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business statistics

Questions and Answers of Business Statistics

Suppose you fit the interaction model y = b0 + b1 x1 + b2 x2 + b3 x1 x2 + e to n = 32 data points and obtain the results below:SSyy = 500 SSE = 21 b n 3 = 10 sbn 3 = 4a. Find R2 and interpret its
Suppose the true relationship between E(y) and the quantitative independent variables x1 and x2 is given by the model below.E1y2 = -5 + x1 + 3x2 - 3x1 x2a. Describe the corresponding
Write an interaction model relating the mean value of y, E(y), toa. two quantitative independent variablesb. three quantitative independent variables [Hint: Include all possible two-way cross-product
Arsenic in groundwater. Refer to the Environmental Science & Technology (Jan. 2005) study of the reliability of a commercial kit designed to test for arsenic in groundwater, presented in Exercise
Usability Professionals, salary survey. The Usability Professionals’ Association (UPA) supports people who research, design, and evaluate the user experience of products and services. The UPA
Predicting runs scored in baseball. Refer to the Chance(Fall 2000) study of runs scored in Major League Baseball games, Exercise 12.19(p. 698). Multiple regression was used to model total number of
Characteristics of lead users. Refer to the Creativity and Innovation Management (Feb. 2008) study of lead users of children’s computer games, Exercise 12.15(p. 698). Recall that the researchers
Explain why we use yn as an estimate of E(y) and to predict y.
Study of adolescents with ADHD. Children with attentiondeficit/hyperactivity disorder (ADHD) were monitored to evaluate their risk for substance (e.g., alcohol, tobacco, illegal drug) use (Journal of
Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study on using the volume of chatter on Twitter.com to
Estimation of urban population by means of satellite images. Can the population of an urban area be estimated without taking a census? Geographical Analysis(Jan. 2007) demonstrated the use of
Whales entangled in fishing gear. Refer to the Marine Mammal Science (April 2010) study of whales entangled in fishing gear, Exercise 10.32(p. 552). Data collected for a sample of 207 entanglements
Dating and disclosure. Refer to the Journal of Adolescence(Apr. 2010) study of adolescents’ disclosure of their dating and romantic relationships, Exercise 8.43 (p. 419).Data collected for a sample
Characteristics of lead users. Creativity and Innovation Management (Feb. 2008) published an article on identifying the social network characteristics of lead users of children’s computer games.
Suppose you fit the first-order model y = b0 + b1 x1 + b2 x2 + b3 x3 + b4 x4 + b5 x5 + e to n = 27 data points and obtain SSE = .33 R2= .92a. Do the values of SSE and R2 suggest that the model
Consider the following first-order model equation in three quantitative independent variables:E1y2 = 2 + 4x1 - 2x2 - 5x3a. Graph the relationship between y and x1 for x2 = -2 and x3 = 2.b. Repeat
Suppose you fit the model y = b0 + b1 x1 + b2 x2 + b3 x3 + e to n = 30 data points and obtain the following result:yn = 2.2 - 2.8x1 + 1.9x2 + .97x3 The estimated standard errors of b n 2 and b n 3
What are the caveats to conducting t-tests on all of the individual b parameters in a multiple-regression model?
List the four assumptions about the random error e required for a multiple-regression analysis.
Write a first-order model relating E(y) toa. two quantitative independent variablesb. four quantitative independent variablesc. five quantitative independent variables
Spall damage in bricks. 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
Long-jump “takeoff error.” The long jump is a trackand-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
Regression through the origin. Sometimes it is known from theoretical considerations that the straight-line relationship between two variables x and y passes through the origin of the xy-plane.
Snow geese feeding trial. 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).
Performance in online courses. Florida State University information scientists assessed the impact of online courses on student performance (Educational Technology& Society, Jan. 2005). Each in a
Dance/movement therapy. 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
Quantum tunneling. At temperatures approaching absolute zero 1 -273°C2, helium exhibits traits that seem to defy many laws of Newtonian physics. An experiment has been conducted with helium in solid
Relation of eye and head movements. How do eye and head movements relate to body movements when a person reacts to a visual stimulus? Scientists at the California Institute of LO9 Technology
Relation of eye and head movements. How do eye and head movements relate to body movements when a person reacts to a visual stimulus? Scientists at the California Institute of Technology designed an
Extending the life of an aluminum smelter pot. An investigation of the properties of bricks used to line aluminum smelter pots was published in The American Ceramic Society Bulletin (Feb. 2005). Six
New method of estimating rainfall. Accurate measurements of rainfall are critical for many hydrological and meteorological projects. Two standard methods of monitoring rainfall use rain gauges and
Removing metal from water. In the Electronic Journal of Biotechnology (Apr. 15, 2004), Egyptian scientists studied a new method for removing heavy metals from water. Metal solutions were prepared in
English as a second language reading ability. What are the factors that allow a native Spanish-speaking person to understand and read English? A study published in the Bilingual Research Journal
Feeding habits of fish. Refer to the Brain and Behavior Evolution (Apr. 2000) study of the feeding behavior of black-bream fish, presented in Exercise 2.162 (p. 124).Recall that the zoologists
Sports news on local TV broadcasts. The Sports Journal LO9 (Winter 2004) published the results of a study conducted to assess the factors that affect the time allotted to sports news on local
Wind turbine blade stress. Mechanical engineers at the University of Newcastle (Australia) investigated the use of timber in high-efficiency small wind turbine LO9 blades (Wind Engineering, Jan.
Consider the following 10 data points.x 3 5 6 4 3 7 6 5 4 7 y 4 3 2 1 2 3 3 5 4 2 LO9 a. Plot the data on a scatterplot.b. Calculate the values of r and r2.c. Is there sufficient evidence to
Consider the following sample data:y 5 1 3 x 5 1 3a. Construct a scatterplot for the data. LO9 b. It is possible to find many lines for whichΣ1y - yn2 = 0. For this reason, the criterionΣ1y - yn2
In fitting a least squares line to n = 20 data points, the following quantities were computed: SSxx = 60, SSyy = 225, SSxy = -75, x = 2.4, and y = 45.a. Find the least squares line.b. Graph the least
True or False. In simple linear regression, about 95% of the y-values in the sample will fall within 2s of their respective LO9 predicted values.
Outline the five steps in a simple linear regression LO9 analysis.
Give the general form of a straight-line model for E(y). LO9
Explain the difference between a probabilistic model and a deterministic model. LO9
Legal advertising—does it pay? To gain a competitive edge, lawyers aggressively advertise their services. Does legal advertising really pay? To partially answer this question, consider the case of
An MBA’s work-life balance. 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
Thickness of dust on solar cells. The performance of a solar cell can deteriorate when atmospheric dust accumulates on the solar panel surface. In the International Journal of Energy and
Impact of dropping ping-pong balls. The impact of dropping hollow balls was investigated in the American Journal of Physics (Mar. 2014). Standard ping-pong balls were dropped vertically onto a force
Life tests of cutting tools. Refer to the data on life tests of cutting tools, Exercise 11.52 (p. 636).a. Use a 90% confidence interval to estimate the mean useful life of a brand-A cutting tool when
Forecasting movie revenues with Twitter. Refer to the IEEE International Conference on Web Intelligence and Intelligent Agent Technology (2010) study of how social media (e.g., Twitter.com) may
Spreading rate of spilled liquid. Refer to the Chemicial Engineering Progress (Jan. 2005) study of the rate at which a spilled volatile liquid will spread across a surface, presented in Exercise
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, presented in Exercise 11.34 (p. 630).a. Find a 99% confidence interval for the mean
Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 11.33(p. 629). The data were used to fit the simple linear regression model, E1y2 = b0 +
Sound waves from a basketball. Refer to the American Journal of Physics (June 2010) study of sound waves in a spherical cavity, Exercise 11.31 (p. 629). You fit a straight-line model relating sound
Game performance of water polo players. Refer to the Biology of Sport (Vol. 31, 2014) study of the physiological performance of top-level water polo players, Exercise 11.24 (p. 626). Recall that the
Do nice guys finish first or last? Refer to the Nature (Mar.20, 2008) study of the use of punishment in cooperation games, Exercise 11.22 (p. 625). Recall that simple linear regression was used to
Refer to Exercise 11.107.a. Using no information about x, estimate and calculate a 95% confidence interval for the mean value of y. [Hint: Use the one-sample t methodology of Section 7.3.]b. Plot the
Consider the following pairs of measurements.x 4 6 0 5 2 3 2 6 2 1 y 3 5 -1 4 3 2 0 4 1 1 LO9 For these data, SSxx = 38.900, SSyy = 33.600, SSxy = 32.8, and yn = -.414 + .843x.a. Construct a
Consider the following pairs of measurements.x 1 2 3 4 5 6 7 y 3 5 4 6 7 7 10 LO9 a. Construct a scatterplot of these data.b. Find the least squares line, and plot it on your scatterplot.c. Find
In fitting a least squares line to n = 5 data points, the following quantities were computed:SSxx = 31, x = 2, SSyy = 24, y = 6, SSxy = 26a. Find the least squares line.b. Graph the least squares
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
True or False. The greater the deviation between x and x, the wider the prediction interval for y will be. LO9
True or False. For a given x, a confidence interval for E(y) will always be wider than a prediction interval LO9 for y.
Explain the difference between y and E(y) for a given x. LO9
Refer again to the drug reaction regression. Predict the reaction time for the LO9 next performance of the experiment for a subject with a drug concentration of 4%. Use a 95% prediction interval.
Refer to the simple linear regression on drug reaction. Find a 95% confidence interval for the mean reaction time when the concentration of the drug in the bloodstream is 4%. LO9
Pain tolerance study. 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
Plants that grow on Swiss cliffs. Refer to the Alpine Botany(Nov. 2012) study of rare plants that grow on the limestone cliffs of the Northern Swiss Jura mountains, Exercise 2.165(p. 125). Data on
Child labor in diamond mines. The role of child laborers in Africa’s colonial-era diamond mines was the subject of LO9 research published in the Journal of Family History (Vol.35, 2010). One
Effect of massage on boxing. Refer to the British Journal of Sports Medicine (Apr. 2000) study of the effect of massage on boxing performance, presented in Exercise 11.70 (p. 643).Find and interpret
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, first presented in Exercise 11.34 (p. 630). Find and interpret the values of r and r2
Do nice guys finish first or last? Refer to the Nature (Mar. 20, 2008) study of the use of punishment in cooperation games, Exercise 11.22 (p. 625). Recall that college students repeatedly played a
Eye anatomy of giraffes. Refer to the African Zoology (Oct.2013) study of giraffe eye characteristics, Exercise 11.71(p. 643). Recall that the researchers fit a simple linear regression equation of
View of rotated objects. Perception & Psychophysics(July 1998) reported on a study of how people view threedimensional objects projected onto a rotating two- dimensional image. Each in a sample of 25
Salary linked to height. 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),
Redshifts of quasi-stellar objects. Refer to the Journal of Astrophysics & Astronomy (Mar./Jun. 2003) study of redshifts in quasi-stellar objects presented in Exercise 11.27 LO9 (p. 627). Recall
Physical activity of obese young adults. Refer to the International Journal of Obesity (Jan. 2007) study of the physical activity of obese young adults, presented in Exercise 6.37 (p. 331). For two
Lobster fishing study. Refer to the Bulletin of Marine Science (Apr. 2010) study of teams of fishermen fishing for the red spiny lobster in Baja California Sur, Mexico,Exercise 11.63 (p. 642). Recall
Going for it on fourth down in the NFL. Each week coaches in the National Football League (NFL) face a decision during the game. On fourth down, should the team punt the ball or go for a first down?
Last name and acquisition timing. Refer to the Journal of Consumer Research (Aug. 2011) study of the speed with which consumers decide to purchase a product, Exercise LO9 9.14 (p. 476). Recall that
RateMyProfessors.com. 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
Use the applet entitled Correlation by the Eye to explore the relationship between the pattern of data in a scatterplot and the corresponding correlation coefficient. LO9 a. Run the applet several
Calculate r2 for the least squares line in Exercise 11.21 LO9 (p. 625).
Calculate r2 for the least squares line in Exercise 11.18(p. 625). LO9
Construct a scatterplot for each data set. Then calculate r and r2 for each data set. Interpret their values.a. x -2 -1 0 1 2 LO9 y -1 2 3 6 9b. x -2 -1 0 1 2 y 9 6 4 3 1c. x 2 3 3 4 4 4 5 y 3 2 4 2
True or False. A value of the correlation coefficient near LO9 1 or near -1 implies a causal relationship between x and y.
Explain what each of the following sample correlation coefficients tells you about the relationship between the x and y LO9 values in the sample:a. r = 1b. r = -1c. r = 0d. r = .90e. r = .10f. r =
Describe the slope of the least squares regression line for LO9 the given information.a. r = -.4b. r = .4c. r = 0d. r2= .81
True or False. The correlation coefficient is a measure of the LO9 strength of the linear relationship between x and y.
Calculate the coefficient of determination for the drug reaction example. The data are repeated in Table 11.4 for convenience. Interpret the result. LO9
Legalized gambling is available on several riverboat casinos operated by a city in Mississippi. The mayor of the city wants to know the correlation between the number of casino employees and the
Spreading rate of spilled liquid. Refer to the Chemical Engineering Progress (Jan. 2005) study of the rate at which a spilled volatile liquid will spread across a surface, Exercise LO9 11.35 (p.
The “name game.” Refer to the Journal of Experimental Psychology—Applied (June 2000) name-retrieval study, presented in Exercise 11.34 (p. 630). Recall that the goal of the study was to
Characterizing bone with fractal geometry. In Medical Engineering & Physics (May 2013), researchers used fractal geometry to characterize human cortical bone.A measure of the variation in the volume
Pain empathy and brain activity. Empathy refers to being able to understand and vicariously feel what others actually feel. Neuroscientists at University College of London investigated the
Eye anatomy of giraffes. Giraffes are believed to have excellent vision. The journal African Zoology (Oct.2013) published a study of giraffe eye characteristics.Data were collected for a sample of 27
Effect of massage on boxers. Refer to the British Journal of Sports Medicine (Apr. 2000) study of the effect of massage on boxing performance, presented in Exercise 10.82 LO9 (p. 580). Two other
Forest fragmentation study. Refer to the Conservation Ecology (Dec. 2003) study on the causes of fragmentation LO9 of 54 South American forests, presented in Exercise 2.166(p. 125). Recall that
Ideal height of your mate. Refer to the Chance (Summer 2008) study of the height of the ideal mate, Exercise 11.33(p. 629). You used the data to fit the simple linear regression LO9 model E1y2 = b0
Sweetness of orange juice. Refer to Exercise 11.32(p. 629) and the simple linear regression relating the sweetness index (y) of an orange juice sample to the amount of water-soluble pectin (x) in the
FCAT scores and poverty. Refer to the Journal of Educational and Behavioral Statistics (Spring 2004) study of scores on the Florida Comprehensive Assessment Test (FCAT), first presented in Exercise

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