New Semester
Started
Get
50% OFF
Study Help!
--h --m --s
Claim Now
Question Answers
Textbooks
Find textbooks, questions and answers
Oops, something went wrong!
Change your search query and then try again
S
Books
FREE
Study Help
Expert Questions
Accounting
General Management
Mathematics
Finance
Organizational Behaviour
Law
Physics
Operating System
Management Leadership
Sociology
Programming
Marketing
Database
Computer Network
Economics
Textbooks Solutions
Accounting
Managerial Accounting
Management Leadership
Cost Accounting
Statistics
Business Law
Corporate Finance
Finance
Economics
Auditing
Tutors
Online Tutors
Find a Tutor
Hire a Tutor
Become a Tutor
AI Tutor
AI Study Planner
NEW
Sell Books
Search
Search
Sign In
Register
study help
business
descriptive statistics
Probability And Statistics For Engineers And Scientists 9th Edition Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying Ye - Solutions
Use Bartlett’s test at the 0.01 level of significance to test for homogeneity of variances in Exercise 13.5 on page 519.
For the data set in Exercise 13.7, use Bartlett’s test to check whether the variances are equal. Useα = 0.05.
It has been shown that the fertilizer magnesium ammonium phosphate, MgNH4PO4, is an effective supplier of the nutrients necessary for plant growth. The compounds supplied by this fertilizer are highly soluble in water, allowing the fertilizer to be applied directly on the soil surface or mixed with
A study measured the sorption (either absorption or adsorption) rates of three different types of organic chemical solvents. These solvents are used to clean industrial fabricated-metal parts and are potential hazardous waste. Independent samples from each type of solvent were tested, and their
The mitochondrial enzyme NADPH:NAD transhydrogenase of the common rat tapeworm (Hymenolepiasis diminuta) catalyzes hydrogen in the transfer from NADPH to NAD, producing NADH.This enzyme is known to serve a vital role in the tapeworm’s anaerobic metabolism, and it has recently been hypothesized
Immobilization of free-ranging white-tailed deer by drugs allows researchers the opportunity to closely examine the deer and gather valuable physiological information. In the study Influence of Physical Restraint and Restraint Facilitating Drugs on Blood Measurements of White-Tailed Deer and Other
In an article “Shelf-Space Strategy in Retailing,”published in Proceedings: Southern Marketing Association, the effect of shelf height on the supermarket sales of canned dog food is investigated. An experiment was conducted at a small supermarket for a period of 8 days on the sales of a single
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 38◦C or more. Perform the analysis of variance and test the hypothesis at the 0.05 level of significance that the mean
Six different machines are being considered for use in manufacturing rubber seals. The machines are being compared with respect to tensile strength of the product. A random sample of four seals from each machine is used to determine whether the mean tensile strength varies from machine to machine.
Case Study: Consider the data set for Exercise 12.12, page 452 (hospital data), repeated here(a) The SAS PROC REG outputs provided in Figures 12.9. and 12.10. supply a considerable amount of information. Goals are to do outlier detection and eventually determine which model terms are to be used in
Show that in choosing the so-called best subset model from a series of candidate models, choosing the model with the smallest s2 is equivalent to choosing the model with the smallest R2 adj.
A study was conducted to determine whether lifestyle changes could replace medication in reducing blood pressure among hypertensives. The factors considered were a healthy diet with an exercise program, the typical dosage of medication for hypertension, and no intervention. The pretreatment body
An article in the Journal of Pharmaceutical Sciences (Vol. 80, 1991) presents data on the mole fraction solubility of a solute at a constant temperature. Also measured are the dispersion x1 and dipolar and hydrogen bonding solubility parameters x2 and x3.A portion of the data is shown in the table
A carbon dioxide (CO2) flooding technique is used to extract crude oil. The CO2 floods oil pockets and displaces the crude oil. In an experiment, flow tubes are dipped into sample oil pockets containing a known amount of oil. Using three different values of
Consider the data of Review Exercise 12.64.Suppose it is of interest to add some “interaction”terms. Namely, consider the model yi = β0 + β1x1i + β2x2i + β3x3i + β12x1ix2i+ β13x1ix3i + β23x2ix3i + β123x1ix2ix3i + i.(a) Do we still have orthogonality? Comment.(b) With the fitted model in
In exercise physiology, an objective measure of aerobic fitness is the oxygen consumption in volume per unit body weight per unit time. Thirty-one individuals were used in an experiment in order to be able to model oxygen consumption against age in years (x1), weight in kilograms (x2), time to run
In a chemical engineering experiment dealing with heat transfer in a shallow fluidized bed, data are collected on the following four regressor variables: fluidizing gas flow rate, lb/hr (x1); supernatant gas flow rate, lb/hr (x2); supernatant gas inlet nozzle opening, millimeters (x3); and
A small experiment was conducted to fit a multiple regression equation relating the yield y to temperature x1, reaction time x2, and concentration of one of the reactants x3. Two levels of each variable were chosen, and measurements corresponding to the coded independent variables were recorded as
Show that, in a multiple linear regression data set,
In the Department of Fisheries and Wildlife at Virginia Tech, an experiment was conducted to study the effect of stream characteristics on fish biomass. The regressor variables are as follows: average depth (of 50 cells), x1; area of in-stream cover (i.e., undercut banks, logs, boulders, etc.), x2;
From a set of streptonignic dose-response data, an experimenter desires to develop a relationship between the proportion of lymphoblasts sampled that contain aberrations and the dosage of streptonignic.Five dosage levels were applied to the rabbits used for the experiment. The data are as follows
In Exercise 12.28, page 462, we have the following data concerning wear of a bearing:
For Exercise 12.57, test H0: β1 = β6 = 0. Give P-values and comment.
The pull strength of a wire bond is an important characteristic. The following data give information on pull strength y, die height x1, post height x2, loop height x3, wire length x4, bond width on the die x5, and bond width on the post x6. (From Myers, Montgomery, and Anderson-Cook, 2009.)(a) Fit
In an effort to model executive compensation for the year 1979, 33 firms were selected, and data were gathered on compensation, sales, profits, and employment. The following data were gathered for the year 1979.
Rayon whiteness is an important factor for scientists dealing in fabric quality. Whiteness is affected by pulp quality and other processing variables. Some of the variables include acid bath temperature, ◦C (x1);cascade acid concentration, % (x2); water temperature, ◦C (x3); sulfide
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 speed and sensor extension
For the quadratic model of Exercise 12.51(b), give estimates of the variances and covariances of the estimates of β1 and β11.
For the model of Exercise 12.50(a), test the hypothesis H0: β4 = 0, H1: β4 = 0.Use a P-value in your conclusion.
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:
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 times, estimate a multiple linear regression model of the type
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 model;(c) stepwise regression with a 0.05 level of
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) Construct a 95% confidence interval for the mean
For the data set given in Exericise 12.16. on page 453, can the response be explained adequately by any two regressor variables? Discuss.
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 hypotheses as well as comparison of the
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 restricted (or reduced) model, and compare them on
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+ β11x2 1i + β22x2 2i + β12x1ix2i + i.Use R2 adj in your comparison. Test H0 : β11 = β22 =β12 = 0. In addition, use the C.V. discussed in
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.Consider an item in the printout indicated
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, R2 adj, and any t-statistics (or F-statistics) you may need to compare the SLR
Consider the data for Exercise 12.36. Compute the following:
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.
A small experiment was conducted to fit a multiple regression equation relating the yield y to temperature x1, reaction time x2, and concentration of one of the reactants x3. Two levels of each variable were chosen, and measurements corresponding to the coded independent variables were recorded as
Repeat Exercise 12.17. on page 461 using an F-statistic.
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.
Test whether the regression explained by the model in Exercise 12.5. on page 450 is significant at the 0.01 level of significance.
Test whether the regression explained by the model in Exercise 12.1. on page 450 is significant at the 0.01 level of significance.
Compute and interpret the coefficient of multiple determination for the variables of Exercise 12.1. on page 450.
Use the data from Exercise 12.16 on page 453.(a) Estimate σ2 using the multiple regression of y on x1, x2, and x3,(b) Compute a 95% prediction interval for the observed gain with the three regressors at x1 = 15.0, x2 = 220.0, and x3 = 6.0.
should be changed? Why or why not?
Using the data from Exercise 12.28, test the following at the 0.05 level.(a) H0: β1 = 0 versus H1: β1 = 0;(b) H0: β2 = 0 versus H1: β2 = 0.(c) Do you have any reason to believe that the model in Exercise
Consider the following data from Exercise 12.13. on page 452.
Using the data of Exercise 12.5. on page 450 and the estimate of σ2 from Exercise 12.19, compute 95% confidence intervals for the predicted response and the mean response when x1 = 75, x2 = 24, x3 = 90, and x4 = 98.
For Exercise 12.8. on page 451, construct a 90%confidence interval for the mean compressive strength when the concentration is x = 19.5. and a quadratic model is used.
Using the data of Exercise 12.2. on page 450 and the estimate of σ2 from Exercise 12.17, compute 95% confidence intervals for the predicted response and the mean response when x1 = 900 and x2 = 1.00.
For the model of Exercise 12.1. on page 450, test the hypotheses that β1 = 2 against the alternative that β1 = 2. Use a P-value in your conclusion.
For the model of Exercise 12.2. on page 450, test the hypothesis that β1 = 0 at the 0.05 level of significance against the alternative that β1 = 0.
For the model of Exercise 12.7. on page 451,
Referring to Exercise 12.5 on page 450, find the estimate of(a) σ2 b2 ;(b) Cov(b1, b4).
Obtain estimates of the variances and the covariance of the estimators b1 and b2 of Exercise 12.2 on page 450.
For the data of Exercise 12.5 on page 450, estimate σ2.
For the data of Exercise 12.1 on page 450, estimate σ2.
For the data of Exercise 12.2 on page 450, estimate σ2.
An engineer at a semiconductor company wants to model the relationship between the gain or hFE of a device (y) and three parameters: emitter-RS(x1), base-RS (x2), and emitter-to-base-RS (x3). The data are shown below:(Data from Myers, Montgomery, and Anderson-Cook, 2009.)(a) Fit a multiple linear
The personnel department of a certain industrial firm used 12 subjects in a study to determine the relationship between job performance rating (y) and scores on four tests. The data are as follows:
Eleven student teachers took part in an evaluation program designed to measure teacher effectiveness and determine what factors are important. The response measure was a quantitative evaluation of the teacher. The regressor variables were scores on four standardized tests given to each teacher. The
A study was performed on a type of bearing to find the relationship of amount of wear y to x1 = oil viscosity and x2 = load. The following data
The following data reflect information from 17 U.S. Naval hospitals at various sites around the world.The regressors are workload variables, that is, items that result in the need for personnel in a hospital. A brief description of the variables is as follows:y = monthly labor-hours, x1 = average
An experiment was conducted to study the size of squid eaten by sharks and tuna. The regressor variables are characteristics of the beaks of the squid. The data are given as follows:
The following data are given:x 0123456 y 1453234(a) Fit the cubic model μY |x = β0 +β1x+β2x2 +β3x3.(b) Predict Y when x = 2.
(a) Fit a multiple regression equation of the form μY |x = β0 + β1x1 + 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 + β1x + β2x2.(b) Test for lack of fit of the model.
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:
An experiment was conducted on a new model of a particular make of automobile to determine the stopping distance at various speeds. The following data were recorded.Speed, v (km/hr) 35 50 65 80 95 110 Stopping Distance, d (m) 16 26 41 62 88 119(a) Fit a multiple regression curve of the form μD|v
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 year’s historical data are available and are presented in the
An experiment was conducted to determine if the weight of an animal can be predicted after a given period of time on the basis of the initial weight of the animal and the amount of feed that was eaten. The following data, measured in kilograms, were recorded:(a) Fit a multiple regression equation
Suppose in Review Exercise 11.53 on page 437 that we were also given the number of class periods missed by the 12 students taking the chemistry course.The complete data are shown.(a) Fit a multiple linear regression equation of the form yˆ = b0 + b1x1 + b2x2.(b) Estimate the chemistry grade for a
In Applied Spectroscopy, the infrared reflectance spectra properties of a viscous liquid used in the electronics industry as a lubricant were studied. The designed experiment consisted of the effect of band frequency x1 and film thickness x2 on optical density y using a Perkin-Elmer Model 621
A set of experimental runs was made to determine a way of predicting cooking time y at various values of oven width x1 and flue temperature x2. The coded data were recorded as follows:Estimate the multiple linear regression equation μY |x1,x2 = β0 + β1x1 + β2x2.
Project: This project can be done in groups or as individuals. Each group or person must find a set of data, preferably but not restricted to their field of study. The data need to fit the regression framework with a regression variable x and a response variable y.Carefully make the assignment as
Consider the fictitious set of data shown below, where the line through the data is the fitted simple linear regression line. Sketch a residual plot.
Show the necessary steps in converting the equation r = b1 s/√Sxx to the equivalent form t = r
Suppose that an experimenter postulates a model of the type Yi = β0 + β1x1i + i, i = 1, 2, . . . , n, when in fact an additional variable, say x2, also contributes linearly to the response. The true model is then given by Yi = β0 + β1x1i + β2x2i + i, i = 1, 2, . . . , n.Compute the expected
In Review Exercise 11.62, the student was required to show that n i=1(yi − yˆi) = 0 for a standard simple linear regression model. Does the same hold for a model with zero intercept? Show why or why not.
Consider the situation of Review Exercise 11.62 but suppose n = 2 (i.e., only two data points are available). Give an argument that the least squares regression line will result in (y1 − yˆ1)=(y2 − yˆ2) = 0.Also show that for this case R2 = 1.0.
Show, in the case of a least squares fit to the simple linear regression model Yi = β0 + β1xi + i, i = 1, 2, . . . , n, that n i=1(yi − yˆi) = n i=1 ei = 0.
For a simple linear regression model Yi = β0 + β1xi + i, i = 1, 2, . . . , n, where the i are independent and normally distributed with zero means and equal variances σ2, show that Y¯and B1 =n i=1(xi − x¯)Yi ni=1(xi − x¯)2 have zero covariance.
Assuming that the i are independent and normally distributed with zero means and common variance σ2, show that B0, the least squares estimator ofβ0 in μY |x = β0 + β1x, is normally distributed with
For the simple linear regression model, prove that E(s2) = σ2.
Suppose a scientist postulates a model Yi = β0 + β1xi + i, i = 1, 2, . . . , n, and β0 is a known value, not necessarily zero.(a) What is the appropriate least squares estimator ofβ1? Justify your answer.(b) What is the variance of the slope estimator?
Physical fitness testing is an important aspect of athletic training. A common measure of the magnitude of cardiovascular fitness is the maximum volume of oxygen uptake during strenuous exercise. A study was conducted on 24 middle-aged men to determine the influence on oxygen uptake of the time
Observations on the yield of a chemical reaction taken at various temperatures were recorded as follows:(a) Plot the data.(b) Does it appear from the plot as if the relationship is linear?(c) Fit a simple linear regression and test for lack of fit.(d) Draw conclusions based on your result in (c).
Consider the vehicle data from Consumer Reports in Figure 11.30 on page 440. Weight is in tons, mileage in miles per gallon, and drive ratio is also indicated. A regression model was fitted relating weight x to mileage y. A partial SAS printout in Figure 11.30 on page 440 shows some of the results
The business section of the Washington Times in March of 1997 listed 21 different used computers and printers and their sale prices. Also listed was the average hover bid. Partial results from regression analysis using SAS software are shown in Figure 11.29 on page 439.(a) Explain the difference
The following data represent the chemistry grades for a random sample of 12 freshmen at a certain college along with their scores on an intelligence test administered while they were still seniors in high school.(a) Compute and interpret the sample correlation coefficient.(b) State necessary
An experiment was designed for the Department of Materials Engineering at Virginia Tech to study hydrogen embrittlement properties based on electrolytic hydrogen pressure measurements. The so- lution used was 0.1 N NaOH, and the material was a certain type of stainless steel. The cathodic charging
With reference to Exercise 11.9 on page 399, construct(a) a 95% confidence interval for the average weekly sales when $45 is spent on advertising;(b) a 95% prediction interval for the weekly sales when$45 is spent on advertising.
The amounts of solids removed from a particular material when exposed to drying periods of different lengths are as shown.
The Statistics Consulting Center at Virginia Tech analyzed data on normal woodchucks for the Department of Veterinary Medicine. The variables of interest were body weight in grams and heart weight in grams. It was desired to develop a linear regression equation in order to determine if there is a
With reference to Exercise 11.8 on page 399, construct(a) a 95% confidence interval for the average course grade of students who make a 35 on the placement test;(b) a 95% prediction interval for the course grade of a student who made a 35 on the placement test.
Showing 200 - 300
of 2250
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Last
Step by Step Answers
Get 50% OFF
Claim Now
