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
Textbook Question
Chapter 12.2, Problem 17E
For the past decade, rubber powder has been used in asphalt cement to improve performance. The article “Experimental Study of Recycled Rubber-Filled High-Strength Concrete” (Magazine of Concrete Res., 2009: 549–556) includes a regression of y = axial strength (MPa) on x = cube strength (MPa) based on the following sample data:
| x | 112.3 | 97.0 | 92.7 | 86.0 | 102.0 | 99.2 | 95.8 | 103.5 | 89.0 | 86.7 |
| y | 75.0 | 71.0 | 57.7 | 48.7 | 74.3 | 73.3 | 68.0 | 59.3 | 57.8 | 48.5 |
- a. Obtain the equation of the least squares line, and interpret its slope.
- b. Calculate and interpret the coefficient of determination.
- c. Calculate and interpret an estimate of the error standard deviation σ in the simple linear repression model
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
The accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel.
Below are the data collected and the regression equation.
Diameter
Strength
200.1
813.7
210.1
785.3
220.1
960.4
230.1
1118.0
240.0
1076.2
Strength = -941.6992 + 8.5988*Diameter
a)The predicted y-hat value for a diameter of 201 is 864. Interpret this predicted value.
b)what is the predicted strength of a weld with a diameter of 51?
A regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X₁ = median age,
X₂ = number of bankruptcies per 1,000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school
graduation percentage.
Click here for the Excel Data File
(a) Using the sample size of 50 people, calculate the tcalc and p-value in the table given below. (Negative values should be indicated
by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.)
Predictor
Intercept
AgeMed
Bankrupt
FedSpend
HSGrad%
Coefficient
t-value =
4,198.5808
-27.3540
17.4893
-0.0124
-29.0314
SE
799.3395
12.5687
12.4033
0.0176
7.1268
tcalc
p-value
(b-1) What is the critical value of Student's t in Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.)
A regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X1 = median age,
X2 = number of bankruptcies per 1,000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school
graduation percentage.
Click here for the Excel Data File
(a) Using the sample size of 45 people, calculate the tcalc and p-value in the table given below. (Negative values should be indicated
by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your t-values to 3 decimal places and p-
values to 4 decimal places.)
Predictor
Intercept
AgeMed
Coefficient
SE
tcalc
p-value
4,641.0430
798.0634
-28.8630
12.4684
Bankrupt
20.1604
12.1079
FedSpend
HSGrad%
-0.0181
0.0181
-30.3196
7.1136
(b-1) What is the critical value of Student's tin Appendix D for a two-tailed test at a = .01? (Round your answer to 3 decimal places.)
-value =
Chapter 12 Solutions
Probability and Statistics for Engineering and the Sciences
Ch. 12.1 - The efficiency ratio for a steel specimen immersed...Ch. 12.1 - The article Exhaust Emissions from Four-Stroke...Ch. 12.1 - Bivariate data often arises from the use of two...Ch. 12.1 - The accompanying data on y = ammonium...Ch. 12.1 - The article Objective Measurement of the...Ch. 12.1 - One factor in the development of tennis elbow, a...Ch. 12.1 - The article Some Field Experience in the Use of an...Ch. 12.1 - Referring to Exercise 7, suppose that the standard...Ch. 12.1 - The flow rate y (m3/min) in a device used for...Ch. 12.1 - Suppose the expected cost of a production run is...
Ch. 12.1 - Suppose that in a certain chemical process the...Ch. 12.2 - Refer back to the data in Exercise 4, in which y =...Ch. 12.2 - The accompanying data on y = ammonium...Ch. 12.2 - Refer to the lank temperature-efficiency ratio...Ch. 12.2 - Values of modulus of elasticity (MOE, the ratio of...Ch. 12.2 - The article Characterization of Highway Runoff in...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - For the past decade, rubber powder has been used...Ch. 12.2 - The following data is representative of that...Ch. 12.2 - The bond behavior of reinforcing bars is an...Ch. 12.2 - Wrinkle recovery angle and tensile strength are...Ch. 12.2 - Calcium phosphate cement is gaining increasing...Ch. 12.2 - a. Obtain SSE for the data in Exercise 19 from the...Ch. 12.2 - The invasive diatom species Didymosphenia geminata...Ch. 12.2 - Prob. 25ECh. 12.2 - Show that the point of averages (x,y) lies on the...Ch. 12.2 - Prob. 27ECh. 12.2 - a. Consider the data in Exercise 20. Suppose that...Ch. 12.2 - Consider the following three data sets, in which...Ch. 12.3 - Reconsider the situation described in Exercise 7,...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - Exercise 16 of Section 12.2 gave data on x =...Ch. 12.3 - During oil drilling operations, components of the...Ch. 12.3 - For the past decade, rubber powder has been used...Ch. 12.3 - Refer back to the data in Exercise 4, in which y =...Ch. 12.3 - Misi (airborne droplets or aerosols) is generated...Ch. 12.3 - Prob. 37ECh. 12.3 - Refer to the data on x = liberation rate and y =...Ch. 12.3 - Carry out the model utility test using the ANOVA...Ch. 12.3 - Prob. 40ECh. 12.3 - Prob. 41ECh. 12.3 - Verify that if each xi is multiplied by a positive...Ch. 12.3 - Prob. 43ECh. 12.4 - Fitting the simple linear regression model to the...Ch. 12.4 - Reconsider the filtration ratemoisture content...Ch. 12.4 - Astringency is the quality in a wine that makes...Ch. 12.4 - The simple linear regression model provides a very...Ch. 12.4 - Prob. 48ECh. 12.4 - You are told that a 95% CI for expected lead...Ch. 12.4 - Prob. 50ECh. 12.4 - Refer to Example 12.12 in which x = test track...Ch. 12.4 - Plasma etching is essential to the fine-line...Ch. 12.4 - Consider the following four intervals based on the...Ch. 12.4 - The height of a patient is useful for a variety of...Ch. 12.4 - Prob. 55ECh. 12.4 - The article Bone Density and Insertion Torque as...Ch. 12.5 - The article Behavioural Effects of Mobile...Ch. 12.5 - The Turbine Oil Oxidation Test (TOST) and the...Ch. 12.5 - Toughness and fibrousness of asparagus are major...Ch. 12.5 - Head movement evaluations are important because...Ch. 12.5 - Prob. 61ECh. 12.5 - Prob. 62ECh. 12.5 - Prob. 63ECh. 12.5 - The accompanying data on x = UV transparency index...Ch. 12.5 - Torsion during hip external rotation and extension...Ch. 12.5 - Prob. 66ECh. 12.5 - Prob. 67ECh. 12 - The appraisal of a warehouse can appear...Ch. 12 - Prob. 69SECh. 12 - Forensic scientists are often interested in making...Ch. 12 - Phenolic compounds are found in the effluents of...Ch. 12 - The SAS output at the bottom of this page is based...Ch. 12 - The presence of hard alloy carbides in high...Ch. 12 - The accompanying data was read from a scatterplot...Ch. 12 - An investigation was carried out to study the...Ch. 12 - Prob. 76SECh. 12 - Open water oil spills can wreak terrible...Ch. 12 - In Section 12.4, we presented a formula for...Ch. 12 - Show that SSE=Syy1Sxy, which gives an alternative...Ch. 12 - Suppose that x and y are positive variables and...Ch. 12 - Let sx and sy denote the sample standard...Ch. 12 - Verify that the t statistic for testing H0: 1 = 0...Ch. 12 - Use the formula for computing SSE to verify that...Ch. 12 - In biofiltration of wastewater, air discharged...Ch. 12 - Normal hatchery processes in aquaculture...Ch. 12 - Prob. 86SECh. 12 - Prob. 87SE
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
- A regression model to predict Y, the state burglary rate per 100,000 people, used the following four state predictors: X₁ = median age, X₂ = number of bankruptcies per 1.000 population, X3 = federal expenditures per capita (a leading predictor), and X4 = high school graduation percentage. Click here for the Excel Data File (a) Using the sample size of 50 people, calculate the calc and p-value in the table given below. (Negative values should be indicated by a minus sign. Leave no cells blank - be certain to enter "0" wherever required. Round your answers to 4 decimal places.) Predictor Intercept AgeMed Bankrupt FedSpend HSGrad% Answer is complete but not entirely correct. *calc 5.2526 -2.1764✔✔ 1.4101✔ Coefficient 4,198.5808 -27.3540 17.4893 -0.0124 -29.0314 SE 799.3395 12.5687 12.4033 0.0176 7.1268 -0.7045 -4.0736 p-value 0.0000 0.0348 0.2935 0.4848 0.0002arrow_forwardThe accompanying data resulted from an experiment in which weld diameter and shear strength (in pounds) were determined for five different spot welds on steel. Below are the data collected and the regression equation. Diameter Strength 200.1 813.7 210.1 785.3 220.1 960.4 230.1 1118.0 240.0 1076.2 Strength = -941.6992 + 8.5988*Diameter The predicted y-hat value for a diameter of 201 is 864. if we observed a weld that had a diameter of 235 that had a strength 1000, what would be its residual?arrow_forwardFor the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x cube strength (MPa) based on the following sample data: 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 74.7 70.7 58.0 49.2 74.3 73.0 68.3 59.5 57.3 48.9 (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.) %3D Interpret the slope. A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. A one MPa decrease in cube strength is associated with an increase in the predicted axial strength equal to the slope. A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope. A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. (b) Calculate the coefficient of determination. (Round your answer to four…arrow_forward
- Pls. help me in my Stat about CORRELATION ANALYSIS, SIMPLE REGRESSION ANALYSIS & PATH ANALYSIS IN Rarrow_forwardFor the past decade, rubber powder has been used in asphalt cement to improve performance. An article includes a regression of y = axial strength (MPa) on x= cube strength (MPa) based on the following sample data: 112.3 97.0 92.7 86.0 102.0 99.2 95.8 103.5 89.0 86.7 75.4 70.9 57.8 49.0 73.8 73.7 67.8 59.6 57.5 48.9 A USE SALT (a) Obtain the equation of the least squares line. (Round all numerical values to four decimal places.) y= Interpret the slope. O A one MPa decrease in cube strength is associated with an increase in the predicted axcial strength equal to the slope. O A one MPa decrease in axial strength is associated with an increase in the predicted cube strength equal to the slope. O A one MPa increase in axial strength is associated with an increase in the predicted cube strength equal to the slope. O A one MPa increase in cube strength is associated with an increase in the predicted axial strength equal to the slope. (b) Calculate the coefficient of determination. (Round your…arrow_forwardIn a certain type of metal test, the normal stress on a specimen is known to be functionally related to the shear resistance. What is the correlation between the two variables using Pearson product-moment correlation coefficient? Normal 27 29 26 28 28 24 Stress(x): 25 27 Shear 27 28 25 27 24 26 Resistance (y): 27 23 22 24arrow_forward
- An agribusiness performed a regression of wheat yield (bushels per acre) using observations on 21 test plots with four predictors (rainfall, fertilizer, soil acidity, hours of sun). The standard error was 1.02 bushels.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_forwardA student collected concentration versus absorbance data for a series of standards and produced a standard curve. Which value of 2 would reflect the linear regression curve the student produced? Absorbance 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 ² = 0.10 ² = 0.76 ² = 0.98 2 = 0.45 1 Absorbance vs. Concentration 2 3 Concentration (ppm) 4 5 6arrow_forward
- A papert gave data on x = change in Body Mass Index (BMI in kilograms/meter2) and y = change in a measure of depression for patients suffering from depression who participated in a pulmonary rehabilitation program. JMP output for these data is shown below. Bivariate Fit of Depression Score Change by BMI Change 20 15 10 -0.5 0.5 1.5 BMI change - Linear Fit Linear Fit Depression score change = 6.8725681 + 5.077821*BMI Change Summary of Fit RSquare 0.234828 RSquare Adj 0.158311 Root Mean Square Error 5.365593 Mean of Response 9.75 Observations (or Sum Wgts) 12 Analysis of Variance Sum of Mean Source DF F Ratio Prob > F Squares Square Model 1 88.35409 88.3541 3.07 0.1104 Error 10 287.89591 28.7896 C. Total 11 376.25000 Depression score changearrow_forwardGiven the table below, Let y, x1, x2, and x3 be the time of concentration (t, in hr), watershed length (L in ft), watershed slope (S in %), and runoff curve number (CN): Evaluate the linear multiple regression model with two or three predictor variables. Compute the multiple correlation coefficient, the standard error of estimate, and the standard deviation of the variable y. Discuss the reliability of the modelarrow_forwardThe statsmodels ols() method is used on a cars dataset to fit a multiple regression model using Quality as the response variable. Speed and Angle are used as predictor variables. The general form of this model is: Y - B, + P;Speed + PyAngle If the level of significance, alpha, is 0.10, based on the output shown, is Angle statistically significant in the multiple regression model shown above? Select one. A text version of this output is available. OLS Regression Results Dep. Variable: Model: Method: Date: Time: No. observations: Df Residuals: of Nodel: Covariancе Туре: R-squar ed: Adj. F-statistic: Prob (F-statistic): Log-Likelihood: Quality 0.97A 0.975 332.2 3.80e-13 -21.142 48.28 50.95 OLS squar ed: Least Squares Sun, 18 Aug 2019 11:39:31 18 15 ATC: BIC: 2 nonrobust coef std err P>t| [0.025 0.975] t Intercept 0.5382 1.9046 4.0280 0.473 0.176 0.178 1.137 Speed Angle -10.834 22.574 0.273 0.000 0.000 -0.471 2.279 3.648 1.547 1.530 4.408 Onnibus: Prob(Onnibus): skew: Kurtosis: 4.358 0.113…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