Statistics for Engineers and Scientists
4th Edition
ISBN: 9780073401331
Author: William Navidi Prof.
Publisher: McGraw-Hill Education
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 8.3, Problem 1E
True or false:
- a. For any set of data, there is always one best model.
- b. When there is no physical theory to specify a model, there is usually no best model, but many that are about equally good.
- c. Model selection methods such as best subsets and stepwise regression, when properly used, are scientifically designed to find the best available model.
- d. Model selection methods such as best subsets and stepwise regression, when properly used, can suggest models that fit the data well.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Used cars 2010 Vehix.com offered several used ToyotaCorollas for sale. The following table displays the ages ofthe cars and the advertised prices.
a) Make a scatterplot for these data.b) Do you think a linear model is appropriate? Explain.c) Find the equation of the regression line.
d) Check the residuals to see if the conditions for infer-ence are met.
Age (yr) Price ($) Age (yr) Price ($)1 15988 6 99951 13988 6 119882 14488 7 89903 10995 8 94883 13998 8 89954 13622 9 59904 12810 10 41005 9988 12 2995
o view the weight and gas mileage data.
t-squares regression line treating weight as the explana
Car weight and MPG
efficient to five decimal places as needed. Round the c
e slope and y-intercept, if appropriate. Choose the corre
er from part a to find this answer.)
Miles per
Weight
(pounds), x
Gallon, y
ntless car will get
miles per gallon, on average. It is n
3661
17
ery pound added to the weight of the car, gas mileage in
3931
17
pt.
2711
25
ery pound added to the weight of the car, gas mileage in
3592
19
h, on average.
ot appropriate to interpret the slope or the y-intercept.
3348
21
3066
22
gas-powered car weighs 3621 pounds and gets 17 miles p
3700
17
2577
25
d average miles per gallon for cars of this weight is
mi
3471
19
ree decimal places as needed.)
3734
18
be reasonable to use the least-squares regression line to p
because the hybrid is a different type of car.
because the absolute value of the correlation coefficient is
Print
Done
=, because the hybrid is partially powered…
Which of the following statements best describes why a linear regression is also called a least
squares réğression modēt?
a. A linear regression is alsp.called a least şguares regręssion model because the
regression line is calculated by minimising thể square of each äctual ý datâ value and
the predictéd y value.
b. A linear regression is alsp.called a least şguares regression modęl because the
regression line is calculąted by minimişing the sum of the square of thē differences
between each actual y dătā válüe and the predicted y value.
C. A linear regręssion is also.called a least şguares regression model þecause the
regression line is calculated, by minimisıng the sum'of the difference bētween each actual
y dátā valuë and the predictēd ý valúe.
d. A linear regression is alsp.called a least sguares regression, model because the
regressionline is calculated by minimising the square of the difference bētween each
actuāl x datä value and the predicted x value.
Chapter 8 Solutions
Statistics for Engineers and Scientists
Ch. 8.1 - In an experiment to determine the factors...Ch. 8.1 - Prob. 2ECh. 8.1 - Prob. 3ECh. 8.1 - The article Application of Analysis of Variance to...Ch. 8.1 - Prob. 5ECh. 8.1 - Prob. 6ECh. 8.1 - Prob. 7ECh. 8.1 - Refer to Exercise 7. a. Find a 95% confidence...Ch. 8.1 - In a study of the lung function of children, the...Ch. 8.1 - Prob. 10E
Ch. 8.1 - Prob. 11ECh. 8.1 - The following MINITAB output is for a multiple...Ch. 8.1 - Prob. 13ECh. 8.1 - Prob. 14ECh. 8.1 - Prob. 15ECh. 8.1 - The following data were collected in an experiment...Ch. 8.1 - The November 24, 2001, issue of The Economist...Ch. 8.1 - The article Multiple Linear Regression for Lake...Ch. 8.1 - Prob. 19ECh. 8.2 - In an experiment to determine factors related to...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - In a laboratory test of a new engine design, the...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.2 - The article Influence of Freezing Temperature on...Ch. 8.3 - True or false: a. For any set of data, there is...Ch. 8.3 - The article Experimental Design Approach for the...Ch. 8.3 - Prob. 3ECh. 8.3 - An engineer measures a dependent variable y and...Ch. 8.3 - Prob. 5ECh. 8.3 - The following MINITAB output is for a best subsets...Ch. 8.3 - Prob. 7ECh. 8.3 - Prob. 8ECh. 8.3 - (Continues Exercise 7 in Section 8.1.) To try to...Ch. 8.3 - Prob. 10ECh. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - The article Ultimate Load Analysis of Plate...Ch. 8.3 - Prob. 14ECh. 8.3 - Prob. 15ECh. 8.3 - Prob. 16ECh. 8.3 - The article Modeling Resilient Modulus and...Ch. 8.3 - The article Models for Assessing Hoisting Times of...Ch. 8 - The article Advances in Oxygen Equivalence...Ch. 8 - Prob. 2SECh. 8 - Prob. 3SECh. 8 - Prob. 4SECh. 8 - In a simulation of 30 mobile computer networks,...Ch. 8 - The data in Table SE6 (page 649) consist of yield...Ch. 8 - Prob. 7SECh. 8 - Prob. 8SECh. 8 - Refer to Exercise 2 in Section 8.2. a. Using each...Ch. 8 - Prob. 10SECh. 8 - The data presented in the following table give the...Ch. 8 - The article Enthalpies and Entropies of Transfer...Ch. 8 - Prob. 13SECh. 8 - Prob. 14SECh. 8 - The article Measurements of the Thermal...Ch. 8 - The article Electrical Impedance Variation with...Ch. 8 - The article Groundwater Electromagnetic Imaging in...Ch. 8 - Prob. 18SECh. 8 - Prob. 19SECh. 8 - Prob. 20SECh. 8 - Prob. 21SECh. 8 - Prob. 22SECh. 8 - The article Estimating Resource Requirements at...Ch. 8 - Prob. 24SE
Additional Math Textbook Solutions
Find more solutions based on key concepts
Empirical versus Theoretical A Monopoly player claims that the probability of getting a 4 when rolling a six-si...
Introductory Statistics
Find all solutions of each equation in the interval .
Precalculus: A Unit Circle Approach (3rd Edition)
For each hour of class time, how many hours outside of class are recommended for studying and doing homework?
Elementary Algebra For College Students (10th Edition)
For Problems 23-28, write in simpler form, as in Example 4. logbFG
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences
1. How is a sample related to a population?
Elementary Statistics: Picturing the World (7th Edition)
First Derivative Test a. Locale the critical points of f. b. Use the First Derivative Test to locale the local ...
Calculus: Early Transcendentals (2nd Edition)
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
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardOlympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?arrow_forwardAn engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. Click here to view the weight and gas mileage data. ..... (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. x + (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) A. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. A weightless car will get miles per gallon, on average. O B. A weightless car will get miles per gallon, on…arrow_forward
- An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. Click here to view the weight and gas mileage data. ..... (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y = + (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) O A. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. It is not appropriate to interpret the y-intercept. B. A weightless car will get miles per gallon, on…arrow_forwardAn engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. Click here to view the weight and gas mileage data. ..... (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y =x+() (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) Car Weight and MPG Miles per Weight (pounds), x Gallon, y 3778 16 3832 16 2778 26 3487 20 3313 22 2896 23 3802 16 2590 24 ar All Check Answer 3441 20 3825 18arrow_forwardAn engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage. v. The une ory tor ine most recent m odel year. Complete parts (a) through (d) accompanying data represent the weights of various domestic cars and their miles per gallon in BEE Click here to view the weight and gas mileage data (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y = 0.00702 * + (43.2) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice.answer trom part a to find this answer O A. For every pound added to the weight of the car, gas mileage in the city will decrease by mile(s) per gallon, on average. A weightless car will get miles per gallon, on averag B. For every pound added to the weight of the car, gas…arrow_forward
- Interest rates for home mortgages have, in general, declined during recent months. With the apparent favorable influence for new-home building, there seems to be a clear relationship between x = the prevailing mortgage interest rate and y = the number of new houses being built per month in a Midwestern city over a period of 18 months. A scatterplot of the data collected shows that the linear model is appropriate. The equation of the least-squares regression line is Number of new houses = 672.89- 30.65 x Interest rate and ² = 0.49. What is the correlation coefficient between Interest rate and Number of new houses being built? (Give your answer to one decimal place.)arrow_forward2. A botanist is willing to understand the relation between volume, girth and height of black cherry trees. To this end, she collects data that is presented in trees table of the datasets library. Build a predictive multiple linear regression model for volume using girth and height as independent variables. a. What does the F-test tell about the model? Explain the result using the null hypothesis of the test. b. Provide confidence and prediction intervals for a black cherry tree with 10 inch of girth and 82 feet tall.arrow_forwardUse the p-value criterion to find the best model for predicting the number of points scored per game by football teams using the accompanying National Football League Data. Does the model make logical sense? Click the icon to view the National Football Leaque Data. Determine the best multiple regression model. Let X, represent Rushing Yards, let X, represent Passing Yards, let X, represent Penalties, let X, represent Interceptions, and let Xg represent Fumbles. Enter the terms of the equation so that the Xy-values are in ascending numeral order by base. Select the correct choice below and fill in the answer boxes within your choice. (Type an integer or decimal rounded to three decimal places as needed.) O A. Points/Game = O B. Points/Game = Oc. Points/Game = OD. Points/Game = + ( DX Points/Game = O E.arrow_forward
- Given the regression model above, do each of the following: A Make a claim about the fit of the model for Model #1. B Make a claim about the significance, degree, and form of the Literacy Rate variable as shown in the table for Model #1. C Write a paragraph to compare Model #1 vs. Model #2 and discuss the effect of the control variable (democracy or not). Use as much of the information from the table above as appropriate.(Hint - don't just discuss control, discuss changes to the fit of model, changes in coefficients, etc.). D Write out the equation of Model #2. E. For Model #2, estimate the government effectiveness score for a democratic country with a literacy rate of 68 and GDP per capital of $20,000. (Hint: Government effectiveness ranges from 0 to 100.)arrow_forwardThis is only one questionarrow_forwardThe Cronch Café, located at the Gulf of Mexico, has an increase in business during the summer vacation season. The owner hires a large number of servers as seasonal help. When he interviews a prospective server, he would like to provide data on the amount a server can earn in tips. He believes that the amount of the bill and the number of diners are both related to the amount of the tip. He gathered this sample information. 1) Develop a multiple regression model with the amount of tips as the dependent variable and the amount of the bill and the amount of diners as independent variables. Write out the regression equation. How much does another diner add to the amount of the tips? 2) Conduct a global test of hypothesis to determine if at least one of the independent variables is significant. What is your conclusion? Customer Amount of Tip ($) Amount of Bill ($) Diners 1 5.15 74.5 2 2 4.5 28.23 4 3 1 10.65 1 4 2.4 19.82 3 5 5 28.62 3 6 4.25 24.83 2 7 0.5 6.25 1…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
College AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Algebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
College Algebra
Algebra
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
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