Probability and Statistics for Engineering and the Sciences
9th Edition
ISBN: 9781305251809
Author: Jay L. Devore
Publisher: Cengage Learning
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 13.1, Problem 7E
a.
To determine
Perform a simple linear regression model and to find out the proportion of observed variation obtained from the model.
b.
To determine
Construct a
Whether the plot suggest the use of linear regression model is appropriate.
c.
To determine
Find the residuals, standardized residuals and construct residual plots.
Identify the suggestions from the plot and determine what type of
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
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…
Computer chips often contain surface imperfections.For a certain type of computer chip, theprobability mass function of the number of defects X is presented in the following table.
The 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,…
Chapter 13 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 13.1 - Suppose the variables x = commuting distance and y...Ch. 13.1 - Prob. 2ECh. 13.1 - Prob. 3ECh. 13.1 - Prob. 4ECh. 13.1 - As the air temperature drops, river water becomes...Ch. 13.1 - The accompanying scatterplot is based on data...Ch. 13.1 - Prob. 7ECh. 13.1 - Prob. 8ECh. 13.1 - Consider the following four (x, y) data sets; the...Ch. 13.1 - a. Show that i=1nei=0 when the eis are the...
Ch. 13.1 - Prob. 11ECh. 13.1 - Prob. 12ECh. 13.1 - Prob. 13ECh. 13.1 - If there is at least one x value at which more...Ch. 13.2 - No tortilla chip aficionado likes soggy chips, so...Ch. 13.2 - Polyester fiber ropes are increasingly being used...Ch. 13.2 - The following data on mass rate of burning x and...Ch. 13.2 - Failures in aircraft gas turbine engines due to...Ch. 13.2 - Prob. 19ECh. 13.2 - Prob. 20ECh. 13.2 - Mineral mining is one of the most important...Ch. 13.2 - Prob. 22ECh. 13.2 - Prob. 23ECh. 13.2 - Kyphosis refers to severe forward flexion of the...Ch. 13.2 - Prob. 25ECh. 13.3 - The following data on y 5 glucose concentration...Ch. 13.3 - The viscosity (y) of an oil was measured by a cone...Ch. 13.3 - Prob. 29ECh. 13.3 - The accompanying data was extracted from the...Ch. 13.3 - The accompanying data on y 5 energy output (W) and...Ch. 13.3 - Prob. 32ECh. 13.3 - Prob. 33ECh. 13.3 - The following data resulted from an experiment to...Ch. 13.3 - The article The Respiration in Air and in Water of...Ch. 13.4 - Cardiorespiratory fitness is widely recognized as...Ch. 13.4 - A trucking company considered a multiple...Ch. 13.4 - Let y = wear life of a bearing, x1 = oil...Ch. 13.4 - Let y = sales at a fast-food outlet (1000s of ),...Ch. 13.4 - The article cited in Exercise 49 of Chapter 7 gave...Ch. 13.4 - The article A Study of Factors Affecting the Human...Ch. 13.4 - An investigation of a die-casting process resulted...Ch. 13.4 - Prob. 43ECh. 13.4 - The accompanying Minitab regression output is...Ch. 13.4 - The article Analysis of the Modeling Methodologies...Ch. 13.4 - A regression analysis carried out to relate y =...Ch. 13.4 - Efficient design of certain types of municipal...Ch. 13.4 - An experiment to investigate the effects of a new...Ch. 13.4 - Prob. 49ECh. 13.4 - Prob. 50ECh. 13.4 - The article Optimization of Surface Roughness in...Ch. 13.4 - Utilization of sucrose as a carbon source for the...Ch. 13.4 - Prob. 53ECh. 13.4 - Prob. 54ECh. 13.5 - The article The Influence of Honing Process...Ch. 13.5 - Prob. 56ECh. 13.5 - In the accompanying table, we give the smallest...Ch. 13.5 - Prob. 58ECh. 13.5 - Prob. 59ECh. 13.5 - Pillar stability is a most important factor to...Ch. 13.5 - Prob. 61ECh. 13.5 - Prob. 62ECh. 13.5 - Prob. 63ECh. 13.5 - Prob. 64ECh. 13 - Curing concrete is known to be vulnerable to shock...Ch. 13 - Prob. 66SECh. 13 - The article Validation of the Rockport Fitness...Ch. 13 - Feature recognition from surface models of...Ch. 13 - Air pressure (psi) and temperature (F) were...Ch. 13 - An aeronautical engineering student carried out an...Ch. 13 - An ammonia bath is the one most widely used for...Ch. 13 - The article An Experimental Study of Resistance...Ch. 13 - The accompanying data on x = frequency (MHz) and y...Ch. 13 - Prob. 74SECh. 13 - Prob. 75SECh. 13 - The article Chemithermomechanical Pulp from Mixed...Ch. 13 - Prob. 77SECh. 13 - Prob. 78SECh. 13 - Prob. 79SECh. 13 - Prob. 80SECh. 13 - Prob. 81SECh. 13 - Prob. 82SECh. 13 - Prob. 83SE
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.Similar questions
- The 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_forwardThe article "Modeling Resilient Modulus and Temperature Correction for Saudi Roads" (H. Wahhab, I. Asi, and R. Ramadhan, Journal of Materials in Civil Engineering, 2001:298– 305) describes a study designed to predict the resilient modulus of pavement from physical properties. The following table presents data for the resilient modulus at 40°Cin10® kPa (y), the surface area of the aggregate in m²/kg (x1), and the softening point of the asphalt in °C (х). y X1 X2 1.48 5.77 60.5 1.70 7.45 74.2 2.03 8.14 67.6 2.86 8.73 70.0 2.43 7.12 64.6 3.06 6.89 65.3 2.44 8.64 66.2 1.29 6.58 64.1 3.53 9.10 68.6 1.04 8.06 58.8 1.88 5.93 63.2 1.90 8.17 62.1 1.76 9.84 68.9 2.82 7.17 72.2 1.00 7.78 54.1 The full quadratic model is y = + P,x, + PzX, + Pz*jXz + Pxx¡ + Bzx; + €. Which submodel of this full model do you believe is most appropriate? Justify your answer by fitting two or more models and comparing the results.arrow_forwardRecently there has been increased use of stainless steel claddings in industrial settings. Claddings are used to finish the exterior walls of a building and help weatherproof the structure. To ensure the quality of claddings, it is essential to know how welding parameters impact the cladding process. The authors of “Mathematical Modeling of Weld Bead Geometry, Quality, and Productivity for Stainless Steel Claddings Deposited by FCAW” (J. Mater. Engr. Perform., 2012: 1862–1872) in vestigated how y 5 deposition rate was influenced by x1 = feed rate (Wf , in m/min) and x2 = welding speed (S, in cm/min). The following 22 observations correspond to the experiment condition where applied voltage was less than 30v: y: 2.718 3.881 2.773 3.924 2.740 3.870 x1 : 17.0 10.0 7.0 10.0 7.0 10.0 x 2 : 30 30 50 50 30 30 y: 2.847 3.901 2.204 4.454 3.324 3.319 x1 : 7.0 10.0 5.5 11.5 8.5 8.5 x2 : 50 50 40 40 40 20 The whole data and Question parts are attachedarrow_forward
- A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 329.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 425.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 389.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 341.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 414.4 441.8 419.9 410.7 473.4 441.2 465.8 USE SALT Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. O Ho: M₁ = H₂ = 13 = H4 = 1₂ H₂: all five μ's are unequal O Ho: My H₂ H3 ‡ M4 # M5 H₂: at least two μ's are equal O Ho: My # H₂ H3 # H4 # H5 H₂: all five us are equal = = o Hỏi khi là không = 3 = Mà khô H₂: at least two μ's are unequal Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Sum of Squares Source Treatments Error…arrow_forwardA study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 315.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 405.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 399.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 353.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 417.4 441.8 419.9 410.7 473.4 441.2 465.8 n USE SALT Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. O Ho: H1# H2 # Hz# H4# H5 H: at least two µ's are equal O Ho: H1 = H2 = H3= H4= H5 H: at least two u's are unequal O Ho: H1 # H2 # Hz# H4# Hs H: all five u's are equal O Ho: H1 = H2 = Hz3 = H4= Hs H: all five u,'s are unequal Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Degrees of freedom Sum of Squares Mean Source…arrow_forwardSilicon chip manufacturers require the use of so-called "clean rooms" in which the air is filtered in a special way to keep the number of dust particles to a minimum. Five air samples were taken in each room and the dust level was measured on a scale of 1 (low) to 10 (high). Room 1 Room 2 Room 3 5 3 1 6.5 6 1.5 4 4 3 7 4.5 2.5 6 3 4 a) Do an analysis of variance and interpret the result.b) Based on the above results, if appropriate, use the Tukey-Kramer test to make all pairwise comparisons of clean rooms.arrow_forward
- A study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 333.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 433.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 382.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 350.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 413.4 441.8 419.9 410.7 473.4 441.2 465.8 LUSE SALT Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. O Hoi Hy #fly #Hz" Ha #Hs H: all five μ's are equal O Hoi H₂H₂ = H3 = HaHs H: at least two μ's are unequal O Hoi H₂ = H₂ = H₂ "HaHs H: all five μ's are unequal O Hoi H₂ #4₂ # Hz*H4 *H5 H: at least two μ's are equal Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Degrees of Sum of Mean freedom Squares Squares Error Total…arrow_forwardA study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 321.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 439.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 390.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 362.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 402.4 441.8 419.9 410.7 473.4 441.2 465.8 USE SALT Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. ○ Ho: H₁ = H₂ = H3 = H4=H5 Ha: all five u's are unequal O Ho: H₁ H₂ H3 H4 H5 Ha: all five μ's are equal Ho H₁ = ₂ = 3 = H4 = 5 H₂: at least two μ's are unequal Ho: H₁ H₂ H3 H4 H5 Ha: at least two μ's are equal Test the relevant hypotheses using analysis of variance with a = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Mean Degrees of Sum of freedom Squares Squares Source Treatments…arrow_forwardThe article "Two Different Approaches for RDC Modelling When Simulating a Solvent Deasphalting Plant" (J. Aparicio, M. Heronimo, et al., Computers and Chemical Engineering, 2002:1369–1377) reports flow rate (in dmh) and specific gravity measurements for a sample of paraffinic hydrocarbons. The natural logs of the flow rates (y) and the specific gravity measurements (x) are presented in the following table. х -1.204 0.8139 -0.580 0.8171 0.049 0.8202 0 673 0.8233 1.311 0.8264 1.959 0.8294 2.614 0.8323 3.270 0.8352 Fit the linear model y = Bo + B,x + ɛ. For each coefficient, test the hypothesis that the coefficient is equal to 0. Fit the quadratic model y = Bo + B,x + B2x? + E. For each coefficient, test the a. b. hypothesis that the coefficient is equal to 0. Fit the cubic model y = Bo + Bix + B2x² + Bax + E. For each coefficient, test the C. hypothesis that the coefficient is equal to 0. Which of the models in parts (a) through (c) is the most appropriate? Explain. Using the most…arrow_forward
- Samples are collected from the River X and pH values are observed. 9 different pH values arelisted in table 3.Table 3Concentrations 4.2 3.8 6.0 3.5 8.1 4.9 4.1 3.2 4.0Draw box plot and finda. Bowley’s coefficient of skewnessb. Karl Pearson’s coefficient of skewnessc. Third momentRubricStages of Process MarksImagine and Plan 2Composition 2Effort 1arrow_forwardA study of the properties of metal plate-connected trusses used for roof support yielded the following observations on axial stiffness index (kips/in.) for plate lengths 4, 6, 8, 10, and 12 in: 4: 323.2 409.5 311.0 326.5 316.8 349.8 309.7 6: 423.1 347.2 361.0 404.5 331.0 348.9 381.7 8: 393.4 366.2 351.0 357.1 409.9 367.3 382.0 10: 362.7 452.9 461.4 433.1 410.6 384.2 362.6 12: 418.4 441.8 419.9 410.7 473.4 441.2 465.8 Does variation in plate length have any effect on true average axial stiffness? State the relevant hypotheses using analysis of variance. H0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: at least two ?i's are equalH0: ?1 = ?2 = ?3 = ?4 = ?5Ha: all five ?i's are unequal H0: ?1 = ?2 = ?3 = ?4 = ?5Ha: at least two ?i's are unequalH0: ?1 ≠ ?2 ≠ ?3 ≠ ?4 ≠ ?5Ha: all five ?i's are equal Test the relevant hypotheses using analysis of variance with ? = 0.01. Display your results in an ANOVA table. (Round your answers to two decimal places.) Source Degrees offreedom Sum…arrow_forwardThe article "Experimental Measurement of Radiative Heat Transfer in Gas-Solid Suspension Flow System" (G. Han, K. Tuzla, and J. Chen, AIChe Journal, 2002:1910- 1916) discusses the calibration of a radiometer. Several measurements were made on the electromotive force readings of the radiometer (in volts) and the radiation flux (in kilowatts per square meter). The results (read from a graph) are presented in the following table. Heat flux (y) 15 31 51 55 67 89 Signal output (x) 1.08 2.42 4.17 4.46 5.17 6.92 Compute the least-squares line for predicting heat flux from the signal output. If the radiometer reads 3.00 V, predict the heat flux. If the radiometer reads 8.00 V, should the heat flux be predicted? If so, predict it. If not, explain why. C.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSON
The Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. Freeman
Introduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman
MATLAB: An Introduction with Applications
Statistics
ISBN:9781119256830
Author:Amos Gilat
Publisher:John Wiley & Sons Inc
Probability and Statistics for Engineering and th...
Statistics
ISBN:9781305251809
Author:Jay L. Devore
Publisher:Cengage Learning
Statistics for The Behavioral Sciences (MindTap C...
Statistics
ISBN:9781305504912
Author:Frederick J Gravetter, Larry B. Wallnau
Publisher:Cengage Learning
Elementary Statistics: Picturing the World (7th E...
Statistics
ISBN:9780134683416
Author:Ron Larson, Betsy Farber
Publisher:PEARSON
The Basic Practice of Statistics
Statistics
ISBN:9781319042578
Author:David S. Moore, William I. Notz, Michael A. Fligner
Publisher:W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:9781319013387
Author:David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:W. H. Freeman
Correlation Vs Regression: Difference Between them with definition & Comparison Chart; Author: Key Differences;https://www.youtube.com/watch?v=Ou2QGSJVd0U;License: Standard YouTube License, CC-BY
Correlation and Regression: Concepts with Illustrative examples; Author: LEARN & APPLY : Lean and Six Sigma;https://www.youtube.com/watch?v=xTpHD5WLuoA;License: Standard YouTube License, CC-BY