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Statistics 12th Edition James T. McClave, Terry T Sincich - Solutions

Calculate r2 for the least squares line in Exercise 11.14.In Exercise 11.14The accompanying table is similar to Table 11.3. It is used to make the preliminary computations for finding the least squares line for the given pairs of x and y values.
A popular Web site among college students is RateMyProfessors.com (RMP). Established over 10 years ago, RMP allows students to post quantitative ratings of their instructors. In Practical Assessment, Research & Evaluation (May 2007), University of Maine researchers investigated whether instructor
Refer to the Bulletin of Marine Science (April 2010) study of teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico, Exercise. Recall that simple linear regression was used to model y = total catch of lobsters (in kilograms) during the season as a function of x =
Wind turbine blade stress. Refer to the Wind Engineering (Jan. 2004) study of two types of timber-radiata pine and hoop pine-used in high-efficiency small wind turbine blades, presented in Exercise. Data on stress (y) and the natural logarithm of the number of blade cycles (x) for each type of
Refer to the Journal of Astrophysics & Astronomy (Mar./Jun. 2003) study of red shifts in quasi-stellar objects presented in Exercise. Recall that simple linear regression was used to model the magnitude (y) of a quasi-stellar object as a function of the redshift level (x). In addition to the least
Are short people shortchanged when it comes to salary? According to business professors T. A. Judge (University of Florida) and D. M. Cable (University of North Carolina), tall people tend to earn more money over their career than short people earn (Journal of Applied Psychology, June 2004). Using
Botanists at the University of Toronto conducted a series of experiments to investigate the feeding habits of baby snow geese (Journal of Applied Ecology, Vol. 32, 1995). Goslings were deprived of food until their guts were empty and then were allowed to feed for 6 hours on a diet of plants or
Refer to the Journal of Experimental Psychology-Applied (June 2000) name-retrieval study. The data for the study are saved in the NAMEGAME2 file. Find and interpret the values of r and r2 for the simple linear regression relating the proportion of names recalled (y) and the position (order) of the
A study published in Psychosomatic Medicine (Mar./Apr. 2001) explored the relationship between reported severity of pain and actual pain tolerance in 337 patients who suffer from chronic pain. Each patient reported his or her severity of chronic pain on a seven-point scale 11 = no pain, 7 = extreme
For a given x, a confidence interval for E (y) will always be wider than a prediction interval for y.
For each of the following, decide whether the proper inference is a prediction interval for y or a confidence interval for E (y): a. A jeweler wants to predict the selling price of a diamond stone on the basis of its size (number of carats). b. A psychologist wants to estimate the average IQ of all
Consider the following pairs of measurements saved in the LM11_94 file.a. Construct a scatterplot of these data.b. Find the least squares line, and plot it on your scatter plot.c. Find s2.d. Find a 90% confidence interval for the mean value of y when x = 4. Plot the upper and lower bounds of the
a. Using no information about x, estimate and calculate a 95% confidence interval for the mean value of y.b. Plot the estimated mean value and the confidence interval as horizontal lines on your scatterplot.c. Compare the confidence intervals you calculated in parts c and d of Exercise with the one
Refer to the Bilingual Research Journal (Summer 2006) study of the relationship of Spanish (first-language) grammatical knowledge to English (second-language) reading, presented in Exercise. Recall that three simple linear regressions were used to model the English reading (ESLR) score (y) as a
Refer to The Sport Journal (Winter 2007) study of a new method for ranking the total driving performance of golfers on the Professional Golf Association (PGA) tour, presented in Exercise. You fit a straight-line model relating diving accuracy (y) to driving distance (x) to the data saved in the
Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise. The frequencies of sound waves resulting from the first 24 resonances (echoes) after striking a basketball with a metal rod are saved in the BBALL file. You fit a straight-line model relating
Refer to the Journal of Experimental Psychology-Applied (June 2000) name-retrieval study, presented in Exercise. The data for the study are saved in the NAMEGAME2 file.a. Find a 99% confidence interval for the mean recall proportion for students in the fifth position during the "name game."
Refer to the Journal of Applied Ecology feeding study of the relationship between the weight change y of baby snow geese and their digestion efficiency x, presented in Exercise. The data for the study are saved in the SNOWGEESE file.In Exercise 11.84a. Fit the simple linear regression model to the
The importance of having employees with a healthy work-life balance has been recognized by U.S. companies for decades. Many business schools offer courses that assist MBA students with developing good work-life balance habits and most large companies have developed work-life balance programs for
Explain the difference between a probabilistic model and a deterministic model.
Outline the five steps in a simple linear regression analysis.
In fitting a least squares line to n = 15 data points, the following quantities were computed: SSxx = 55, SSyy = 198, SSxy = -88, x̄ = 1.3, and y-bar = 35.a. Find the least squares line.b. Graph the least squares line.c. Calculate SSE.d. Calculate s2.e. Find a 90% confidence interval for β1.
Consider the following 10 data points saved in the LM11_116 file.a. Plot the data on a scatterplot. b. Calculate the values of r and r2. c. Is there sufficient evidence to indicate that x and y are linearly correlated? Test at the Î± = .10 level of significance.
Real-estate investors, home buyers, and homeowners often use the appraised value of property as a basis for predicting the sale of that property. Data on sale prices and total appraised value of 78 residential properties sold recently in an upscale Tampa, Florida, neighborhood named
College protests of labor exploitation. Refer to the Journal of World-Systems Research (Winter 2004) study of student "sit-ins" for a "sweat-free campus" at universities, presented in Exercise. Recall that the SITIN file contains data on the duration (in days) of each sit-in, as well as the number
Refer to the Bilingual Research Journal (Summer 2006) study of the relationship of Spanish (first-language) grammatical knowledge to English (second-language) reading, presented in Exercise. Recall that each in a sample of n = 55 native Spanish-speaking adults took four standardized exams: Spanish
Accurate measurements of rainfall are critical for many hydrological and meteorological projects. Two standard methods of monitoring rainfall use rain gauges and weather radar.Both, however, can be contaminated by human and environmental interference. In the Journal of Data Science (Apr. 2004),
Chemists at Kyushu University (Japan) examined the linear relationship between the maximum absorption rate y (in nanomoles) and the Hammett substituent constant x for metacyclophane compounds (Journal of Organic Chemistry, July 1995). The data for variants of two compounds are given in the
In Chance (Winter 2000), statistician Howard Wainer and two students compared men's and women's winning times in the Boston Marathon. One of the graphs used to illustrate gender differences is reproduced below. The scatterplot graphs the winning times (in minutes) against the year in which the race
In cotherapy, two or more therapists lead a group. An article in the American Journal of Dance Therapy (Spring/Summer 1995) examined the use of cotherapy in dance/movement therapy. Two of several variables measured on each of a sample of 136 professional dance/movement therapists were years x of
The Sasakawa Sports Foundation conducted a national survey to assess the physical activity patterns of Japanese adults. The next table lists the frequency (average number of days in the past year) and the amount of time (average number of minutes per single activity) Japanese adults spent
The long jump is a track-and-field event in which a competitor attempts to jump a maximum distance into a sandpit after a running start. At the edge of the pit is a takeoff board. Jumpers usually try to plant their toes at the front edge of this board to maximize their jumping distance. The
A recent civil suit revolved around a five-building brick apartment complex located in the Bronx, New York, which began to suffer spalling damage (i.e., a separation of some portion of the face of a brick from its body). The owner of the complex alleged that the bricks were manufactured
List the four assumptions about the random error e required for a multiple-regression analysis.
What are the caveats to conducting t-tests on all of the individual b parameters in a multiple-regression model?
MINITAB was used to fit the model y = Î²0 + Î²1 x1 + Î²2 x2 + Îµ to n = 20 data points, and the printout (top of page 628) was obtained.a. What are the sample estimates of Î²0, Î²1, and Î²2?b. What is the least squares prediction equation?c. Find SSE, MSE, and s. Interpret the
Suppose you fit the first-order multiple-regression modely = β0 + β1x1 + β2x2 + εto n = 25 data points and obtain the prediction equationy = 6.4 + 3.1x1 + .92x2The estimated standard deviations of the sampling distributions of β1 and β2 are 2.3 and .27, respectively.a. Test H0: β1 = 0
Consider the following first-order model equation in three quantitative independent variables: E(y) = 1 + 2x1 + x2 - 3x3 a. Graph the relationship between y and x1 for x2 = 1 and x3 = 3. b. Repeat part a for x2 = – 1 and x3 = 1. c. How do the graphed lines in parts a and b relate to each other?
If the analysis-of-variance F-test leads to the conclusion that at least one of the model parameters is nonzero, can you conclude that the model is the best predictor for the dependent variable y? Can you conclude that all of the terms in the model are important in predicting y? What is the
Refer to the Journal of Adolescence (April 2010) study of adolescents’ disclosure of their dating and romantic relationships, Exercise. Data collected for a sample of 222 high school students were used to determine the level of disclosure of the date’s identity to an adolescent’s mother
Can the population of an urban area be estimated without taking a census? In Geographical Analysis (Jan. 2007) geography professors at the University of Wisconsin at Milwaukee and Ohio State University demonstrated the use of satellite image maps in estimating urban population. A portion of
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
Many tourists choose a vacation destination on the basis of the newness or uniqueness (i.e., the novelty) of the itinerary. Texas A&M University professor J. Petrick investigated the relationship between novelty and vacationing golfers€™ demographics (Annals of Tourism Research, April
Refer to the U.S. Army Corps of Engineers data on fish contaminated from the toxic discharges of a chemical plant located on the banks of the Tennessee River in Alabama, shown below. Recall that the engineers measured the length (in centimeters), weight (in grams), and DDT level (in parts per
A quasar is a distant celestial object (at least 4 billion light-years away) that provides a powerful source of radio energy. The Astronomical Journal (July 1995) reported on a study of 90 quasars detected by a deep-space survey. The survey enabled astronomers to measure several different
Because the coefficient of determination, R2, always increases when a new independent variable is added to a model, it is tempting to include many variables in the model in order to force R2 to be near 1. However, doing so reduces the number of degrees of freedom available for estimating σ2, which
The vineyards in the Bordeaux region of France are known for producing excellent red wines. However, the uncertainty of the weather during the growing season, the phenomenon that wine tastes better with age, and the fact that some Bordeaux vineyards produce better wines than others encourage
Which interval will be narrower, a 95% confidence interval for E (y) or a 95% prediction interval for y? (Assume that the values of the x’s are the same for both intervals.)
Predicting runs scored in baseball. Refer to the Chance (Fall 2000) study of runs scored in Major League Baseball games, Exercise. Multiple regression was used to model total number of runs scored (y) of a team during the season as a function of number of walks (x1), number of singles (x2), number
Refer to The Astronomical Journal study of quasars, presented in Exercise. Recall that a first-order model was used to relate a quasar€™s equivalent width (y) to its redshift (x1), line flux (x2), line luminosity (x3), and AB1450 (x4). A portion of the SPSS spreadsheet showing 95%
An article published in Geography (July 1980) used multiple regression to predict annual rainfall levels in California. Data on the average annual precipitation (y), altitude (x1), latitude (x2), and distance from the Pacific coast (x3) for 30 meteorological stations scattered throughout California
In a production facility, an accurate estimate of hours needed to complete a task is crucial to management in making such decisions as hiring the proper number of workers, quoting an accurate deadline for a client, or performing cost analyses regarding budgets. A manufacturer of boiler drums wants
If two variables x1 and x2 do not interact, how would you describe their effect on the mean response E (y)?
Suppose the true relationship between E (y) and the quantitative independent variables x1 and x2 is E(y) = 3 + x1 + 2x2 - x1 x2 a. Describe the corresponding three-dimensional response surface. b. Plot the linear relationship between y and x2 for x2 = 0, 1, 2, where 0 ≤ x2 ≤ 5. c. Explain
MINITAB was used to fit the model to n = 15 data points.y = Î²0 + Î²1x1 + Î²b2x2 + Î²3x1x2 + ÎµThe resulting printout is shown below.a. What is the prediction equation for the response surface?b. Describe the geometric form of the response
Retail interest is defined by marketers as the level of interest a consumer has in a given retail store. Marketing professors at the University of Tennessee at Chattanooga and the University of Alabama investigated the role of retailer interest in consumers€™ shopping behavior (Journal of
While waiting in a long line for service (e.g., to use an ATM or at the post office), at some point you may decide to leave the line. The Journal of Consumer Research (Nov. 2003) published a study of consumer behavior while waiting in a line. College students (sample size n = 148) were asked to
An International Journal of Research (March 2010) study of the influence of reality TV shows on one’s desire to undergo cosmetic surgery, Exercise 12.23 (p. 631). Recall that psychologists modeled desire to have cosmetic surgery (y) as a function of gender (x1), self-esteem (x2), body
Psychologists define implicit self-esteem as unconscious evaluations of one’s worth or value. In contrast, explicit self-esteem refers to the extent to which a person consciously considers oneself as valuable and worthy. An article published in Journal of Articles in Support of the Null
Refer to the Environmental Science & Technology (Jan. 2005) study of the reliability of a commercial kit to test for arsenic in groundwater, presented in Exercise. Recall that you fit a first-order model for arsenic level (y) as a function of latitude (x1), longitude (x2), and depth (x3) to
In the model E(y) = β0 + β1x + β3x2, a. Which b represents the y -intercept? b. Which b represents the shift? c. Which b represents the rate of curvature?
Suppose you fit the quadratic modelE(y) = β0 + β1x + β2x2To a set of n = 20 data points and find that R2 = .91, SSyy = 29.94, and SSE = 2.63.a. Is there sufficient evidence to indicate that the model contributes information relevant to predicting y? Test using α = .05.b. What null and
MINITAB was used to fit the complete second-order modelE(y) = Î²0 + Î²1x1 + Î²2x2 + Î²3x1x2 + Î²4x12 + Î²5x22To n = 39 data points. (See the MINITAB printout on page 652.)a. Is there sufficient evidence to indicate that at least one
The eating patterns of families of overweight preschool children was the subject of an article published in the Journal of Education and Human Development (Vol. 3, 2009). A sample of 10 overweight children living in a rural area of the United States was selected. A portion of the research focused
Management professors at Columbia University examined the relationship between assertiveness and leadership (Journal of Personality and Social Psychology, Feb. 2007). The sample comprised 388 people enrolled in a full-time master€™s in business administration (MBA) program. On the basis of
Do chief executive officers (CEOs) and their top managers always agree on the goals of the company? Goal importance congruence between CEOs and vice presidents (VPs) was studied in the Academy of Management Journal (Feb 2008). The researchers used regression to model a VP’s attitude toward the
Refer to the Development Psychology (Mar. 2003) study of the behavior of elementary school children, presented in Exercise. The researchers used a quadratic equation to model the level (y) of aggressive fantasies experienced by a child as a function of the child’s age (x). [Level y was measured
The Internet Movie Database (www.imdb.com) monitors the gross revenues of all major motion pictures. The table below gives both the domestic (United States and Canada) and international gross revenues for a sample of 20 popular movies. The data are saved in the IMDB file.a. Write a first-order
Researchers at National Semiconductor experimented with tin-lead solder bumps used to manufacture silicon wafer integrated circuit chips (International Wafer Level Packaging Conference, Nov. 3–4, 2005). The failure times of the microchips (in hours) were determined at different solder
The optomotor responses of tree frogs were studied in the Journal of Experimental Zoology (Sept. 1993). Microspectrophotometry was used to measure the threshold quantal flux (the light intensity at which the optomotor response was first observed) of tree frogs tested at different spectral
Write a regression model relating E(y) to a qualitative independent variable that can assume three levels. Interpret all the terms in the model.
MINITAB was used to fit the modely = Î²0 + Î²0x1 + Î²0x2 + Îµwhereto n = 15 data points. The results are shown in the accompanying MINITAB printout (top of next column). a. Report the least squares prediction equation. b. Interpret the values of
In addition to state-of-the-art technologies, 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 Bordeaux wine. A
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, March 2005). For one application, the nitrate concentration y (milligrams per liter) in a water
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. Multiple regression was used to estimate the effect of coaching on SAT-Mathematics scores. Data on 3,492 students (573 of whom were coached) were
Refer to the Journal of Applied Psychology (June 2002) study of recall of television commercials, presented in Exercise 10.33 (p. 495). Participants were assigned to watch one of three types of TV programs, with nine commercials embedded in each show. Group V watched a TV program with a
Refer to The Archives of Disease in Childhood (Apr. 2000) study of whether height influences a child€™s progression through elementary school, presented in Exercise. Recall that Australian schoolchildren were divided into equal thirds (tertiles) based on age (youngest third, middle third, and
Consider a multiple-regression model for a response y with one quantitative independent variable x1 and one qualitative variable at three levels.a. Write a first-order model that relates the mean response E(y) to the quantitative independent variable.b. Add the main-effect terms for the qualitative
Write a model that relates E (y) to two independent variables, one quantitative and one qualitative (at four levels). Construct a model that allows the associated response curves to be second order but does not allow for interaction between the two independent variables.
Consider the modelWhere x1 is a quantitative variable and The resulting least squares prediction equation is a. What is the equation of the response curve for E(y) when x2 = 0 and x3 = 0? When x2 = 1 and x3 = 0? When x2 = 0 and x3 = 1? b. On the same graph, plot the least squares prediction
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. Recall that the sample consisted of 148 rookie cards of National Football League (NFL) players who were inducted into the
Refer to the Chance (Winter 2000) study of men’s and women’s winning times in the Boston Marathon, presented in Exercise. Suppose the researchers want to build a model for predicting winning time (y) of the marathon as a function of year (x1) in which race is run and gender of winning runner
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, April 15, 2004). The proportion
A study of the atmospheric pollution on the slopes of the Blue Ridge Mountains (in Tennessee) was conducted. The file LEADMOSS 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 well as the elevation of
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 takes has any effect and
Explain why the F-test used to compare complete and reduced models is a one-tailed, upper-tailed test.
Suppose you fit the regression model y = β0 + β1x1 + β2x2 + β3x1x2 + β4x21 + β5 x22 + ε to n = 30 data points and you wish to test H0: β3 = β4 = β5 = 0 a. State the alternative hypothesis Ha. b. Give the reduced model appropriate for conducting the test. c. What are the numerator and
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 (y), was measured
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. Consider a model for the heat rate (kilojoules per kilo-watt per hour) produced by a gas turbine as a function of cycle speed
Refer to the Body Image: An International Journal of Research (March 2010) study of the influence of reality TV shows on one's desire to undergo cosmetic surgery, Exercise. Recall that psychologists modeled desire to have cosmetic surgery (y) as a function of gender (x1), self-esteem (x2), body
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 E(y) = β0 + β1x1 + β2x21 + β3x2 + β4x1x2 + β5x21x2 Where y = Emotional distress x1 = Experience (years) x2
Give two caveats associated with using the stepwise regression results as the final model for predicting y.
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 variable, defined as the relative error
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 (Modeling and Simulation in Materials Science and Engineering , Vol. 13, 2005). To illustrate, the engineers build a regression model for
A marine biologist was hired by the EPA to determine whether the hot-water runoff from a particular power plant located near a large gulf is having an adverse effect on the marine life in the area. The biologist’s goal is to acquire a prediction equation for the number of marine animals located
Define a regression residual.
Give two properties of the regression residuals from a model.
Identify the problem(s) in each of the residual plots shown on page 707.a.b. c. d.
The Journal of Organizational Culture, Communications and Conflict (July 2007) published a study on women in upper management positions at U.S. firms. Monthly data (n = 252 months) were collected for several variables in an attempt to model the number of females in managerial positions (y). The
Refer to Exercise 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 independent variable nickel (x4) was highly correlated

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