Questions and Answers of Applied Statistics and Probability

Consider the regression model fit to the X-ray inspection data in Exercise 12-15. Use rads as the response.(a) What proportion of total variability is explained by this model?(b) Construct a normal
Consider the NFL data in Exercise 12-21.(a) Find 95% confidence intervals on the regression coefficients.(b) What is the estimated standard error of μ̂Y|x0 when the percentage of completions is
Consider the stack loss data in Exercise 12-20.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 95% confidence interval on mean stack loss when x1 = 80, x2 = 25
Consider the regression model fit to the gray range modulation data in Exercise 12-19. Use the useful range as the response.(a) Calculate 99% confidence intervals on each regression coefficient.(b)
Consider the regression model fit to the nisin extraction data in Exercise 12-18.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 95% confidence interval on mean
Consider the regression model fit to the coal and limestone mixture data in Exercise 12-17. Use density as the response.(a) Calculate 90% confidence intervals on each regression coefficient.(b)
Consider the regression model fit to the arsenic data in Exercise 12-16. Use arsenic in nails as the response and age, drink use, and cook use as the regressors.(a) Calculate 99% confidence intervals
Consider the regression model fit to the X-ray inspection data in Exercise 12-15. Use rads as the response.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 99%
Consider the regression model fit to the shear strength of soil in Exercise 12-5.(a) Calculate 95% confidence intervals on each regression coefficient.(b) Calculate a 95% confidence interval on mean
Use the second-order polynomial regression model from Exercise 12-4,(a) Find a 95% confidence interval on both the first-order and the second-order term in this model.(b) Is zero in the confidence
Referring to the regression model from Exercise 12-3,(a) Find a 95% confidence interval for the coefficient of spending on higher education.(b) Is zero in the confidence interval you found in part
Using the regression from Exercise 12-2,(a) Find a 95% confidence interval for the coefficient of hourly 1 test.(b) Find a 95% confidence interval for the mean final grade for students who score 80
Using the regression model from Exercise 12-1,(a) Find a 95% confidence interval for the coefficient of height.(b) Find a 95% confidence interval for the mean percent of body fat for a man with a
Data from a hospital patient satisfaction survey were presented in Exercise 12-9.(a) Fit a regression model using only the patient age and severity regressors. Test the model from this exercise for
Data from a hospital patient satisfaction survey were presented in Exercise 12-9.(a) Test the model from this exercise for significance of regression. What conclusions can you draw if Î±
Consider the bearing wear data in Exercise 12-23.(a) For the model with no interaction, test for significance of regression using Î± = 0.05. What is the P-value for this test? What are
Exercise 12-2 presented a regression model to predict final grade from two hourly tests.(a) Test the hypotheses that each of the slopes is zero.(b) What is the value of R2 for this model?(c) What is
Constrained Least Squares. Suppose we wish to find the least squares estimator of a in the model y = XÎ² + Îµ subject to a set of equality constraints, say, TÎ² =
Consider the multiple linear regression model y = Xβ + ε. If β adenotes the least squares estimator of β, show that β = β + Re, where (X'X)-1 X'.
You have fit a regression model with two regressors to a data set that has 20 observations. The total sum of squares is 1000 and the model sum of squares is 750.(a) What is the value of R2 for this
An article in Technometrics (1974, Vol. 16, pp. 523€“531) considered the following stack-loss data from a plant oxidizing ammonia to nitric acid. Twenty-one daily responses of stack loss
Consider the NFL data in Exercise 12-21.(a) Test for significance of regression using Î± = 0.05. What is the P-value for this test?(b) Conduct the t-test for each regression coefficient.
Consider the regression model fit to the stack loss data in Exercise 12-20. Use stack loss as the response.(a) Test for significance of regression using Î± = 0.05. What is the P-value
Consider the regression model fit to the gray range modulation data in Exercise 12-19. Use the useful range as the response.(a) Test for significance of regression using Î± = 0.05. What
Consider the regression model fit to the nisin extraction data in Exercise 12-18. Use nisin extraction as the response.(a) Test for significance of regression using Î± = 0.05. What is
Consider the regression model fit to the X-ray inspection data in Exercise 12-15. Use rads as the response.(a) Test for significance of regression using α = 0.05. What is the P-value for this
Consider the regression model fit to the arsenic data in Exercise 12-16. Use arsenic in nails as the response and age, drink use, and cook use as the regressors.(a) Test for significance of
Consider the following computer output.(a) Fill in the missing quantities. You may use bounds for the P-values.(b) What conclusions can you draw about the significance of regression?(c) What
Consider the linear regression model from Exercise 12-4. Is the second-order term necessary in the regression model?Exercise 12-4Hsuie, Ma, and Tsai (€˜€˜Separation and
Consider the regression model of Exercise 12-3 attempting to predict the percent of engineers in the workforce from various spending variables.(a) Are any of the variables useful for prediction?
Exercise 12-2 presented a regression model to predict final grade from two hourly tests.(a) Test the hypotheses that each of the slopes is zero.(b) What is the value of R2 for this model?(c) What is
Recall the regression of percent of body fat on height and waist from Exercise 12-1. The simple regression model of percent of body fat on height alone shows the following:(a) Test whether the
Table E12-12 presents statistics for the National Hockey League teams from the 2008€“2009 season (The Sports Network). Fit a multiple linear regression model that relates wins to the
Table E12-11 presents quarterback ratings for the 2008 National Football League season (The Sports Network). (a) Fit a multiple regression model to relate the quarterback rating to the
An article in Optical Engineering [€œOperating Curve Extraction of a Correlator€™s Filter€ (2004, Vol. 43, pp. 2775€“2779)] reported on the use of an optical
An article in Biotechnology Progress (2001, Vol. 17, pp. 366€“368) reported on an experiment to investigate and optimize nisin extraction in aqueous two-phase systems (ATPS). The nisin
An article in IEEE Transactions on Instrumentation and Measurement (2001, Vol. 50, pp. 2033€“2040) reported on a study that had analyzed powdered mixtures of coal and limestone for
An article in Cancer Epidemiology, Biomarkers and Prevention (1996, Vol. 5, pp. 849€“852) reported on a pilot study to assess the use of toenail arsenic concentrations as an indicator of
An article in Electronic Packaging and Production (2002, Vol. 42) considered the effect of X-ray inspection of integrated circuits. The rads (radiation dose) were studied as a function of current (in
Table E12-3 provides the highway gasoline mileage test results for 2005 model year vehicles from DaimlerChrysler. The full table of data (available on the book€™s Web site) contains the
The data from a patient satisfaction survey in a hospital are in Table E12-1.The regressor variables are the patient€™s age, an illness severity index (higher values indicate greater
You have fit a multiple linear regression model and the (X'X)ˆ’1matrix is:(a) How many regressor variables are in this model?(b) If the error sum of squares is 307 and there are 15
Hsuie, Ma, and Tsai (‘‘Separation and Characterizations of Thermotropic Copolyesters of p-Hydroxybenzoic Acid, Sebacic Acid, and Hydroquinone,’’ (1995, Vol. 56) studied the effect of the
Can the percentage of the workforce who are engineers in each U.S. state be predicted by the amount of money spent in on higher education (as a percent of gross domestic product), on venture capital
A class of 63 students has two hourly exams and a final exam. How well do the two hourly exams predict performance on the final?The following are some quantities of interest:(a) Calculate the least
Exercise 11.1 described a regression model between percent of body fat (%BF) as measured by immersion and BMI from a study on 250 male subjects. The researchers also measured 13 physical
Table E11-21 shows the population and the average count of wood storks sighted per sample period for South Carolina from 1991 to 2004. Fit a regression line with population as the response and the
The data in Table E11-20 related diamond carats to purchase prices. It appeared in Singapore€™s Business Times, February 18, 2000.(a) Graph the data. What is the relation between carat and
Cesium atoms cooled by laser light could be used to build inexpensive atomic clocks. In a study reported in IEEE Transactions on Instrumentation and Measurement (2001, Vol. 50, pp.
Consider the propellant data is Exercise 11-13. Assume that strength less than 2100 psi is considered a failure. Relate propellant age to the probability of failure with a logistic regression
The World Health Organization defines obesity in adults as having a body mass index (BMI) higher than 30. Of the 250 men in the study mentioned in Exercise 11-1, 23 are by this definition obese. How
The vapor pressure of water at various temperatures is in Table E11-11:(a) Draw a scatter diagram of these data. What type of relationship seems appropriate in relating y to x?(b) Fit a simple linear
Consider the (x, y) data in Table E11-10. Calculate the correlation coefficient. Graph the data and comment on the relationship between x and y. Explain why the correlation coefficient does not
Refer to the NFL quarterback ratings data in Exercise 11-5.(a) Estimate the correlation coefficient between the ratings and the average yards per attempt.(b) Test the hypothesis H0: Ï = 0
The weight and systolic blood pressure of 26 randomly selected males in the age group 25 to 30 are shown in the Table E11-8. Assume that weight and blood pressure are jointly normally
Repeat Exercise 11-60 using an error term with a standard deviation of 4. What impact has increasing the error standard deviation had on the values of R2?(a) Fit the linear regression model by least
Refer to the data in Exercise 11-15 on oxygen demand. Find a 99% confidence interval on each of the following:(a) Î²1 (b) Î²0(c) Find a 95% confidence interval on mean BOD
Refer to the data in Exercise 11-14 on the microstructure of zirconia. Find a 95% confidence interval on each of the following:(a) Slope(b) Intercept(c) Mean length when x = 1500(d) Find a 95%
Show that by expanding etXin a power series and taking expectations term by term we may write the momentgenerating function asThus, the coefficient of tr / r! in this expansion is
A study was performed to investigate new automobile purchases. A sample of 20 families was selected. Each family was surveyed to determine the age of their oldest vehicle and their total family
Consider the simple linear regression model Y = β0 + β1x + ε, with E(e) = 0, V(e) = σ2, and the errors e uncorrelated.(a) Show that E(σ̂) = E(MSE) σ2. (b) Show that E(MSR) = σ2 + β12
Consider the following data. Suppose that the relation - ship between Y and x is hypothesized to be Y = (Î²0+ Î²1x + e)ˆ’ . 1 Fit an appropriate model to the data.
An article in the IEEE Transactions on Instrumentation and Measurement [€œDirect, Fast, and Accurate Measurement of VTand K of MOS Transistor Using VT-Sift Circuit€ (1991, Vol.
The market research department of a soft drink manufacturer is investigating the effectiveness of a price discount coupon on the purchase of a two-liter beverage product. A sample of 5500 customers
The compressive strength of an alloy fastener used in aircraft construction is being studied. Ten loads were selected over the range 2500€“4300 psi, and a number of fasteners were tested at
A study was conducted attempting to relate home ownership to family income. Twenty households were selected and family income was estimated along with information concerning home ownership (y = 1
Determine if the following models are intrinsically linear. If yes, determine the appropriate transformation to generate the linear model.(a) Y = β0 xβ1 ε(b) Y = 3 + 5x/x + ε(c) Y = β0 βx1
The monthly absolute estimate of global (land and ocean combined) temperature indexes (degrees C) in 2000 and 2001 (www.ncdc.noaa.gov/oa/climate/) are:(a) Graph the data and fit a regression line to
In an article in IEEE Transactions on Instrumentation and Measurement (2001, Vol. 50, pp. 986€“990), researchers reported on a study of the effects of reducing current draw in a magnetic
Suppose that data are obtained from 20 pairs of (x, y) and the sample correlation coefficient is 0.75.(a) Test the hypothesis that H0: ρ = 0 against H1: ρ> 0 with α = 0.05. Calculate the
Suppose that data are obtained from 20 pairs of (x, y) and the sample correlation coefficient is 0.8.(a) Test the hypothesis that H0: ρ = 0 against H1: ρ ≠ 0 with α = 0.05. Calculate the
Studentized Residuals. Show that the variance of the ith residual isThe ith studentized residual is defined as(a) Explain why ri has unit standard deviation.(b) Do the standardized residuals have
An article in the Journal of the American Statistical Association [€œMarkov Chain Monte Carlo Methods for Computing Bayes Factors: A Comparative Review€ (2001, Vol. 96, pp.
Refer to the compressive strength data in Exercise 11-3. Use the summary statistics provided to calculate R2 and provide a practical interpretation of this quantity.Exercise 11-3An article in
Consider the simple linear regression model y = 10 + 30x + ε where the random error term is normally and independently distributed with mean zero and standard deviation 1. Use software to generate a
Refer to the NFL quarterback ratings data in Exercise 11-5. Find a 95% confidence interval on each of the following:(a) Slope (b) Intercept(c) Mean rating when the average yards per attempt is
Using the regression from Exercise 11-2,(a) Find a 95% confidence interval for the slope.(b) Find a 95% confidence interval for the mean weight for a man 25 years old.(c) Find a 95% prediction
Using the regression from Exercise 11-1,(a) Find a 95% confidence interval for the slope.(b) Find a 95% confidence interval for the mean percent body fat for a man with a BMI of 25.(c) Find a 95%
Consider the data in Exercise 11-15 on y = oxygen demand and x = time.(a) Test for significance of regression using α = 0.01. Find the P-value for this test. What conclusions can you draw?(b)
An article in The Journal of Clinical Endocrinology and Metabolism [€œSimultaneous and Continuous 24-Hour Plasma and Cerebrospinal Fluid Leptin Measurements: Dissociation of Concentrations
Consider the data in Exercise 11-16 on y = deflection and x = stress level.(a) Test for significance of regression using α = 0.01. What is the P-value for this test? State the conclusions that
Consider the data from Exercise 11-9 on y = green liquor Na2S concentration and x = production in a paper mill.(a) Test for significance of regression using α = 0.05. Find the P-value for this
Consider the National Football League data in Exercise 11-5.(a) Test for significance of regression using α = 0.01. Find the P-value for this test. What conclusions can you draw?(b) Estimate the
Consider the following computer output.The regression equation isAnalysis of Variance(a) Fill in the missing information. You may use bounds for the P-values.(b) Can you conclude that the model
Consider the following computer output. The regression equation isAnalysis of Variance(a) Fill in the missing information. You may use bounds for the P-values.(b) Can you conclude that the model
Consider the simple linear regression model y = 10 + 25x + ε where the random error term is normally and independently distributed with mean zero and standard deviation 2. Use software to generate a
Suppose that in Exercise 11-24 weight is measured in kg instead of lbs.(a) How will the estimates of the slope and intercept change?(b) Estimate the error standard deviation.(c) Estimate the standard
Recall the regression of weight on age from Exercise 11-2.(a) Estimate the error standard deviation.(b) Estimate the standard deviation of the slope.(c) What is the value of the t-statistic for the
Recall the regression of percent body fat on BMI from Exercise 11-1.(a) Estimate the error standard deviation.(b) Estimate the standard deviation of the slope.(c) What is the value of the t-statistic
Suppose that we wish to fit a regression model for which the true regression line passes through the point (0, 0). The appropriate model is Y = Î²x + Îµ. Assume that we have n
Consider the regression model developed in Exercise 11-8. Suppose that engine displacement is measured in cubic centimeters instead of cubic inches.(a) Write the new regression model.(b) What change
In an article in Statistics and Computing [€œAn Iterative Monte Carlo Method for Nonconjugate Bayesian Analysis€ (1991, pp. 119€“128)], Carlin and Gelfand investigated
An article in Wood Science and Technology [€œCreep in Chipboard, Part 3: Initial Assessment of the Influence of Moisture Content and Level of Stressing on Rate of Creep and Time to
An article in the Journal of the Environmental Engineering Division [€œLeast Squares Estimates of BOD Parameters€ (1980, Vol. 106, pp. 1197€“1202)] took a sample from
An article in the Journal of the American Ceramic Society [€œRapid Hot-Pressing of Ultrafi ne PSZ Powders€ (1991, Vol. 74, pp. 1547€“1553)] considered the
A rocket motor is manufactured by bonding together two types of propellants, an igniter and a sustainer. The shear strength of the bond y is thought to be a linear function of the age of the
Table E11-3 presents the highway gasoline mileage performance and engine displacement for DaimlerChrysler vehicles for model year 2005 (U.S. Environmental Protection Agency).(a) Fit a simple linear
An article in Technometrics by S. C. Narula and J. F. Wellington [€œPrediction, Linear Regression, and a Minimum Sum of Relative Errors€ (1977, Vol. 19)] presents data on the
See Table E11-1 for data on the ratings of quarterbacks for the 2008 National Football League season (The Sports Network). It is suspected that the rating (y) is related to the average number of
An article in Concrete Research [“Near Surface Characteristics of Concrete: Intrinsic Permeability” (1989, Vol. 41)] presented data on compressive strength x and intrinsic permeability y of

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