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Applied Regression Analysis And Other Multivariable Methods 5th Edition David G. Kleinbaum, Lawrence L. Kupper, Azhar Nizam, Eli S. Rosenberg - Solutions
In an analysis of daily soil evaporation (EVAP), Freund (1979) identified the following predictor variables:MAXAT = Maximum daily air temperatureMINAT = Minimum daily air temperatureAVAT = Integrated area under the daily air temperature curve (i.e., a measure of average air temperature)MAXST =
The raw data for Problem 22, from Freund (1979), appear below. For the model of Problem 22,a. Fit the model.b. What discrepancies do you note between the results of (a) and the data summary presented in Problem 22?c. Examine the correlation matrix for all predictor variables in this problem. Are
Radial keratotomy is a type of refractive surgery in which radial incisions are made in the cornea of myopic (nearsighted) patients in an effort to reduce their myopia. Theoretically, the incisions allow the curvature of the cornea to become less steep, reducing the refractive error of the
In 1990, Business Week magazine compiled financial data on the 1,000 companies that had the biggest impact on the U.S. economy. Data from this compilation were presented in Problem 13 of Chapter 8. In addition to the company name, data on the following variables were shown in that problem: 1990
In Problem 19 of Chapter 5, data from the 1990 Census were shown for 26 randomly selected Metropolitan Statistical Areas (MSAs). Of interest are factors potentially associated with the rate of owner occupancy of housing units. Three variables included in the data set were as follows: OWNEROCC:
a.-c. Repeat parts (a) through (c) of Problem 1 using the data of Problems 3 through 14 of Chapter 5.
In an environmental engineering study of a certain chemical reaction, the concentrations of 18 separately prepared solutions were recorded at different times (three measurements at each of six times). The natural logarithms of the concentrations were also computed. The data recorded are reproduced
a.-e. Repeat Problem 8, parts (a) through (e), but use orthogonal polynomials.f. Compare the results obtained here to those obtained in Problems 8 and 9.Problem 8This problem uses the data presented in the table for Problem 12 in Chapter 5. Use α = .05.a. Use a computer program to fit a natural
This problem uses the data from Problem 13 in Chapter 5. Use α = .10.a. Use a computer program to fit a quadratic natural polynomial model for predicting latency as a function of weight minus average weight.b.-e. Repeat parts (b) through (e) from Problem 8 for this analysis.f. Compare the results
This problem uses the data from Problem 15 in Chapter 5.a. Using a computer program, fit a cubic polynomial model with BLOODTOL as the response and PPM_TOLU as the predictor. Center PPM_TOLU. Provide the prediction equation.b.-e. Repeat parts (b) through (e) from Problem 8 for this analysis.f.
a. For the data from Problem 15 in Chapter 5, specify the orthogonal polynomial codings needed for coding PPM_TOLU linear, quadratic, and cubic terms. Repeat part (a) of Problem 12, but use the orthogonal coding.b.-e. Repeat parts (b) through (e) from Problem 8 for this analysis.In Problem 12a.
To promote safe driving habits and to better protect its customers, an insurance company offers a discount of between 5% and 20% on renewal insurance premiums to customers who have completed a defensive driving course. The following table of data shows the number of customers who have applied for
Refer to Problem 14. Using the computer output for that problem, and the accompanying output here, answer the following questions.a. Determine the variance inflation factors for the estimated model in part (b) of Problem 14. Does collinearity appear to be a problem?b. Determine the estimated
Columbus Airlines introduced a new, specially discounted line of air fares in 1995. Annual ticket revenues Y (in $ 1,000s) are shown in the following table, along with the time period X (in months, with X = 1 for January 1995).Month
With the addition of five pairs of observations€”(18,000, 39.2), (22,400, 27.9), (24,210, 22.3), (5,400, 11.7), and (9,340, 32.5)€”to the data in Problem 3 in Chapter 5, the accompanying computer output is obtained for the regression of TIME (Y) on INC (X).a. Using the accompanying computer
a.-g. For the data on DIST (Y) and MPH (X) in Problem 7 in Chapter 5, use the following information to answer the same questions as in parts (a) through (g) of Problem 2.Degree 1 fit: Ŷ = -122.345 + 6.227XDegree 2 fit: Ŷ = 32.901 - 3.05 IX + 0.1176X2Degree 3 fit: Ŷ = 114.621 - 10.62OX+ 0.3247X2
For the data on VOTE (Y) and TVEXP (X) in Problem 5 in Chapter 5, it was found that the straight-line model was adequate. Using the accompanying computer output for quadratic regression, do the following:a. Plot the fitted straight-line model and the fitted quadratic model on the scatter diagram
For the regression of PCI (Y) on YNG (X) for the African countries considered in Problem 2 in Chapter 12, use the accompanying information to do the following:a. Plot the estimated straight-line and quadratic models on the scatter diagram for the data on the African countries.b. Test for the
For the data given in Problem 11 in Chapter 7, which concerns the relationship between the temperature (X) of a certain medium and the growth (Y) of human amniotic cells in a tissue culture, researchers wish to evaluate whether a parabolic model is more appropriate than a straight-line model. Use
The skin response in rats to different concentrations of a newly developed vaccine was measured in an experiment, resulting in the data, models, and computer output that follow.a. Plot the straight-line, quadratic, and cubic equations on the scatter diagram for this data set.b. Test sequentially
This problem uses the data presented in the table for Problem 12 in Chapter 5. Use α = .05.a. Use a computer program to fit a natural polynomial cubic model for predicting vocabulary size as a function of age in years. Provide estimated regression coefficients.b. Using variables-added-in-order
a.-e. Repeat Problem 8, parts (a) through (e), after centering the predictor (age).f. Compare the results obtained here to those obtained in Problem 8.Problem 8This problem uses the data presented in the table for Problem 12 in Chapter 5. Use α = .05.a. Use a computer program to fit a natural
Add the variables (HGT)2 and (AGE × HGT) to the data set for WGT, HGT, AGE, and (AGE)2 given in Section 16.3. Then, using an available regression program and the accompanying computer output, determine the best regression model relating WGT to the five independent variables as
In Problem 9, the first-order interactions between Z and the predictor variables X1, X3, and X4 were not included in the model selection process. Investigate whether this was appropriate, as follows (using the accompanying computer output).a. Conduct a test to investigate the importance of the
In 1990, Business Week magazine compiled financial data on the 1,000 companies that had the biggest impact on the U.S. economy. Data from a sample of the top 500 companies in Business Week's report were presented in Problem 13 in Chapter 8. In addition to the company name, the following variables
Radial keratotomy is a type of refractive surgery in which radial incisions are made in a myopic (nearsighted) patient's cornea to reduce the person's myopia. Theoretically, the incisions allow the curvature of the cornea to become less steep, thereby reducing the patient's refractive error. This
Using the data given in Problem 2 in Chapter 5 (with SBP as the dependent variable) and the accompanying computer output, find the best regression model, using α = .05 and the independent variables AGE, QUET, and SMK as follows.a. Use the forward approach.b. Use the backward
For the same data set considered in Problem 2 (and employing the accompanying computer output), use the stepwise regression approach to find the best regression models of SBP on QUET, AGE, and QUET × AGE for smokers and nonsmokers separately. (Use α = .05.) Compare the results for each group here
For the data given in Problem 4 in Chapter 8 (plus the accompanying computer output), find (using α = .10) the best regression model relating homicide rate (Y) to population size (X1), percentage of families with income less than $5,000 (X2), and unemployment fate (X3).a. Use the stepwise
The data set listed in the following table contains information on AGE, SEX (1 = male, 2 = female), work problems index (WP), marital conflict index (MC), and depression index (DEP) for a sample of 39 new admissions to a psychiatric clinic at a large university hospital. For each sex separately,
For the data in Problem 15 in Chapter 5, use LN_BRNTL as the response variable and LN_PPMTL, LN_BLDTL, AGE, and WEIGHT as predictors. (Use α = .05.)a. Indicate a plausible fixed order for testing predictors, based on the nature of the data. Briefly defend your choice.b. Use a computer program to
Consider the data of Bethel et al. (1985), discussed in Problem 19 in Chapter 14. Delete the three female subjects, leaving 16 observations. Use FEV1 as the response and AGE, WEIGHT, and HEIGHT as predictors.a. Use the all possible regressions procedure to suggest a best model.b. Consider a model
Use the data from Freund (1979), presented in Problem 22 in Chapter 14. Taking the model discussed there as the maximum model, repeat parts (a) through (h) of Problem 6. In part (h), note the possible role of collinearity.In Problem 6a. Indicate a plausible fixed order for testing predictors, based
A random sample of data was collected on residential sales in a large city. The accompanying table shows the selling price (Y, in $ 1,000s), area (X1, in hundreds of square feet), number of bedrooms (X2), total number of rooms (X3), house age (X4, in years), and location (Z = 0 for in-town and
Five treatments for fever blisters, including a placebo, were randomly assigned to 30 patients. For each of the five treatments, the data in the accompanying table identify the number of days from initial appearance of the blisters until healing is complete.Treatment
Three replicate water samples were taken at each of four locations in a river to determine whether the quantity of dissolved oxygen€”a measure of water pollution€” varied from one location to another (the higher the level of pollution, the lower the dissolved oxygen reading). Location 1 was
Consider the data from Problem 15 in Chapter 5. The dependent variable of interest is LN_BPNTL. Use α = .05.a. Conduct a one-way ANOVA, with dosage level (PPM_TOLU) as a categorical predictor.b. Using the Bonferroni technique, compute all pairwise comparisons.c. Repeat part (b) using the
Repeat Problem 11, skipping part (e), but use LN_BLDTL as the dependent variable.Problem 11a. Conduct a one-way ANOVA, with dosage level (PPM_TOLU) as a categorical predictor.b. Using the Bonferroni technique, compute all pairwise comparisons.c. Repeat part (b) using the Tukey-Kramer method.d.
The accompanying source table relates to a study involving the effects of trimethylin doses of 0, 3, 6, and 9 mg/kg on a sample of 48 rats. Each rat received only one dose. The response variable was the log of the activity counts after one hour spent in a residential maze. Compute the unknown
For each of the following contrasts, indicate the null hypothesis that is being tested.
Persistent patent ductus arteriosus (PDA) is a medical condition that affects more than 40% of very low birth weight infants. Infants with PDA have an increased risk of ailments such as cerebral hemorrhage and bronchopulmonary dysplasia, as well as of death. In a study, Varvarigou et al. (1996)
In the PDA research described in Problem 15, one of the outcome variables was mean airway pressure (measured in cm H2O) seven days after birth€”a measure of respiratory status. The data on this outcome are summarized in the accompanying table.a.-c. Repeat parts (a)-(c) of Problem 15, using mean
A survey was conducted to examine the effects of pharmaceutical drug advertising on physician practices. Self-administered questionnaires were delivered to randomly selected physicians in various practice types: general practice, family practice, and internal medicine. Physicians reported on their
Customer portfolio analyses provide retailers with data on customer characteristics, including expenditure patterns. Based on this information, retailers can make marketing and operational adjustments to improve their market position. ABC Foods, a large supermarket chain, conducted a survey of the
The data in the accompanying table were sampled from U.S. News & World Report's 1996 story on the "Best Mutual Funds." The following variables are shown for each fund:CAT (fund category):1 = Aggressive growth; 2 = Long-term growth; 3 = Growth and income; 4 = Income.LOAD (load status):N = No
The following data are replicate measurements of the sulfur dioxide concentration in each of three cities:City I: 2, 1, 3City II: 4, 6, 8City III: 2, 5, 2a. Complete the ANOVA table in the accompanying computer output for simultaneously comparing the mean sulfur dioxide concentrations in the three
This problem refers to the data of Problem 19.a. Suppose that an ANOVA is to be performed to compare the average OPI values for funds with different volatilities. State precisely the ANOVA model. Is fund volatility a fixed- or random-effects factor?b. In the SAS output that follows, complete the
Radial keratotomy is a type of refractive surgery in which radial incisions are made in a myopic (nearsighted) patient's cornea to reduce the person's myopia. Theoretically, the incisions allow the curvature of the cornea to become less steep, thereby reducing the patient's refractive error.The
Data on law and business schools were sampled from U.S. News & World Report's 1996 report on the "America's Best Graduate Schools 1996 Annual Guide." The school's reputation rank among academics and the 1995 median starting salary for graduates are shown in the accompanying table for 12
In September 1996, U.S. News & World Report published a report on America's health maintenance organizations (HMOs). The report was intended to serve as a consumer guide to HMO quality. For each HMO included in the report, data were provided on several variables, including the
Each of three chemical laboratories performed four replicate determinations of the concentration of suspended particulate matter in a certain area using the "Hi-Vol" method of analysis. The resulting data are presented next.a. Identify the appropriate ANOVA table for these data.b. Test the null
Ten randomly selected mental institutions were examined to determine the effects of three different antipsychotic drugs on patients with the same types of symptoms. Each institution used one and only one of the three drugs exclusively for a one-year period. The proportion of treated patients in
Suppose that a random sample of five active members in each of four political parties in a certain western European country was given a questionnaire purported to measure (on a 100-point scale) the extent of "general authoritarian attitude toward interpersonal relationships." The means and standard
A psychosociological questionnaire was administered to a random sample of 200 persons on an island in the South Pacific that has become increasingly westernized over the past 30 years. From the questionnaire data, each of the 200 persons was classified into one of three groups€”HI-POS, NO-DIF,
To examine whether mathematics skills of the average high school graduate in urban areas of the United States have declined over the past 10 years, the average scores on the math section of the SAT Reasoning Test (MSAT) were compared for a random sample of five big-city high schools for the years
Three persons (denoted A, B, and C) claiming to have unusual psychic ability underwent ESP tests at an eastern U.S. psychic research institute. On each of five randomly selected days, each person was asked to specify for 26 pairs of cards whether both cards in a given pair were of the same color or
The average generation times for four different strains of influenza virus were determined using six cultures for each strain. The data are summarized in the following table.a. Test whether the true mean generation time differs among the four strains.b. What is the appropriate ANOVA table for these
A private research corporation conducted an experiment to investigate the toxic effects of three chemicals (I, II, and III) used in the tire-manufacturing industry. In this experiment, three adjacent 1-inch squares were marked on the back of each of eight rats, and the three chemicals were applied
An educator has obtained class average scores on a standardized test for classes from each grade from first through seventh at each of four schools in a city. These are shown in the following table. To assess differences among schools, the educator decides to conduct a randomized-blocks ANOVA,
A company evaluated three new production-line technologies, one involving high automation, the second involving moderate automation, and the third involving low automation. All three technologies were intended to improve productivity through increased automation, but they continued to require
An advertising company evaluated three types of television ads for a new low-cost subcompact automobile: visual-appeal ads, budget-appeal ads, and feature-appeal ads. To control for age differences, the company randomly selected viewers from four age groups to evaluate the persuasiveness of the ads
In a study of the psychosocial changes in individuals who participated in a community-based intervention program, individuals who were clinically identified as hypertensives were randomly assigned to one of two treatment groups (with n individuals in each group). Group 1 was given the usual care
An experiment was conducted at the University of North Carolina to see whether the biochemical oxygen demand (BOD) test for water pollution is biased by the presence of copper. In this test, the amount of dissolved oxygen in a sample of water is measured at the beginning and at the end of a
Using the accompanying computer output based on the data in Problem 7 in Chapter 17, conduct a randomized-blocks analysis, treating the high schools as blocks, to test whether significant differences exist among the average math SAT (MSAT) scores for the years 2002, 2007, and 2012. Do the results
Using the accompanying computer output based on the data in Problem 8 in Chapter 17, conduct a randomized-blocks analysis, treating the days as blocks, to test whether the three persons have significantly different ESP ability. Does blocking on days seem appropriate?
The promotional policies of four companies in a certain industry were compared to determine whether their rates for promoting blacks and whites differed. Data on the variable "rate discrepancy" were obtained for the four companies in each of three different two-year periods. This variable was
Suppose that, in a study to compare body sizes of three genotypes of fourth-instar silkworms, the mean lengths (in millimeters) for separately reared cocoons of heterozygous (HET), homozygous (HOM), and wild (WLD) silkworms were determined at five laboratory sites, as detailed in the following
In Problem 3, the independent variable of interest, copper ion concentration, is an interval-scaled variable. a. Treating copper ion concentration as a five-level categorical predictor (as in the randomized-blocks analysis) corresponds to including a collection of polynomial terms for copper ion
Assume that the following table came from an analysis of a randomized-blocks study.a.-f. Complete the ANOVA table by determining the numerical values for the entries a through f. Show your work.g. Provide tests concerning treatment and block effects using α = .05. What are your conclusions?
The data in the following table and accompanying computer output come from an animal experiment designed to investigate whether levorphanol reduces stress as reflected in the cortical sterone level. The four treatment groups contained five animals eacha. These data may be analyzed by means of
Consider an ANOVA table of the following form.Use a = .05 for all parts of this problem. In each case, decide what effects (if any) are significant, and what conclusions to draw, based on a two-way ANOVA table with the following P-values: a. P1, = .03, P2 = .51, P3 = .31 b. P1 = .001, P2 = .63, P3
Assume that a total of 75 subjects were tested in a balanced two-way fixed-effects factorial experiment. A plot of the means from the study is shown next. The dependent variable is Y, and the factors are A and B.a. Give the left two columns (the source and degrees-of-freedom columns) of the ANOVA
Assume that the following ANOVA table came from balanced two-way fixed-effects ANOVA. Show the formula used (with numbers filled in) and the numerical value of each letter in the table.Also, indicate which (if any) family or families of means should be evaluated with multiple comparisons.
The data in the following table and accompanying computer output are from a hypothetical study of human body temperature as affected by air temperature and a dietary supplement that is hoped to increase heat tolerance. Body temperatures (in degrees Celsius) were measured for 36 athletes immediately
The experiment in Problem 11 in Chapter 18 was repeated€”this time using three workers per technology/experience combination rather than just one. For each cell the following table, the outputs (in number of units per hour) are listed for three randomly chosen workers at the given
An advertising company evaluated three types of television ads for a new, low-cost, subcompact automobile: visual-appeal ads, budget-appeal ads, and feature-appeal ads. To control for age differences, viewers from four age groups were chosen to evaluate the persuasiveness of the ads (as measured on
This question refers to the U.S. News & World Report mutual fund data presented in Problem 19 in Chapter 17. The variables described in that question were: CAT (fund category): 1 = Aggressive growth; 2 = Long-term growth; 3 = Growth and income; 4 = Income. LOAD (load status): N = No load; L =
This question refers back to the U.S. News & World Report graduate school data presented in Problem 22 in Chapter 17. a. Suppose that a two-way ANOVA is to be performed, with 1995 starting salary as the dependent variable and school type (SCHOOL) and reputation rank (REP = 1 if in top 25; 2 if not)
The following table gives the performance competency scores for a random sample of family nurse practitioners (FNPs) with different specialties, from hospitals in three cities.a. Classify each factor as either fixed or random, and justify your classification. b. Form the table of sample means (use
The following table gives the average patient waiting time in minutes for patients from a random sample of 16 physicians, classified by type of practice and type of physiciana. Classify each factor as either fixed or random, and justify your classification scheme. b. Using the accompanying computer
A study was undertaken to measure and compare sexist attitudes of students at various types of colleges. Random samples of 10 undergraduate seniors of each sex were selected from each of three types of colleges. A questionnaire was then administered to each student, from which a score for "degree
Random samples of 100 persons awaiting trial on felony charges were selected from rural, urban, and suburban court locations in each of two states, one (state 1) in the Northeast and the other (state 2) in the South. The following table summarizes the data on the time Y (in months) between arrest
An experiment was conducted at a large state university to determine whether two different instructional methods for teaching a beginning statistics course would yield different levels of cognitive achievement. One instructional method involved using a self-instructional format, including a
The following table and accompanying computer output present data on the uric acid level found in the bloodstreams of persons with Down's syndrome and in the bloodstreams of non€”Down's syndrome subjects. All subjects were between the ages of 21 and 25. Analyze these data, using the ANOVA
An experiment was conducted to investigate the survival of diplococcus pneumonia bacteria in chick embryos under relative humidities (RH) of 0%, 25%, 50%, and 100% and under temperatures (Temp) of 10°C, 20°C, 30°C, and 40°C, using 10 chicks for each RH-Temp combination. The partially completed
The diameters (Y) of three species of pine trees were compared at each of four locations, using samples of five trees per species at each location. The resulting data are given in the following table.a. Comment on whether each of the two factors should be considered fixed or random. b. Use the
Consider hypothetical data based on a study concerning the effects of rapid cultural change on blood pressure levels for native citizens of an island in Micronesia. Blood pressures were taken on a random sample of 30 males over age 40 from a certain province. These persons, who commuted to work in
The experimenters described in Problem 9 hoped that home cage would not affect activity level in any systematic fashion. Explore this question by repeating Problem 9, but replacing SEX with CAGE in your analysis.In Problem 9a. Tabulate the DOSAGE X SEX cell sample sizes. Explain why this might be
A manufacturer conducted a pricing experiment to explore the effects of price decreases on sales of one of its breakfast cereals. The two largest supermarket chains in a particular area participated in the experiment. Ten stores from each chain were randomly selected, and each store was assigned a
The manager of a market research company conducted an experiment to investigate the productivity of three employees on each of two computerized data-entry systems. The employees conducted phone surveys, entering the survey data into the computer during the phone call. Productivity was measured as
a. Suppose that a two-way ANOVA is to be performed, with five-year postoperative change in refractive error as the dependent variable (Y) and diameter of clear zone (CLRZONE) and baseline average corneal curvature (BASECURV = 1 if curvature is < 43 diopters; = 2 if curvature is between 43 and 44
a. Suppose that a two-way ANOVA is to be performed, with 1995 starting salary as the dependent variable and with school type (SCHOOL) and reputation rank among academics (REP1 = 1 if reputation rank is in the top 10; = 2 if rank is 11 to 20; = 3 if rank is 21 or worse) as the two factors. State
A study was conducted to assess the combined effects of patient attitude and patient physician communication on patient satisfaction with medical care during pregnancy. A random sample of 110 pregnant women under the care of private physicians was followed from the first visit with the physician
The data listed in the table on the following page are from an unpublished study by Harbin and others (1985). Subjects were young (ages 18 through 29) or old (ages 60 through 86) men. Each subject was exposed to 0 or 100 parts per million (ppm) of carbon monoxide (CO) for a period before and during
a.-d. Repeat Problem 3, using REACTIM2 as the dependent variable and referring to the accompanying computer output.In problem 3a. Observe the cross-tabulation of AGEGROUP and PPM_CO in the accompanying SAS PROC FREQ computer output. Why might this be called a nearly orthogonal two-way design? Any
A crime victimization study was undertaken in a medium-size southern city. The main purpose was to determine the effects of being a crime victim on confidence in law enforcement authority and in the legal system itself. A questionnaire was administered to a stratified random sample of 40 city
The effect of a new antidepressant drug on reducing the severity of depression was studied in manic-depressive patients at two state mental hospitals. In each hospital all such patients were randomly assigned to either a treatment (new drug) or a control (old drug) group. The results of this
A study was conducted by a television network in a certain state to evaluate the viewing characteristics of adult females. Each individual in a stratified random sample of 480 women was sent a questionnaire; the strata were formed on the basis of the following three factors: season (winter or
Suppose that the following data were obtained by an investigator studying the influence of estrogen injections on change in the pulse rate of adolescent chimpanzees:a. What are the factors in this experiment? Should they be designated as fixed or random?b. Demonstrate that the cell frequencies for
The data listed in the following table relate to a study by Reiter and others (1981) concerning the effects of injecting triethyl-tin (TET) into rats once at age 5 days. The animals were injected with 0, 3, or 6 mg per kilogram of body weight. The response was the log of the activity count for 1
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