A study was done to assess the cost effectiveness of driving a four-door sedan instead of a van or an SUV (sports utility vehicle). The continuous variables are odometer reading and octane of the gasoline used. The response variable is miles per gallon. The data are presented here.
(a) Fit a linear regression model including two indicator variables. Use (0, 0) to denote the four door sedan.
(b) Which type of vehicle appears to get the best gas mileage?
(c) Discuss the difference between a van and an SUV in terms of gas mileage.
MPG Car Type Odometer 75,000 60,000 88,000 15,000 25,000 35,000 102,000 98,000 56,000 72,000 14,500 22,000 66,500 35,000 97,500 65,500 42,000 65,000 55,500 26,500 11,500 38,000 77,500 19,500 87,000 Octane 34.5 33.3 sedan sedan sedan 87.5 87.5 78.0 78.0 30.4 32.8 sedan sedan 35.0 90.0 29.0 sedan 78.0 32.5 sedan 90.0 sedan 29.6 16.8 87.5 87.5 90.0 van 19.2 van 22.6 van 87.5 24.4 van 90.0 20.7 van 78.0 25.1 18.8 90.0 87.5 van van 15.8 van 78.0 17.4 van 78.0 15.6 SUV 78.0 17.3 SUV 87.5 20.8 22.2 SUV SUV 87.5 90.0 16.5 SUV 78.0 21.3 SUV 90.0 20.7 SUV 78.0 24.1 SUV 90.0
> An experiment was conducted to compare three types of coating materials for copper wire. The purpose of the coating is to eliminate “flaws” in the wire. Ten different specimens of length 5 millimeters were randomly ass
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> The following data represent the final grades obtained by 5 students in mathematics, English, French, and biology: Test the hypothesis that the courses are of equal difficulty. Use a P-value in your conclusions and discuss your findings. Subject S
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> Do Duncan’s test for paired comparisons for the data of Exercise 13.6 on page 519. Discuss the results. Exercise 13.6: A study measured the sorption (either absorption or adsorption) rates of three different types of organic chemical s
> The printout in Figure 13.5 on page 532 gives information on Duncan’s test, using PROC GLM in SAS, for the aggregate data in Example 13.1. Give conclusions regarding paired comparisons using Duncan’s test results. Fig
> The following table (from A. Hald, Statistical Theory with Engineering Applications, John Wiley & Sons, New York, 1952) gives tensile strengths (in deviations from 340) for wires taken from nine cables to be used for a high-voltage network. Each cabl
> A random variable X follows an exponential distribution with mean 1/β. Assume the prior distribution of β is another exponential distribution with mean 2.5. Determine the Bayes estimate of β under the absolute-error loss function.
> The data in the following table represent the number of hours of relief provided by five different brands of headache tablets administered to 25 subjects experiencing fevers of 38â—¦C or more. Perform the analysis of variance and test t
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> In the study An Evaluation of the Removal Method for Estimating Benthic Populations and Diversity conducted by Virginia Tech on the Jackson River, 5 different sampling procedures were used to determine the species counts. Twenty samples were selected at
> An investigation was conducted to determine the source of reduction in yield of a certain chemical product. It was known that the loss in yield occurred in the mother liquor, that is, the material removed at the filtration stage. It was thought that diff
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> The study Loss of Nitrogen Through Sweat by Preadolescent Boys Consuming Three Levels of Dietary Protein was conducted by the Department of Human Nutrition and Foods at Virginia Tech to determine perspiration nitrogen loss at various dietary protein leve
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> Consider the data of Review Exercise 13.45 on page 555. Make significance tests on the following contrasts: (a) B versus A, C, and D; (b) C versus A and D; (c) A versus D. Exercise 13.45: Four laboratories are being used to perform chemical analysis. Sa
> Use Bartlett’s test at the 0.05 level of significance to test for homogeneity of variances in Exercise 13.6 on page 519. Exercise 13.6: A study measured the sorption (either absorption or adsorption) rates of three different types of o
> A random variable X follows a negative binomial distribution with parameters k = 5 and p [i.e.,b ∗ (x; 5, p)]. Furthermore, we know that p follows a uniform distribution on the interval (0, 1). Find the Bayes estimate of p under the squared-error loss fu
> Use Cochran’s test at the 0.01 level of significance to test for homogeneity of variances in Exercise 13.4 on page 519. Exercise 13.4: Immobilization of free-ranging white-tailed deer by drugs allows researchers the opportunity to clos
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> (a) Fit a multiple regression equation of the form μY |x = β0 + β1x + β2x2 to the data of Example 11.8 on page 420. (b) Estimate the yield of the chemical reaction for a temperature of 225 ◦ C.
> The following is a set of coded experimental data on the compressive strength of a particular alloy at various values of the concentration of some additive: (a) Estimate the quadratic regression equation μY |x = β0 + Î&s
> An experiment was conducted in order to determine if cerebral blood flow in human beings can be predicted from arterial oxygen tension (millimeters of mercury). Fifteen patients participated in the study, and the following data were collected: Estimat
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> A client from the Department of Mechanical Engineering approached the Consulting Center at Virginia Tech for help in analyzing an experiment dealing with gas turbine engines. The voltage output of engines was measured at various combinations of blade spe
> For the quadratic model of Exercise 12.51(b), give estimates of the variances and covariances of the estimates of β1 and β11. Exercise 12.51(b): The following is a set of data for y, the amount of money (in thousands of dollars)
> For the model of Exercise 12.50(a), test the hypothesis H0: β4 = 0, H1: β4 ≠0. Use a P-value in your conclusion. Exercise 12.50(a): For the punter data in Case Study 12.2, an additional response, â€
> Suppose that a sample consisting of 5, 6, 6, 7, 5, 6, 4, 9, 3, and 6 comes from a Poisson population with mean λ. Assume that the parameter λ follows a gamma distribution with parameters (3, 2). Under the squared-error loss function, find the Bayes estim
> The following is a set of data for y, the amount of money (in thousands of dollars) contributed to the alumni association at Virginia Tech by the Class of 1960, and x, the number of years following graduation: (a) Fit a regression model of the type &Ici
> For the punter data in Case Study 12.2, an additional response, “punting distance,” was also recorded. The average distance values for each of the 13 punters are given. (a) Using the distance data rather than the hang
> The electric power consumed each month by a chemical plant is thought to be related to the average ambient temperature x1, the number of days in the month x2, the average product purity x3, and the tons of product produced x4. The past yearâ€&
> Use the techniques of backward elimination with α = 0.05 to choose a prediction equation for the data of Table 12.8.
> For the data of Exercise 12.15 on page 452, use the techniques of (a) forward selection with a 0.05 level of significance to choose a linear regression model; (b) backward elimination with a 0.05 level of significance to choose a linear regression mode
> Consider the “hang time” punting data given in Case Study 12.2, using only the variables x2 and x3. (a) Verify the regression equation shown on page 489. (b) Predict punter hang time for a punter with LLS = 180 pounds and Power = 260 foot-pounds. (c) C
> A study was done to determine whether the gender of the credit card holder was an important factor in generating profit for a certain credit card company. The variables considered were income, the number of family members, and the gender of the card hold
> For the data set given in Exericise 12.16 on page 453, can the response be explained adequately by any two regressor variables? Discuss. Exericise 12.16: An engineer at a semiconductor company wants to model the relationship between the gain or hFE of a
> Consider the data of Exercise 12.13 on page 452. Can the response, wear, be explained adequately by a single variable (either viscosity or load) in an SLR rather than with the full two-variable regression? Justify your answer thoroughly through tests of
> Suppose that the time to failure T of a certain hinge is an exponential random variable with probability density f(t) = θe−θt, t>0. From prior experience we are led to believe that θ is a value
> In Example 12.8, a case is made for eliminating x1, powder temperature, from the model since the P-value based on the F-test is 0.2156 while P-values for x2 and x3 are near zero. (a) Reduce the model by eliminating x1, thereby producing a full and a rest
> Consider Example 12.3 on page 447. Compare the two competing models. First order: yi = β0 + β1x1i + β2x2i + €i, Second order: yi = β0 + β1x1i + β2x2i+ β11x21i + β22x22i + β12x1ix2i + i. Use R2adj in your comparison. Test H0 : β11 = β22 =β12 = 0. In addit
> Consider Example 12.4. Figure 12.1 on page 459 displays a SAS printout of an analysis of the model containing variables x1, x2, and x3. Focus on the confidence interval of the mean response μY at the (x1, x2, x3) locations representing the 13 data points
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> Consider the data of Exercise 11.55 on page 437. Fit a regression model using weight and drive ratio as explanatory variables. Compare this model with the SLR (simple linear regression) model using weight alone. Use R2, R2adj, and any t-statistics (or F-
> Consider the data for Exercise 12.36. Compute the following: R(β1 | β0), R(β1 | β0, β2, β3), R(β2 | β0, β1), R(β2 | β0, &I
> Consider the electric power data of Exercise 12.5 on page 450. Test H0: β1 = β2 = 0, making use of R(β1, β2 | β3, β4). Give a P-value, and draw conclusions. Exercise 12.5: The elec
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> Repeat Exercise 12.17 on page 461 using an F-statistic. Exercise 12.17: For the data of Exercise 12.2 on page 450, estimate σ2. Exercise 12.2: In Applied Spectroscopy, the infrared reflectance spectra properties of a viscous liquid used in
> For the model of Exercise 12.5 on page 450, test the hypothesis H0: β1 = β2 = 0, H1: β1 and β2 are not both zero. Exercise 12.5: The electric power consumed each month by a chemical plant is thought to be
> Suppose that in Example 18.7 the electrical firm does not have enough prior information regarding the population mean length of life to be able to assume a normal distribution for μ. The firm believes, however, that μ is surel
> Estimate the proportion of defectives being produced by the machine in Example 18.1 if the random sample of size 2 yields 2 defectives.
> This is an extract from Ducker, H., Head, A., McDonnell, B., O’Brien, R. and Richardson, S. (1998), A Creative Approach to Management Accounting: Case Studies in Management Accounting and Control, Sheffield Hallam University Press, ISBN
> This case study is taken from Ducker, J., Head, A., McDonnell, B., O'Brien, R. and Richardson, S. (1998), A Creative Approach to Management Accounting: Case Studies in Management Accounting and Control, Sheffield Hallam University Press, ISBN 086339 791
> Southern Paper Inc. is a global packaging company headquartered in the United States. The company was founded in the 1880s and has three principal business sectors – forest products, packaging and papers. The forest products division supplies lumber to t
> This case study is taken from Ducker, J., Head, A., McDonnell, B., O'Brien, R. and Richardson, S. (1998), A Creative Approach to Management Accounting: Case Studies in Management Accounting and Control, Sheffield Hallam University Press, ISBN 086339 791
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> The Application of Linear Programming to Management Accounting Midland Airport Ltd LEARNING OBJECTIVES: After reading this case study and completing the questions you will be able to: • Formulate the initial linear programming model (ob
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> This case study is taken from Ducker, J., Head, A., McDonnell, B., O'Brien, R. and Richardson, S. (1998), A Creative Approach to Management Accounting: Case Studies in Management Accounting and Control, Sheffield Hallam University Press, ISBN 086339 791
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