An article in Concrete Research ("Near Surface Characteristics of Concrete: Intrinsic Permeability," Vol. 41, 1989), presented data on compressive strength x and intrinsic permeability y of various concrete mixes and cures. Summary quantities are n = 14, Ey; = 572, y = 23,530, Ex = 43, Ex? = 157.42, andEx;y, = 1697.80. Assume that the two variables are related according to the simple linear regression model.
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- Second-Hand Smoke: Data Set 12 “Passive and Active Smoke” in Appendix B includes cotinine levels measured in a group of nonsmokers exposed to tobacco smoke (n = 40, Mean = 60.58 ng>mL, s = 138.08 ng>mL) and a group of nonsmokers not exposed to tobacco smoke (n = 40, Mean = 16.35 ng>mL, s = 62.53 ng>mL). Cotinine is a metabolite of nicotine, meaning that when nicotine is absorbed by the body, cotinine is produced. Use a 0.05 significance level to test the claim that nonsmokers exposed to tobacco smoke have a higher mean cotinine level than nonsmokers not exposed to tobacco smoke. Construct the confidence interval appropriate for the hypothesis test in part a. What do you conclude about the effects of second-hand smoke?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 (the amount of ammonia escaping) were measured with air flow x1, temperature x2, and acid concentration x3. y = 42, 37, 37, 28, 18, 18, 19, 20, 15, 14, 14, 13, 11, 12, 8, 7, 8, 8, 9, 15, 15 x1 = 80, 80, 75, 62, 62, 62, 62, 62, 58, 58, 58, 58, 58, 58, 50, 50, 50, 50, 50, 56, 70 x2 = 27, 27, 25, 24, 22, 23, 24, 24, 23, 18, 18, 17, 18, 19, 18, 18, 19, 19, 20, 20, 20 x3 = 89, 88, 90, 87, 87, 87, 93, 93, 87, 80, 89, 88, 82, 93, 89, 86, 72, 79, 80, 82, 91 (a) Fit a linear regression model relating the results of the stack loss to the three regressor variables. (b) Estimate σ2. (c) Find the standard error se(βj). (d) Use the model in part (a) to predict stack loss when x1 = 60, x2 = 26, and x3 = 85.The article “Effect of Varying Solids Concentration and Organic Loading on the Performance of Temperature Phased Anaerobic Digestion Process” (S. Vandenburgh and T. Ellis, Water Environment Research, 2002:142–148) discusses experiments to determine the effect of the solids concentration on the performance of treatment methods for wastewater sludge. In the first experiment, the concentration of solids (in g/L) was 43.94 ± 1.18. In the second experiment, which was independent of the first, the concentration was 48.66 ± 1.76. Estimate the difference in the concentration between the two experiments, and find the uncertainty in the estimate.
- Snowpacks contain a wide spectrum of pollutants thatmay represent environmental hazards. The article“Atmospheric PAH Deposition: Deposition Velocitiesand Washout Ratios” (J. of EnvironmentalEngineering, 2002: 186–195) focused on the depositionof polyaromatic hydrocarbons. The authors proposeda multiple regression model for relating depositionover a specified time period (y, in mg/m2) to tworather complicated predictors x1 (mg-sec/m3) and x2 (mg/m2), defined in terms of PAH air concentrations forvarious species, total time, and total amount of precipitation.Here is data on the species fluoranthene andcorresponding Minitab output:obs x1 x2 flth1 92017 .0026900 278.782 51830 .0030000 124.533 17236 .0000196 22.654 15776 .0000360 28.685 33462 .0004960 32.666 243500 .0038900 604.707 67793 .0011200 27.698 23471 .0006400 14.189 13948 .0004850 20.6410 8824 .0003660 20.6011 7699 .0002290 16.6112 15791 .0014100 15.0813 10239 .0004100 18.0514 43835 .0000960 99.7115 49793 .0000896 58.9716 40656…Is at least one of the two variables (weight and horsepower) significant in the model?A study is made for a particular allergy medication in order to determine the length of relief it provides Y (in hours) in relation to the dosage of medication X (in mg). For this reason, ten patients were given different doses of the medication and were asked to report back when the medication seemed to wear off. Patient #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 Dosage (x) Relief Hours (y) 3 3.5 4 5 6 6.5 7 8 8.5 9 9.1 5.5 12.3 9.2 14.2 16.8 22.0 18.3 24.5 22.7 (i) Draw a scatter diagram. (ii) Calculate the product moment correlation coefficient and comment on your answer. (iii) Construct the least squares regression line.
- An article in the Fire Safety Journal (“The Effect of Nozzle Design on the Stability and Performance of Turbulent Water Jets,” Vol. 4, August 1981) describes an experiment in which a shape factor was determined for several different nozzle designs at six levels of jet efflux velocity. Interest focused on potential differences between nozzle designs (blocks), with velocity considered as a nuisance variable. The data are shown below: Jet Efflux Velocity (m/s) Nozzle Design 11.73 14.37 16.59 20.43 23.46 28.74 1 0.78 0.80 0.81 0.75 0.77 0.78 2 0.85 0.85 0.92 0.86 0.81 0.83 3 0.93 0.92 0.95 0.89 0.89 0.83 4 1.14 0.97 0.98 0.88 0.86 0.83 5 0.97 0.86 0.78 0.76 0.76 0.75 1) Write the null hypothesis and the alternative hypothesis (for the factor). 2) Find the ANOVA table. (round to five decimal places). 3) What is your decision about the null hypothesis, consider ?. 4) If your decision in part (4) was reject , perform Tukey test to determine which pairwise means are…Below is are paired data X Y X Y X Y 22 18 19 25 11 17 15 16 7 36 5 6 9 31 6 27 26 45 7 8 46 45 19 30 4 2 11 18 8 18 45 36 27 18 1 3 19 12 19 37 9 7 26 16 36 42 18 28 35 47 25 20 46 21 49 22 16 12 9 25 A. Determine the price of the regression equation y '= BYX X + AYX by first determining the BYX data yx value from the data b. Find the value of correlation coefficients and write down the interpretation of the correlation coefficient with R2An article in the Journal of Applied Polymer Science (Vol. 56, pp. 471–476, 1995) studied the effect of the mole ratio of sebacic acid on the intrinsic viscosity of copolyesters.- The data follows: Viscosity 0.45 0.2 0.34 0.58 0.7 0.57 0.55 0.44 Mole ratio 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 (a) Construct a scatter diagram of the data.
- A U.S. state's Bureau of Economic Geology published a study on the economic impact of using carbon dioxide enhanced oil recovery (EOR) technology to extract additional oil from fields that have reached the end of their conventional economic life. The following table gives the approximate number of jobs for the citizens that would be created at various levels of recovery. Percent Recovery (%) 20 40 80 100 Jobs Created (Millions) 6 9 12 18 Find the regression line. j(r) = Use the regression line to estimate the number of jobs that would be created at a recovery level of 60%. _____ million jobsInterpret the estimated regression coefficient corresponding to the Z variable. Data Salary Education Experience Sex 29.7985 15 3 1 21.8219 4 0 0 22.8978 4 0 0 22.0917 1 1 0 21.8993 5 0 0 22.4829 3 1 1 28.0772 15 0 0 y=salary 23.6292 6 1 1 x1=education level in schooling years 32.3595 0 15 1 x2=experience level in employment level 21.794 1 0 0 d=sex (1 for male,0 for female) 19.8762 3 0 0 Ln(Y) = alpha +beta1X1 +Beta2X2+ Beta3D +Beta4Z +e 21.0253 3 0 0 where z =X2D 24.6323 0 5 1 19.0247 0 0 0 18.8857 0 0 0 21.8552 1 0 0 24.2675 6 1 0 18.7931 0 0 0 18.9276 0 0 0 23.4441 5 1 1 20.8047 2 0 0 18.26 0 0 0 20.6726 0 2 1 21.7815 3 0 0…The table below shows (lifetime) peptic ulcer rates (per 100 population), UU, for various family incomes, xx, as reported by the 1989 National Health Interview Survey. Income 4000 6000 8000 12000 16000 20000 30000 45000 60000 Ulcer rate 14.1 13.1 13.8 12.6 11.8 11.7 11.5 9.3 7.6 (a) Find the equation of the regression line. Ulcer rate, U(x)= . (b) Estimate the peptic ulcer rate for an income level of x0= 25000 according to the linear model in part (a). Ulcer rate, U(x0)= .