Analysis Of Variance Design And Regression 2nd Edition Ronald Christensen - Solutions

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Traceability tools are not:a) Specification treesb) Text-based references and hyperlinksc) Trace matricesd) Trace requirement documents
The business case is developed for:a) The current solutionb) The proposed solutionc) All scenariosd) All stakeholders’ identified needs
Who signs off in a Scrum project?a) The stakeholdersb) The product ownerc) The Scrum Masterd) The development team
Bliss and James (1966) give data on the median survival time z of house flies following application of the pesticide DDT at a level of molar concentration x. Letting y = 100/z, fit the model yi =β0+β1xi(xi+β2)+εi to the data given in Table 23.4.Test whether each parameter is equal to zero,
Following Bliss and James (1966), fit the model yi = (xiβ0)(xi+β1)+εi to the following data on the relationship between reaction velocity y and concentration of substrate x.x .138 .220 .291 .560 .766 1.460 y .148 .171 .234 .324 .390 .493 Test whether each parameter is equal to zero, give 99%
For pregnant women, Day (1966) modeled the relationship between weight z and week of gestation x with E(y) =β0+exp[β1+β2x]where y = 1/√z−z0 and z0 is the initial weight of the woman. For a woman with initial weight of 138 pounds, the data in Table 23.3 were recorded.Fit the model yi = β0
Fit the nonlinear regression (23.4.2) to the Hooker data and compare the fit of this model to the fit of the linearized model described in Section 7.3.
One way to compare the predictive ability of models is to compute R2 as the squared sample correlation betweens the values (yh, ˆ yh). Based on this criterion, will gamma regression always look better than its special case exponential regression?
Howwould you define fitted values, residuals, and “crude” standardized residuals(ones that do not account for variability associated with fitting the model) in gamma regression?
The time to an event is a measurement of time. Can you think of any reasons why time measurements should be treated differently from other measurements?
Reanalyze the Feigl-Zelen data by taking a log transform and using the methods of Chapter 15. How do the results change? Do you have any way to decide which analysis is superior?
Fit Model (22.1.4) to the Feigl-Zelen data using gamma regression and compare the Wald test of H0 : γ = −1 to the deviance (generalized likelihood ratio) test.
Find two data sets from earlier chapters that are good candidates for analysis by log-linear models and reanalyze them. (There are many data sets that consist of counts.)Table 21.16: Grille defectives.Treatment subscripts Case a b c d e f g h j Defectives 1 0 0 0 0 1 0 1 0 1 56 2 1 0 0 0 1 0 0 1 0
Reanalyze the data of Table 21.11 using a model based on TETRA and PREG rather than TL and PL. How much does deleting Case 4 affect the conclusions in either analysis?
Bisgaard and Fuller (1995) give the data in Table 21.16 on the numbers of defectives per grille in a process examined by Chrysler Motors Engineering. The data are from a fractional factorial design. The factors are: A, Mold Cycle; B, Viscosity; C, Mold Temp; D, Mold Table 21.14: Tool life
Watkins, Bergman, and Horton (1994) presented data on a complicated designed experiment that generated counts. The dependent variable is the number of ends cut by a tool.The experiment was a half replication of an experiment with five factors each at two levels, i.e., a half rep. of a 25 or a
For the n = 12 version of the mouse data, reanalyze it using the log of the dose as a predictor variable. Create a version of the data with n = 120 and reanalyze both the x and log(x) versions. Compare. Among other things compare the deviances and R2 values.
Use the results of Subsection 12.5.2 and the not-so-obvious fact thatΣni=1 ˆ pi/n = Σni=1 yi/n ≡ ¯ y to show that, for the mouse data of Section 20.1, the formula for R2 when n = 12, Nh ≡ N = 10 is R2 =[Σni=1( ˆ pi− ¯ y)(yi− ¯ y)]2[Σni=1( ˆ pi− ¯ y)2] [Σni=1(yi− ¯ y)2]but
Chapman, Masinda, and Strong (1995) give the data in Table 20.19. These Table 20.18: Heights and chest circumferences.Heights Chest 64–65 66–67 68–69 70–71 71–73 Total 39 142 442 341 117 20 1062 40 118 337 436 153 38 1082 Total 260 779 777 270 58 2144 Table 20.19: Unpopped kernels.Trials
Stigler (1986, p. 208) reports data from the Edinburgh Medical and Surgical Journal (1817) on the relationship between heights and chest circumferences for Scottish militia men. Measurements were made in inches. We concern ourselves with two groups of men, those with 39-inch chests and those with
Fit a logistic model to the data of Table 20.17 that relates probability of conviction to year. Is there evidence of a trend in the conviction rates over time? Is there evidence for a lack of fit?
Reconsider the data of Exercises 15.5.2, 15.5.3, and Table 15.10 from Smith, Gnanadesikan, and Hughes (1962). Perform a multivariate ACOVA on the data. Are the data repeated measures data? Is it reasonable to apply a split-plot model to the data? If so, do so.
People who really want to test their skill may wish to examine the data presented in Snedecor and Haber (1946) and repeated in Table 19.22. The experiment was to examine the effects of three cutting dates on asparagus. Six blocks were used. One plot was assigned a cutting date of June 1 (a), one a
Reanalyze the data of Example 17.4.1 assuming that the Disk-by-Window interaction is a random effect. Include estimates of both variance components.Table 19.22: Snedecor and Haber (1946) cutting dates on asparagus.Treatments Year a b c a b c a b c 29 201 301 362 185 236 341 209 226 357 30 230 296
Reanalyze Mandel’s (1972) data from Example 12.4.1 and Table 12.4 assuming that the five laboratories are a random sample from a population of laboratories. Include estimates of both variance components.
In Exercise 16.4.1 and Table 16.19 we presented Baten’s (1956) data on lengths of steel bars. The bars were made with one of two heat treatments (W, L) and cut on one of four screw machines (A, B, C, D) at one of three times of day (8 am, 11 am, 3 pm). There are Table 19.21: Gear test data.Volume
Day and del Priore (1953) report data from an experiment on the noise generated by various reduction gear designs. The data were collected because of the Navy’s interest in building quiet submarines. Primary interest focused on the direction of lubricant application. Lubricants were applied
Wilm (1945) presented data involving the effect of logging on soil moisture deficits under a forest. Treatments consist of five intensities of logging. Treatments were identified as the volume of the trees left standing after logging that were larger than 9.6 inches in diameter. The logging
In Exercises 17.11.3, 17.11.4, and 18.7.1, we considered data from Cornell(1988) on scaled vinyl thicknesses. Exercise 17.11.3 involved five blends of vinyl and we discussed the fact that the production process was set up eight times with a group of five blends run on each setting. The eight
Consider the milk production data in Table 18.8 and the corresponding analysis of variance in Table 18.10. Relative to the periods, the squares on the left of Table 11.8 always have treatment A followed by B, B followed by C, and C followed by A. The squares on the right always have treatment A
Exercises 17.11.7, 17.11.8, 17.11.9, and the previous exercise used subsets of data reported in Garner (1956). The experiment was designed to examine differences among operators and machines when using Suter hydrostatic pressure-testing machines. No interaction between machines and operators was
As in Exercise 17.11.7, we consider differences in hydrostatic pressure tests due to operators. Table 18.13 contains two Latin squares. Analyzing these together, give an appropriate analysis of variance table and report on any differences that can be established among the operators.
Consider the milk production data in Table 18.8 and the corresponding analysis of variance in Table 18.9. Relative to the periods, the squares on the left of Table 18.8 always Table 18.12: Tensile strength of uniform twill.o1 o2 o3 m1 m2 m3 m4 m1 m2 m3 m4 m1 m2 m3 m4 s1 18 7 5 9 12 16 15 9 18 13 10
Garner (1956) presented data on the tensile strength of fabrics as measured with Scott testingmachines. The experimental procedure involved selecting eight 4×100-inch strips from available stocks of uniform twill, type I. Each strip was divided into sixteen 4×6 inch samples(with some left over).
The process condition treatments in Exercise 17.11.3 on vinyl thickness had factorial treatment structure. Give the factorial analysis of variance table for the data. The data are repeated below.Rate High Low Low High Temp Low High Low High Rep. 1 7.8 11.0 7.4 11.0 Rep. 2 7.6 8.8 7.0 9.2
The data in Exercises 14.5.1, 14.5.3, and 16.4.3 were all balanced incomplete block designs. Determine the values of t, r,b, k, and λ for each experiment.
George Snedecor (1945a) asked for the appropriate variance estimate in the following problem. One of six treatments was applied to the 10 hens contained in each of 12 cages. Each treatment was randomly assigned to two cages. The data were the number of eggs laid by each hen.(a) What should you tell
Table 17.23 presents data given from Nelson (1993) on disk drives from a Graeco-Latin square design (see Exercise 17.10.9). The experiment was planned to investigate the effect of four different substrates on the drives. The dependent variable is the amplitude of a signal read from the disk where
Table 17.21 is incomplete. The data were actually obtained from a Graeco-Latin square that incorporates four different operators as well as the four different machines. The Table 17.21: Hydrostatic pressure tests: Machine, yield.2 4 3 1 39.0 39.0 41.0 41.0 1 3 4 2 36.5 42.5 40.5 38.5 4 2 1 3 40.0
Table 17.21 contains data similar to that in the previous exercise except that in this Latin square differences among four machines: 1, 2, 3, 4, were investigated rather than differences among operators. Machines 1 and 2 were operated with a hand lever, while machines 3 and 4 were operated with a
An experiment was conducted to examine differences among operators of Suter hydrostatic testing machines. These machines are used to test the water repellency of squares of fabric. One large square of fabric was available but its water repellency was thought to vary along the length (warp) and
In the study of the optical emission spectrometer discussed in Example 17.4.1 and Table 17.1, the target value for readings was 0.89. Subtract 0.89 from each observation and repeat the analysis.What new questions are of interest?Which aspects of the analysis have changed and which have not?
Table 17.19 presents data on yields of cowpea hay. Four treatments are of interest, variety I of hay was planted 4 inches apart (I4), variety I of hay was planted 8 inches apart(I8), variety II of hay was planted 4 inches apart (II4), and variety II of hay was planted 8 inches apart (II8). Three
Johnson (1978) and Mandel and Lashof (1987) present data on measurements of P2O5 (phosphorous pentoxide) in fertilizers. Table 17.18 presents data for five fertilizers, each analyzed in five labs. Our interest is in differences among the labs. Analyze the data.Table 17.19: Cowpea hay yields.Block
In data related to that of the previous problem, Cornell (1988) has scaled thickness values for vinyl under four different process conditions. The process conditions were A, high rate of extrusion, low drying temperature; B, low rate of extrusion, high drying temperature; C, low rate of extrusion,
Cornell (1988) considered data on scaled thickness values for five formulations of vinyl designed for use in automobile seat covers. Eight groups of material were prepared.The production process was then set up and the five formulations run with the first group. The production process was then
Snedecor (1945b) presented data on a spray for killing adult flies as they emerged from a breeding medium. The data were numbers of adults found in cages that were set over the medium containers. The treatments were different levels of the spray’s active ingredient, namely 0, 4, 8, and 16 units.
Using the notation of Section 16.1, write the models [A0][A1][C],[A0][A1][C] A21 = A31, and [A0][A1][C] A21 = A31,A20 = A30 in matrix form. (Hint: To obtain[A0][A1][C] A21 = A31 from [A0][A1][C], replace the two columns of X corresponding to A21 and A31 with one column consisting of their sum.) Use
The data of Table 16.21 were presented in Finney (1964) and Bliss (1947).The observations are serum calcium values of dogs after they have been injected with a dose of parathyroid extract. The doses are the treatments and they have factorial structure. One factor involves using either the standard
Bethea et al. (1985) reported data on an experiment to determine the effectiveness of four adhesive systems for bonding insulation to a chamber. The adhesives were applied both with and without a primer. Tests of peel-strength were conducted on two different thicknesses Table 16.19: Steel bar
Baten (1956) presented data on lengths of steel bars. An excessive number of bars had recently failed to meet specifications and the experiment was conducted to identify the causes of this problem. The bars were made with one of two heat treatments (W, L) and cut on one of four screw machines (A,
Consider the analysis of covariance for a one-way ANOVA with one covariate.Find the form for a 99% prediction interval for an observation, say, from the first treatment group with a given covariate value z.EXERCISE 15.5.9. Assume that in Model (15.1.2), Cov(y¯i·,γˆ) = 0. Show that Var aΣi=1λi
Write models (15.1.1), (15.1.2), and (15.1.3) in matrix form. For each model use a regression program on the heart weight data of Table 15.1 to find 95% and 99% prediction intervals for a male and a female each with body weight of 3.0. Hint: Use models without intercepts whenever possible.
Referring back to Subsection 7.3.3, test the need for a power transformation in each of the following problems from the previous chapter. Use all three constructed variables on each data set and compare results.(a) Exercise 14.5.1.(b) Exercise 14.5.2.(c) Exercise 14.5.3.(d) Exercise 14.5.4.Table
Apply Shillington’s test to the data of Exercise 9.12.3 and Table 9.3. The challenge is to come up with some method of identifying near replicates. (A clustering algorithm is a good idea but beyond the scope of this book.)
The data of Exercise 14.5.1 and Table 14.8 involved two factors, one of which had unequally spaced quantitative levels. Find the smallest polynomial that gives an adequate fit in place of treating “days in storage” as a factor variable.
Smith, Gnanadesikan, and Hughes (1962) also give data on the variable y2 that measures chloride in the urine of young men. These data are also reported in Table 15.10. As in the previous problem, the men were divided into four categories based on obesity. Perform an analysis of covariance on y2
Smith, Gnanadesikan, and Hughes (1962) gave data on urine characteristics of young men. The men were divided into four categories based on obesity. The data contain a covariate z that measures specific gravity. The dependent variable is y1; it measures pigment creatinine.These variables are
Table 15.9 contains data from Sulzberger (1953) and Williams (1959) on y, the maximum compressive strength parallel to the grain of wood from ten hoop pine trees. The data also include the temperature of the evaluation and a covariate z, the moisture content of the wood.Analyze the data. Examine
Explain how dropping the last term out of Model (14.4.7) gives results that are different from dropping the indicator for the last factor level out of a one-way ANOVA model with four groups. Focus on the intercept.
Repeat the analyses of this chapter after eliminating Litter I from the data in Table 14.1. This requires extending the ideas on homologous factors to situations with unequal numbers of factor levels.
Repeat the analyses of this chapter after eliminating Litter I and Mother J from the data in Table 14.1.
Repeat the analyses of this chapter after eliminating Litter I and Mother I from the data in Table 14.1.
Garner (1956) presented data on the tensile strength of fabrics. Here we consider a subset of the data. The complete data and a more extensive discussion of the experimental procedure are given in Exercise 18.7.2. The experiment involved testing fabric strengths on four different machines. Eight
Nelson (1993) presents data on the average access times for various disk drives. The disk drives are five brands of half-height fixed drives. The performance of disk drives depends on the computer in which they are installed. The computers could only hold four disk Table 14.9: Percentage of
Inman et al. (1992) report data on the percentages of Manganese (Mn) in various samples as determined by a spectrometer. Ten samples were used and the percentage of Mn in each sample was determined by each of 4 operators. The data are given in Table 14.9. The operators actually made two readings;
Cochran and Cox (1957) presented data from Pauline Paul on the effect of cold storage on roast beef tenderness. Treatments are labeled A through F and consist of 0, 1, 2, 4, 9, and 18 days of storage, respectively. The data are tenderness scores and are presented in Table 14.8.Table 14.7: Cp
Restate the least significant difference method in terms of testing Biggest, Full, Reduced, and Smallest models.
Use Scheff´e’s method with α = 0.05 and the data of Exercise 12.7.9 to test the significance of the contrast Age 0.5 1.0 4.0 4.5 5.0 5.5 6.0 Coeff. −5 −5 2 2 2 2 2
For the Cushing’s syndrome data of Exercise 12.7.8, use all appropriate methods to compare all pairwise differences among the three groups. Pick an α level but clearly state the level chosen.
For the weight gain data of Exercise 12.7.7, use the LSD, Bonferroni, and Scheff´e methods to test whether the following contrasts are zero: 1) the contrast that compares the two drugs and 2) the contrast that compares the control with the average of the two drugs. Pick anα level but clearly
In Exercise 12.7.6 on the peel-strength of different adhesive systems, parts(b) and (c) amount to doing LSD multiple comparisons for all pairs of systems. Compare the LSD results with the results obtained using Tukey’s methods with α = .01.
In Exercise 12.7.5 on the stress of four types of rubber, an outlier was noted in material B. Redo the multiple comparisons of the previous problem eliminating the outlier and using only the methods that are still applicable.
Exercise 12.7.4 contained data on stress measurements for four different types of rubber. Four observations were taken on each type of rubber; the means are repeated below,Material A B C D Mean 26.4425 26.0225 23.5325 29.9600 and the sample variance of the 16 observations is 14.730793. Test for
Use Bonferroni’s method with an α near 0.01 to give simultaneous confidence intervals for the mean weight in each height group for Exercise 12.7.3.
Use Scheff´e’s method with α = 0.01 to test whether the contrast in Exercise 12.7.2d is zero.
Exercise 12.7.1 involved measurements from different laboratories on the stress at 600% elongation for a certain type of rubber. The summary statistics are repeated in Table 13.1. Ignoring any reservations you may have about the appropriateness of the analysis of variance model for these data,
Prove formulas (12.5.3) and (12.5.4).
Conover (1971, p. 326) presented data on the amount of iron found in the livers of white rats. Fifty rats were randomly divided into five groups of ten and each group was given a different diet. We analyze the logs of the original data. The total sample variance of the 50 observations is 0.521767
Suppose a one-way ANOVA involves four diet treatments: Control, Beef, Pork, Lima Beans, and Soy Beans. As in Subsection 12.4.1, construct a reasonable hierarchy of models that involves four rows, one of which involves a semicolon.
Suppose a one-way ANOVA involves four diet treatments: Control, Beef A, Beef B, Pork, and Beans. As in Subsection 12.4.1, construct a reasonable hierarchy of models to examine that involves five rows and no semicolons.
Recall that if Z ∼ N(0,1) and W ∼ χ 2(r) with Z and W independent, then by Definition 2.1.3, ZW/r has a t(r) distribution. Also recall that in a one-way ANOVA with independent normal errors, a contrast has aΣi=1λi ¯ yi· ∼ N aΣi=1λiμi,σ 2 aΣi=1λ 2 iNi,SSE σ 2 ∼ χ 2(dfE), and
Shewhart (1939, p. 69) also presented the gravitational constant data of Heyl(1930) that was considered in the previous problem, but Shewhart reports six observations for gold instead of five. Shewhart’s data are given below. Analyze these data and compare your results to those of the previous
Lehmann (1975), citing Heyl (1930) and Brownlee (1960), considered data on determining the gravitational constant of three elements: gold, platinum, and glass. The data Lehmann gives are the third and fourth decimal places in five determinations of the gravitational constant. Analyze the following
Draper and Smith (1966, p. 41) considered data on the relationship between Table 12.18: Tetrahydrocortisone values for patients with Cushing’s syndrome.a b c 3.1 8.3 15.4 10.2 3.0 3.8 7.7 9.2 1.9 3.9 6.5 9.6 3.8 7.8 5.7 53.8 4.1 9.1 13.6 15.8 1.9 Table 12.19: Age and costs of maintenance for
Aitchison and Dunsmore (1975) presented data on Cushing’s syndrome.Cushing’s syndrome is a condition in which the adrenal cortex overproduces cortisol. Patients are divided into one of three groups based on the cause of the syndrome: a—adenoma, b— bilateral hyperplasia, and c—carcinoma.
Table 12.17 contains weight gains of rats from Box (1950). The rats were given either Thyroxin or Thiouracil or were in a control group. Do a complete analysis of variance on the data. Give the model, check assumptions, make residual plots, give the ANOVA table, and examine appropriate
Bethea et al. (1985) reported data on an experiment to determine the effectiveness of four adhesive systems for bonding insulation to a chamber. The data are a measure of the peel-strength of the adhesives and are presented in Table 12.16. A disturbing aspect of these data is that the values for
In Exercise 12.7.4 on the stress of four types of rubber, the observations on material B were 22.96, 22.93, 22.49, and 35.71. Redo the analysis, eliminating the outlier. The sample variance of the 15 remaining observations is 9.3052838.
In addition to the data discussed earlier, Mandel (1972) reported data from one laboratory on four different types of rubber. Four observations were taken on each type of rubber. The means are given below.Material A B C D Mean 26.4425 26.0225 23.5325 29.9600 The sample variance of the 16
Table 12.15 gives summary statistics on heights and weights of people. Give the analysis of variance table and test for differences among the four groups. Give a 99% confidence interval for the mean weight of people in the 72-inch height group.
Snedecor and Cochran (1967, Section 6.18) presented data obtained in 1942 from South Dakota on the relationship between the size of farms (in acres) and the number of acres planted in corn. Summary statistics are presented in Table 12.14. Note that the sample standard deviations rather than the
In addition to the data in Table 12.4, Mandel (1972) reported stress test data from five additional laboratories. Summary statistics are given in Table 12.13. Based on just these five additional labs, compute the analysis of variance table and test for differences in means between all pairs of
Do a principal components regression on the body fat data of Exercise 9.12.6
Do a principal components regression on the pollution data of Exercise 9.12.5.
Do a principal components regression on the Chapman data of Exercise 9.12.4.
Do a principal components regression on the Prater data from Exercise 9.12.3.
Do a principal components regression on the Younger data from Exercise 9.12.1.
Using eigenvalues, discuss the level of collinearity in:(a) the Younger data from Exercise 9.12.1,(b) the Prater data from Exercise 9.12.3,(c) the Chapman data of Exercise 9.12.4,(d) the pollution data from Exercise 9.12.5,(e) the body fat data of Exercise 9.12.6.
Use Proposition 1.2.11 to show that E(AY +c) = AE(Y)+c and Cov(AY +c) = ACov(Y)A.

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Analysis Of Variance Design And Regression 2nd Edition Ronald Christensen - Solutions

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