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 78SE
a.
To determine
Interpret for the number –0.0003020 given in the column of Coef.
b.
To determine
Identify whether the fiber contentprovides useful information to explain the variation in seepage velocity.
Test using appropriate hypothesis.
c.
To determine
Identify whether there is any evidence to conclude that the average seepage velocity is some value other than 0.10.
Test using appropriate hypotheses at 5% level of significance
d.
To determine
Identify whether at least one of the second order predictors give useful information about seepage velocity than the first order predictors.
Test using appropriate hypothesis.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Would someone familiar with SPSS be able to help me complete the table and the questions?
(a) Explain which of the variables have statistically significant effects at the α = 0.05 level.
(b) Are the conclusions different to the results obtained by univariate regression? Explain why and which approach is likely to be preferable?
As part of a study designed to compare hybrid and similarly equipped conventional vehicles, Consumer Reports tested a variety of classes of hybrid and all-gas model cars and sport utility vehicles (SUV’s). You are given the required information in the Excel data-file named HybridTest. Test for any significant effect due to Class, Type using multiple regressions. Create dummy variables for Class and Type. Use alpha=0.05
Make/Model
Class
Type
MPG
Honda Civic
Small Car
Hybrid
37
Honda Civic
Small Car
Conventional
28
Toyota Prius
Small Car
Hybrid
44
Toyota Corolla
Small Car
Conventional
32
Chevrolet Malibu
Midsize Car
Hybrid
27
Chevrolet Malibu
Midsize Car
Conventional
23
Nissan Altima
Midsize Car
Hybrid
32
Nissan Altima
Midsize Car
Conventional
25
Ford Escape
Small SUV
Hybrid
27
Ford Escape
Small SUV
Conventional
21
Saturn Vue
Small SUV
Hybrid
28
Saturn Vue
Small SUV
Conventional
22
Lexus RX
Midsize SUV
Hybrid
23
Lexus RX
Midsize SUV
Conventional
19…
A researcher was investigating variables that might be associated with the academic performance of high school students. The data included the average Math SAS score of all high school seniors in the city that took the exam (labeled as the variable SAT-M), the average number of dollars per pupil spent on education by the city (labeled as the variable $Per Pupil), and the percentage of high school seniors in the city that took the exam (labeled as the variable %Taking). The researcher ran the following multiple linear regression model as SAT-M=Beta0 + Beta1($Per Pupil) + Beta2(%Taking). This model was fit to the data using the method of least-squares, results shown inside of table within photo.
If we want to test using ANOVA F-test with hypotheses Ho: Beta1=Beta2=0 versus H1: at least one of the Beta is not 0, what would the value of our F-statistic mean?
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
- A fast-food chain decided to carry out an experiment to assess the influence of advertising expenditure on sales. Different relative changes in advertising expenditure, compared to the previous year, were made in eight regions of the country, and resulting changes in sales levels were observed the accompanying table shows the results. Increase in advertising expenditure (%) 0 5 15 20 25 30 35 40 Increase in sales (%) 5 10 18 25 35 50 60 65 Determine the value of regressions coefficients and write down the simple linear regression model.arrow_forwardA research department of an American automobile company wants to develop a model topredict gasoline mileage (measured in MPG) of the company’s vehicles by using theirhorsepower and weights (measured in pounds). To do this, it took a random sample of 50vehicles to perform a regression analysis as follows: SUMMARYOUTPUTRegression StatisticsMultiple R 0.865689R Square 0.749417Adjusted RSquare 0.738754Standard Error 4.176602Observations 50ANOVAdf SS MS FRegression a 2451.973702 1225.987 dResidual b 819.8680976 cTotal 49 3271.8418CoefficientsStandardError t StatIntercept 58.15708 2.658248208 21.87797Horsepower -0.11753 0.032643428 -3.60028Weight -0.00687 0.001401173 -4.90349(a) State the multiple regression equation. Interpret the meanings of the coefficients forhorsepower and weight.(b) Test the validity of this multiple regression equation at the significance level of 1%. Showyour reasoning.(c) The research department claims that the weight of the vehicle is negatively linearly related…arrow_forwardThe owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car Age Price 1 10 10.8 2 6 9.1 3 12 4.3 4 16 5 5 8 5.1 6 7 11.5 7 9 11.6 8 13 8 9 12 8 10 16 3.9 11 4 12.8 12 4 11.1 Determine the regression equation. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.) a= 14.010 b= ? Estimate the selling price of a 9-year-old car (in $000). (Round your answer to 3 decimal places.) So for each additional year, the car price decreases 8.862 in value. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount.) For each additional year, the car price decreases $_____ in value.arrow_forward
- The owner of Maumee Ford-Mercury-Volvo wants to study the relationship between the age of a car and its selling price. Listed below is a random sample of 12 used cars sold at the dealership during the last year. Car Age Price 1 10 10.8 2 6 9.1 3 12 4.3 4 16 5 5 8 5.1 6 7 11.5 7 9 11.6 8 13 8 9 12 8 10 16 3.9 11 4 12.8 12 4 11.1 Determine the regression equation. (Negative value should be indicated by a minus sign. Round your answers to 3 decimal places.) a= b= Estimate the selling price of a 9-year-old car (in $000). (Round your answer to 3 decimal places.) So for each additional year, the car price decreases ____ in value. Interpret the regression equation (in dollars). (Round your answer to the nearest dollar amount.)arrow_forwardShow that an interaction term of a dummy variable and a regressor changes the slope of a regression line..arrow_forwardA consumer buying cooperative tested the effective heating area of 20 differentelectric space heaters with different wattages. Here are the results. a. Compute the correlation between the wattage and heating area. Is there a direct oran indirect relationship?b. Conduct a test of hypothesis to determine if it is reasonable that the coefficient isgreater than zero. Use the .05 significance level.c. Develop the regression equation for effective heating based on wattage.d. Which heater looks like the “best buy” based on the size of the residual?arrow_forward
- A researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45Total 15 Perform the F Test making sure to state the null and alternative hypothesis. f) Given an interpretation of the term “R-sq” and comment on its value.arrow_forwardA researcher interested in explaining the level of foreign reserves for the country of Barbadosestimated the following multiple regression model using yearly data spanning the period 2001 to 2016: ??=?+????+????+????Where FR = yearly foreign reserves ($000’s), OIL = annual oil prices, EXP = yearly total exports ($000’s) and FDI = annual foreign direct investment ($000’s). The sample of data was processed using MINITAB and the following is an extract of the output obtained:Predictor Coef StDev t-ratio p-value Constant 5491.38 2508.81 2.1888 0.0491OIL 85.39 18.46 4.626 0.0006EXP -377.08 112.19 * 0.0057FDI -396.99 160.66 -2.471 ** S = 2.45 R-sq = 96.3% R-sq(adj) = 95.3%Analysis of VarianceSource DF SS MS F pRegression 3 1991.31 663.77 ? ??Error 12 77.4 6.45Total 15a) What is dependent and independent variables? [2]b) Fully write out the regression equation [1] c) Fill in the missing values ‘*’, ‘**’, ‘?’and ‘??’ [4] d) Hence test whether ? is significant. Give reasons for your answer. [4]…arrow_forwardIs there evidence of significant linear correlation and find the critical values of r.arrow_forward
- Listed below are the chest sizes (in inches) and weights (in pounds) of randomly selected bears that were anesthetized and measured (based on data from Gary Alt ena Minitab, Inc.). Since it is much more difficult to weigh a bear than to measure its chest size, the presence of a correlation could result in a method for estimating weight based on chest size.a) Calculate the correlation coefficient and test the significance at 5% probability;b) Determine the simple linear regression equation;c) Find the prediction for the weight (in pounds) of a bear with a chest size of 50 inches.arrow_forwardThe calories and sugar content per serving size of ten brands of breakfast cereal are fitted with a least squares regression line with computer outputs:arrow_forward
arrow_back_ios
arrow_forward_ios
Recommended textbooks for you
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics 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:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction 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