate your organs upon death? This was the question of interest in research published in Death Studies(Vol. 38, 2014). A sample of n = 307 Australians participated in the study. Willingness to donate organs upon death was measured for each
The complete model y = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x4 + e was fit to n = 22 data points, with SSE = 146.99. The reduced model y = b0 + b1 x1 + b2 x2 + e was also fit, with SSE = 165.37.a. How many b parameters are in the complete model?The reduced model?b. Specify the null and alternative
Suppose you fit the regression model y = b0 + b1 x1 + b2 x2 + b3 x1 x2 + b4 x21+ b5 x22+ e to n = 30 data points and you wish to test H0: b3 = b4 = b5 = 0a. State the alternative hypothesis Ha.b. Give the reduced model appropriate for conducting the test.c. What are the numerator and denominator
Explain why the F-test used to compare complete and reduced models is a one-tailed, upper-tailed test.
Determine which pairs of models that follow are nested models. For each pair of nested models, identify the complete and reduced model.a. E1y2 = b0 + b1 x1 + b2 x2b. E1y2 = b0 + b1 x1c. E1y2 = b0 + b1 x1 + b2 x21d. E1y2 = b0 + b1 x1 + b2 x2 + b3 x1 x2e. E1y2 = b0 + b1 x1 + b2 x2 + b3 x1 x2 + b4
A botanist conducted an experiment to study the growth of carnations as a function of the temperature x1 1°F2 in a greenhouse and the amount of fertilizer x2 [kilograms (kg)per plot] applied to the soil. Twenty-seven plots of equal size were treated with fertilizer in amounts varying between 50
Iron supplement for anemia. Many women suffer from anemia. A female physician who is also an avid jogger wanted to know if women who exercise regularly have a different mean red blood cell count than women who do not. She also wanted to know if the amount of a particular iron supplement a woman
Chemical composition of rainwater. Refer to the Journal of Agricultural, Biological, and Environmental Statistics(Mar. 2005) study of the chemical composition of rainwater, presented in Exercise 12.90 (p. 732). Recall that the nitrate concentration y (milligrams per liter) in a sample of rainwater
Lead levels in mountain moss. A study of the atmospheric pollution on the slopes of the Blue Ridge Mountains (in Tennessee) was conducted. The file MOSS contains the levels of lead found in 70 fern moss specimens (in micrograms of lead per gram of moss tissue) collected from the mountain slopes, as
Workplace bullying and intention to leave. Workplace bullying is defined as harassment, persistent criticism, withholding of key information, spreading of rumors, or intimidation on the job. In Human Resource Management Journal (Oct. 2008), researchers employed multiple regression to examine
Agreeableness, gender, and wages. Do agreeable individuals get paid less, on average, than those who are less agreeable on the job? And is this gap greater for males than for females? These questions were addressed in the Journal of Personality and Social Psychology (Feb.2012). Several variables
Personality traits and job performance. Refer to the Journal of Applied Psychology (Jan. 2011) study of the relationship between task performance and conscientiousness, Exercise 12.67 (p. 722). Recall that the researchers used a quadratic model to relate y = task performance score(measured on a
Winning marathon times. Refer to the Chance (Winter 2000) study of men’s and women’s winning times in the Boston Marathon, presented in Exercise 11.146 (p. 675).Suppose the researchers want to build a model for predicting winning time (y) of the marathon as a function of year 1x12 in which race
Whales entangled in fishing gear. Refer to the Marine Mammal Science (Apr. 2010) study of whales entangled in fishing gear, Exercise 12.87, (p. 731). Now consider a model for the length (y) of an entangled whale (in meters) that is a function of water depth of the entanglement (in meters)and gear
Impact of race on football card values. Refer to the Electronic Journal of Sociology (2007) study of the impact of race on the value of professional football players’“rookie” cards, presented in Exercise 12.89 (p. 732).Recall that the sample consisted of 148 rookie cards of National Football
Do blondes raise more funds? Refer to the Economic Letters (Vol. 100, 2008) study of whether the color of a female solicitor’s hair affects the level of capital raised, Exercise 12.88 (p. 731). Recall that 955 households were contacted by a female solicitor to raise funds for hazard mitigation
Consider the model y = b0 + b1 x1 + b2 x1 2 + b3 x2 + b4 x3 + b5 x1 x2+ b6 x1 x3 + b7 x1 2 x2 + b8 x1 2 x3 + e where x1 is a quantitative variable and x2 = e 1 if level 2 0 otherwise x3 = e 1 if level 3 0 otherwise The resulting least squares prediction equation is yn = 45.6 - 4.7x1 + .07x1 2 -
Consider the model y = b0 + b1 x1 + b2 x2 + b3 x3 + e where x1 is a quantitative variable and x2 and x3 are dummy variables describing a qualitative variable at three levels, using the coding scheme x2 = e 1 if level 2 0 otherwise x3 = e 1 if level 3 0 otherwise The resulting least squares
Refer to Exercise 12.100.a. Write a complete second-order model that relates E(y) to the quantitative variable.b. Add the main-effect terms for the qualitative variable(at three levels) to the model of part a.c. Add terms to the model of part b to allow for interaction between the quantitative and
An industrial psychologist conducted an experiment to investigate the relationship between worker productivity and a measure of salary incentive for two manufacturing plants; one plant operates under “disciplined management practices” and the other plant uses a traditional management style. The
Refer to the mean monthly sales models. Substitute the appropriate values of the dummy variables in Model 3 above to obtain the equations of the three response lines in Figure 12.23.
Community responses to a violent crime. How communities respond to a disaster or a violent crime was the subject of research published in the American Journal of Community Psychology (Vol. 44, 2009). Psychologists at the University of California tracked monthly violent crime incidents in two Texas
Extinct New Zealand birds. Refer to the Evolutionary Ecology Research (July 2003) study of the patterns of extinction in the New Zealand bird population, presented in Exercise 2.24 (p. 70). Recall that the NZBIRDS file contains qualitative data on flight capability (volant or flightless),
Homework assistance for college students. Do college professors who provide their students with assistance on homework help improve student grades? This was the research question of interest in the Journal of Accounting Education (Vol. 25, 2007). A sample of 175 accounting students took a pretest
Expert testimony in homicide trials of battered women.An article published in the Duke Journal of Gender Law &Policy (Summer 2003) examined the impact of expert testimony on the outcome of homicide trials that involve battered woman syndrome. On the basis of data collected on individual juror votes
Study of recall of TV commercials. Refer to the Journal of Applied Psychology (June 2002) study of recall of television commercials, presented in Exercise 10.37 (p. 553).Participants were assigned to watch one of three types of TV programs, with nine commercials embedded in each show.Group V
Major depression and personality disorders. A team of physicians, psychiatrists, and psychologists investigated whether depressed patients exhibit more or fewer personality disorder symptoms than nondepressed patients in the American Journal of Psychiatry (May 2010). A study group of over 400
Ascorbic acid reduces goat stress. Refer to the Animal Science Journal (May 2014) study on the use of ascorbic acid (AA) to reduce the stress in goats during transportation, Exercise 10.7 (p. 537). Recall that 24 healthy goats were randomly divided into four groups (A, B, C, and D)of six animals
Detecting quantitative traits in genes. In gene therapy, it is important to know the location of a gene for a disease on the genome (genetic map). Although many genes yield a specific trait (e.g., disease or not), others cannot be categorized, since they are quantitative in nature (e.g., extent of
Chemical composition of rainwater. Researchers at the University of Aberdeen (Scotland) developed a statistical model for estimating the chemical composition of water(Journal of Agricultural, Biological, and Environmental Statistics, Mar. 2005). For one application, the nitrate concentration y
Impact of race on football card values. University of Colorado sociologists investigated the impact of race on the value of professional football players’ “rookie” cards(Electronic Journal of Sociology, 2007). The sample consisted of 148 rookie cards of National Football League(NFL) players
Do blondes raise more funds? During fundraising, does the physical appearance of the solicitor affect the level of capital raised? An economist at the University of Nevada–Reno designed an experiment to answer this question and published the results in Economic Letters (Vol. 100, 2008).Each in a
Whales entangled in fishing gear. Refer to the Marine Mammal Science (Apr. 2010) study of whales entangled in fishing gear, Exercise 12.17 (p. 698). These entanglements involved one of three types of fishing gear: set nets, pots, and gill nets. Consequently, the researchers used gear type as a
Production technologies, terroir, and quality of Bordeaux wine. The production of quality wine is strongly influenced by the natural endowments of the grape-growing region—called the “terroir.” The Economic Journal (May 2008)published an empirical study of the factors that yield a quality
Modeling number of children. As part of a study on how children affect parents’ depression in old age, researchers fit a model for total number of children in a family (Social Science & Medicine, Jan. 2014). One of the key independent variables used in the model is whether the first birth was a
The model E1y2 = b0 + b1 x1 + b2 x2 + b3 x3, where x1 = e 1 if level 2 0 if not x2 = e 1 if level 3 0 if not x3 = e 1 if level 4 0 if not was used to relate E(y) to a single qualitative variable with four levels. This model was fit to n = 45 data points, and the result was and the following result

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