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
Question
Chapter 13, Problem 79SE
a.
To determine
Explain which of the model would be recommended.
b.
To determine
Explain which of the model would be recommended.
Expert Solution & Answer
Trending nowThis is a popular 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…
2. The authors of the paper "Age, Spacing and Growth Rate of Tamarix as an Indication of
Lake Boundary Fluctuations at Sebkhet Kelbia, Tunisia" (J. of Arid Environ. (1982):43-
51) used a simple linear regression model to describe the relationship between y = vigor
(average width in centimeters of the last two annual rings) and x
(stems/m?). Data on which the estimated model was based is as follows.
4
= stem density
6
9
14
15
15
19
21
22
y
.75
1.20
.55
.60
.65
.55
.35
.45
.40
Construct a scatter plot for the data.
a)
b) Find the estimated regression line and draw it on your scatter plot.
Determine and interpret the coefficient of determination.
c)
d) What is your estimate of the average change in vigor associated with a 1-unit increase in
stem density?
What would you predict vigor to be for a plant whose density was 17 stems/m2?
e)
A researcher records age in years (x) and systolic blood pressure (y) for volunteers. They perform a
regression analysis was performed, and a portion of the computer output is as follows:
ŷ = 4.5+ 14.4x
Coefficients
(Intercept)
x
Estimate
4.5
Ho: B₁ = 0
H₁: B₁ > 0
Ho: B₁ = 0
Ha: B₁ <0
14.4
Ho: B₁ = 0
Ha:
B₁ #0
Std. Error Test statistic
2.9
4.7
1.55
3.06
P-value
Specify the null and the alternative hypotheses that you would use in order to test whether a linear
relationship exists between x and y.
0.07
0
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
- An article in the Journal of Environmental Engineering (1989, Vol. 115(3), pp. 608–619) reported the results of a study on the occurrence of sodium and chloride in surface streams in central Rhode Island. The following data are chloride concentration y (in milligrams per liter) and roadway area in the watershed x (in percentage).arrow_forward5.25. Representative data on x = carbonation depth (in millimeters) and y = strength (in megapascals) for a sample of concrete core specimens taken from a particular building were read from a plot in the article “The Carbonation of Concrete Structures in the Tropical Environment of Singapore” (Magazine of Concrete Research [1996]: 293-300): Depth, x 8.0 20.0 20.0 30.0 35.0 40.0 50.0 55.0 65.0 Strength, y 22.8 17.1 21.1 16.1 13.4 12.4 11.4 9.7 6.8 a. Construct a scatterplot. Does the relationship between carbonation depth and strength appear to be linear? Yes, the relationship between carbonation depth and strength appears to be linear however it is a negative linear relation. b. Find the equation of the of the least-squares line.c. What would you predict for strength when carbonation depth is 25 mm?d. Explain why it would not be reasonable to use the least-squares line to predict strength when carbonation depth…arrow_forwards) Use the Durbin-Watson test to test, at 5% level of significance, for the presence of significant linear correlation among error terms in the following cases: a) Given that the sample size is n=20, the Durbin Watson (DW) statistic 0.62, when the regression model is of the form E(Y) = Bo + B,X b) Given that the sample size is #=35, the Durbin Watson (DW) statistic = 1.82, when the regression model is of the form E(Y) = Bo + B,X, + B,X2 . c) Given that the sample size is n-40, the Durbin Watson (DW) statistic =2.78, when the regression model is of the form E(Y) = Bo + BzX, + B2X2 + B,X3 +B,X4 Table Criical value for the Durbin-Watson d Statistic (a = 05)arrow_forward
- You have estimated a multiple regression model with 6 explanatory variables and an intercept from a sample with 46 observations. What is the critical value of the test statistic (tc) if you want to perform a test for the significance of a single right-hand side (explanatory) variable at α = 0.05? a.) 2.023 b.) 2.708 c.) 2.423 d.) 2.704arrow_forwardAn articie in Technometrics by S.C. Narula and J. F. Wallington Prediction, Lincar Regression, and a Minimum Sum of Relative Errors" Vol. 19, 1977) presents data on the sallingprica (y) and annual taas (x) for 24 houses. The taxes include local, school and county taxes. The data are shown in the following table. Sale Price/1000 Taxas/1000 25.9 4.9176 29.5 5.0208 27.9 4.5429 25.9 4.5573 29.9 5.0597 29.9 3.8910 30.9 5.8980 28.9 5.6039 35.9 5.8282 31.5 5.3003 31.0 6.2712 30.9 5.9592 30.0 5.0500 36.9 8.2464 41.9 6.6969 40.5 7.7841 43.9 9.0384 37.5 5.9894 37.9 7.5422 44.5 8.7951 37.9 6.0831 38.9 8.3607 36.9 8.1400 45.8 9.1416 (a) Calculate the least squares estimates of the slops and intercspt. (Round your answer to 3 decimal places.) (Round your answer to 2 decimal places.) (b) Find the mean selling price given that the taxes paid arex-8.9. (Round your answer to 2 decimal places.)arrow_forwardQ3. Find out the regression coefficients of Y on X and of x on Y on the basis of following data: Ex = 50, X = 5, EY = 60, Y = 6, EXY = 350 Variance of X= 4, Variance of Y= 9arrow_forward
- A multiple regression analysis between yearly income(y in $1,000s), college grade point average(X1) , age of the individuals (X2), and the gender of the individual (X3); zero representing female and one representing male) was performed on a sample of 10 people, and the following results were obtained. Coefficient Standard Error Constant 4.0928 1.4400 X1 10.0230 1.6512 X2 0.1020 0.1225 X3 -4.4811 1.4400 Analysis of Variance Source of Degrees of Sum of Mean Variance Freedom Squares Square F Regression 360.59 Error 23.91 Write the regression equation for the above. Interpret the meaning of the coefficient of X3. Compute the coefficient…arrow_forwardSnowpacks 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…arrow_forwardManagers of an outdoor coffee stand in Coast City are examining the relationship between (hot) coffee sales and daily temperature, hoping to be able to predict a day's total coffee sales from the maximum temperature that day. The bivariate data values for the coffee sales (denoted by y, in dollars) and the maximum temperature (denoted by x, in degrees Fahrenheit) for each of randomly selected days during the past year are given below. These data are plotted in the scatter plot below. (a)For these data, temperature values that are less than the mean of the temperature values tend to be paired with coffee sales values that are ▼(Choose one) the mean of the coffee sales values. (b)According to the regression equation, for an increase of one degree in temperature, there is a corresponding ▼(Choose one) of 9.94 dollars in coffee sales. (c)From the regression equation, what is the predicted coffee sales value (in dollars) when the temperature is 74.6 degrees Fahrenheit? (Round your…arrow_forward
- Wrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".† x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 y 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Constant absorb S = 3.60498 Coef 321.878 156.711 SOURCE Regression Residual Error Total SE Coef 2.483 6.464 R-Sq = 98.5% DF 1 9 10 SS 7639.0 117.0 7756.0 T 129.64 24.24 0.000 0.000 R-Sq (adj) = 98.3% MS 7639.0 13.0 F P 587.81 (a) Does the simple linear regression model appear to be…arrow_forwardWrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t 半 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 334 342 355 363 365 372 381 392 400 412 420 Here is regression output from Minitab: Predictor Coef SE Coef P Constant 321.878 2.483 129.64 0.000 absorb 156.711 6.464 24.24 0.000 S = 3.60498 R-Sq = 98.5% R-Są (adj) - 98.3% SOURCE DF MS F P Regression 1 7639.0 7639.0 587.81 0.000 Residual Error 9 117.0 13.0 Total 10 7756.0 (a) Does the simple linear regression model appear to be…arrow_forwardWrinkle recovery angle and tensile strength are the two most important characteristics for evaluating the performance of crosslinked cotton fabric. An increase in the degree of crosslinking, as determined by ester carboxyl band absorbance, improves the wrinkle resistance of the fabric (at the expense of reducing mechanical strength). The accompanying data on x = absorbance and y = wrinkle resistance angle was read from a graph in the paper "Predicting the Performance of Durable Press Finished Cotton Fabric with Infrared Spectroscopy".t x 0.115 0.126 0.183 0.246 0.282 0.344 0.355 0.452 0.491 0.554 0.651 y 334 342 355 363 365 372 381 400 392 412 420 Here is regression output from Minitab: Predictor Constant absorb S = 3.60498 Coef 321.878 156.711 SOURCE Regression Residual Error Total R-Sq= 98.5% DF SE Coef 2.483 6.464 1 9 10 SS 7639.0 117.0 7756..0 T 129.64 24.24 P 0.000 0.000. R-Sq (adj) 98.3% MS 7639.0 13.0 F 587.81 (a) Does the simple linear regression model appear to be appropriate?…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Calculus For The Life Sciences
Calculus
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:Pearson Addison Wesley,
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
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