Bivariate data often arises from the use of two different techniques to measure the same quantity. As an example, the accompanying observations on x = hydrogen concentration (ppm) using a gas chromatography method and y = concentration using a new sensor method were read from a graph in the article “A New Method to Measure the Diffusible Hydrogen Content in Steel Weldments Using a Polymer Electrolyte-Bused Hydrogen Sensor” (Welding Res., July 1997: 251s–256s).
x | 47 | 62 | 65 | 70 | 70 | 78 | 95 | 100 | 114 | 118 |
y | 38 | 62 | 53 | 67 | 84 | 79 | 93 | 106 | 117 | 116 |
x | 124 | 127 | 140 | 140 | 140 | 150 | 152 | 164 | 198 | 221 |
y | 127 | 114 | 134 | 139 | 142 | 170 | 149 | 154 | 200 | 215 |
Construct u
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Chapter 12 Solutions
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- Foot ulcers are a common problem for people with diabetes. Higher skin temperatures on the foot indicate an increased risk of ulcers. The article "An Intelligent Insole for Diabetic Patients with the Loss of Protective Sensation" (Kimberly Anderson, M.S. Thesis, Colorado School of Mines), reports measurements of temperatures, in °F, of both feet for 181 diabetic patients. The results are presented in the following table. Left Foot Right Foot 80 80 85 85 75 80 88 86 89 87 87 82 78 78 88 89 89 90 76 81 89 86 87 82 78 78 80 81 87 82 86 85 76 80 88 89 Construct a scatterplot of the right foot temperature (y) versus the left foot temperature (x). Verify that a linear model is appropriate. b. Compute the least-squares line for predicting the right foot temperature from the left foot temperature. If the left foot temperatures of two patients differ by 2 degrees, by how much would you predict their right foot temperatures to differ? Predict the right foot temperature for a patient whose left…arrow_forwardFollowing are measurements of soil concentrations (in mg /kg) of chromium (Cr) and nickel (Ni) at20 sites in the area of Cleveland, Ohio. These data are taken from the article "Variation in NorthAmerican Regulatory Guidance for Heavy Metal Surface Soil Contamination at Commercial andIndustrial Sites" (A. Jennings and J. Ma, J. Environment Eng, 2007:587-609). Cr: 260 19 36 247 263 319 317 277 319 264 23 29 61 119 33 281 21 35 64 30Ni: 435 377 359 53 38 38 54 188 397 33 92 490 28 35 799 347 321 32 74 508 (a) Construct a histogram for each set of concentrations. (b) Find the 1st, 2nd and 3rd quartiles for the Cr concentrations (c) Find the 1st, 2nd and 3rd quartiles for the Ni concentrations.arrow_forwardFollowing are measurements of soil concentrations (in mg /kg) of chromium (Cr) and nickel (Ni) at20 sites in the area of Cleveland, Ohio. These data are taken from the article "Variation in NorthAmerican Regulatory Guidance for Heavy Metal Surface Soil Contamination at Commercial andIndustrial Sites" (A. Jennings and J. Ma, J. Environment Eng, 2007:587-609).Cr: 260 19 36 247 263 319 317 277 319 264 23 29 61 119 33 281 21 35 64 30Ni: 435 377 359 53 38 38 54 188 397 33 92 490 28 35 799 347 321 32 74 508 (d) Use these to construct comparative boxplots for the two sets of concentrations. (e) Using the boxplots, what differences can be seen between the two sets of concentrations?arrow_forward
- The article "Characteristics and Trends of River Discharge into Hudson, James, and Ungava Bays, 1964-2000" (S. Dery, M. Stieglitz, et al., Journal of Climate, 2005:2540-2557) presents measurements of discharge rate x (in kmlyr) andpeakflow y (in m/s) for 42 rivers that drain into the Hudson, James, and Ungava Bays. The data are shown in the following table: Discharge Peak Flow 94.24 4110.3 66.57 4961.7 59.79 10275.5 48.52 6616.9 40.00 7459.5 32.30 2784.4 31.20 3266.7 30.69 4368.7 26.65 1328.5 22.75 4437.6 21.20 1983.0 20.57 1320.1 19.77 1735.7 18.62 1944.1 17.96 3420.2 17.84 2655.3 16.06 3470.3 1561.6 14.69 11.63 869.8 11.19 936.8 11.08 1315.7 10.92 1727.1 9.94 768.1 7.86 483.3arrow_forwardThe depth of wetting of a soil is the depth to which water content will increase owing to extemal factors. The article "Discussion of Method for Evaluation of Depth of Wetting in Residential Areas" (J. Nelson, K. Chao, and D. Overton, Journal of Geotechnical and Geoenvironmental Engineering, 2011:293-296) discusses the relationship between depth of wetting beneath a structure and the age of the structure. The article presents measurements of depth of wetting, in meters, and the ages, in years, of 21 houses, as shown in the following table. Age Depth 7.6 4 4.6 6.1 9.1 3 4.3 7.3 5.2 10.4 15.5 5.8 10.7 4 5.5 6.1 10.7 10.4 4.6 7.0 6.1 14 16.8 10 9.1 8.8 Compute the least-squares line for predicting depth of wetting (y) from age (x). b. Identify a point with an unusually large x-value. Compute the least-squares line that results from deletion of this point. Identify another point which can be classified as an outlier. Compute the least-squares line that results from deletion of the outlier,…arrow_forwardThe efficiency ratio for a steel specimen immersed in a phosphating tank is the weight of the phosphate coating divided by the metal loss (both in mg/ft2). The article “Statistical Process Control of a Phosphate Coating Line” (Wire J. Intl., May 1997: 78–81) gave the accompanying data on tank temperature (x) and efficiency ratio (y).Temp. 170 172 173 174 174 175 176Ratio .84 1.31 1.42 1.03 1.07 1.08 1.04Temp. 177 180 180 180 180 180 181Ratio 1.80 1.45 1.60 1.61 2.13 2.15 .84Temp. 181 182 182 182 182 184 184Ratio 1.43 .90 1.81 1.94 2.68 1.49 2.52Temp. 185 186 188Ratio 3.00 1.87 3.08a. Construct stem-and-leaf displays of both temperature and efficiency ratio, and comment on interesting features.b. Is the value of efficiency ratio completely and uniquely determined by tank temperature? Explain your reasoning.c. Construct a scatterplot of the data. Does it appear that efficiency ratio could be very well predicted by the value of temperature? Explain your reasoning.arrow_forward
- The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens. TOST RBOT 4200 370 TOST RBOT 3575 3750 3700 340 375 315 4050 350 4870 4475 3450 400 375 285 (a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.) 2795 195 2725 3750 220 345 3275 290 Interpret the value of the sample correlation coefficient. O The value of r indicates that there is a strong, negative linear relationship between TOST and RBOT. O The value of r indicates that there is a strong, positive linear relationship between TOST and RBOT. O The value of r indicates that there is a weak, negative linear relationship between TOST and RBOT. O The value of r indicates that there is a weak, positive linear relationship between TOST and RBOT. (b) How…arrow_forwardBody Fat. In the paper “Total Body Composition by Dual- Photon (153 Gd) Absorptiometry” (American Journal of Clinical Nutrition, Vol. 40, pp. 834–839), R. Mazess et al. studied methods for quantifying body composition. Eighteen randomly selected adults were measured for percentage of body fat, using dual-photon absorptiometry. Each adult’s age and percentage of body fat are shown on the WeissStats site. a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d). b. Obtain the coefficient of determination. c. Determine the percentage of variation in the observed values of the response variable explained by the regression, and interpret your answer. d. State how useful the regression equation appears to be for making predictions.arrow_forwardThe Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations on x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens. TOST 4200 3600 3750 3675 4050 2745 RBOT 370 335 375 310 350 200 TOST 4870 4475 3450 2675 3750 3275 RBOT 400 370 285 230 345 290 (a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.) r3= Interpret the value of the sample correlation coefficient. O The value of rindicates that there is a weak, positive linear relationship between TOST and RBOT. O The value of r indicates that there is a strong, negative linear relationship between TOST and RBOT. O The value of r indicates that there is a weak, negative linear relationship between TOST and RBOT. O The value of rindicates that there is a strong, positive linear relationship between TOST and RBOT. (b)…arrow_forward
- The Turbine Oil Oxidation Test (TOST) and the Rotating Bomb Oxidation Test (RBOT) are two different procedures for evaluating the oxidation stability of steam turbine oils. An article reported the accompanying observations for x = TOST time (hr) and y = RBOT time (min) for 12 oil specimens. TOST 4200 3575 3750 3700 4050 2770 4870 4475 3450 2700 3750 3325 RBOT 370 345 375 310 350 205 400 375 285 220 345 280 (a) Calculate the value of the sample correlation coefficient. (Round your answer to four decimal places.)r = Interpret the value of the sample correlation coefficient. The value of r indicates that there is a strong, negative linear relationship between TOST and RBOT.The value of r indicates that there is a weak, positive linear relationship between TOST and RBOT. The value of r indicates that there is a strong, positive linear relationship between TOST and RBOT.The value of r indicates that there is a weak, negative…arrow_forwardWire electrical-discharge machining (WEDM) is a process used to manufacture conductive hard metal components. It uses a continuously moving wire that serves as an electrode. Coating on the wire electrode allows for cooling of the wire electrode core and provides animproved cutting performance. The article “High-Performance Wire Electrodes for Wire Electrical-Discharge Machining—A Review” (J. of Engr. Manuf.,2012: 1757–1773) gave the following sample observationson total coating layer thickness (in mm) of eightwire electrodes used for WEDM:21 16 29 35 42 24 24 25Calculate a 99% CI for the standard deviation of thecoating layer thickness distribution. Is this interval validwhatever the nature of the distribution? Explain.arrow_forwardStructural engineers use wireless sensor networks to monitor the condition of dams and bridges. The article "Statistical Analysis of Vibration Modes of a Suspension Bridge Using Spatially Dense Wireless Sensor Network" (S. Pakzad and G. Fenves, Journal of Structural Engineering, 2009:863-872) desaribes an experiment in which accelerometers were placed on the Golden Gate Bridge for the purpose of estimating vibration modes. For 18 vertical modes, the system was underdamped (damping ratio 1)? Explain why or why not f. e. For what damping ratio would you predict a frequency of 2.0?arrow_forward
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,