STATISTICS F/BUSINESS+ECONOMICS-TEXT
13th Edition
ISBN: 9781305881884
Author: Anderson
Publisher: CENGAGE L
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 15.5, Problem 21E
The following estimated regression equation was developed for a model involving two independent variables.
ŷ = 40.7 + 8.63x1 + 2.71x2
After x2 was dropped from the model, the least squares method was used to obtain an estimated regression equation involving only x1 as an independent variable.
ŷ = 42.0 + 9.01x1
- a. Give an interpretation of the coefficient of x1 in both models.
- b. Could multicollinearity explain why the coefficient of x1 differs in the two models? If so, how?
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
A biologist is interested in predicting the brain weight (in grams) of a certain species of bird from its
body weight (in grams). A least squares regression line was fit to data collected from a random
sample of 28 birds of this species. The equation of the line is
ŷ = 3.79 + 0.08x
where ŷ is the predicted brain weight and x is the body weight of the bird. Which of the following
gives the best interpretation of the slope of the regression line?
(A) There is an increase of 0.08 grams in the predicted brain weight of this species of bird for every
increase of 1 gram in body weight.
(B) There is an increase of 0.08 grams in the predicted body weight of this species of bird for every
increase of 1 gram in brain weight.
(C) There is an increase of 3.79 grams in the predicted brain weight of this species of bird for every
increase of 1 gram in body weight.
(D) There is an increase of 3.79 grams in the predicted body weight of this species of bird for every
increase of 1 gram in brain weight.…
The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y-hat = -0.0127 + 0.0180x. Wendall drinks 4 beers and has a blood alcohol level of .08. What is Wendall’s residual?
The relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y = -0.0127 + 0.0180x. Suppose that the legal limit to drive is a blood alcohol content of 0.08. If Ricky consumed 5 beers the model would predict that he would be:
Chapter 15 Solutions
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Ch. 15.2 - The estimated regression equation for a model...Ch. 15.2 - Consider the following data for a dependent...Ch. 15.2 - In a regression analysis involving 30...Ch. 15.2 - A shoe store developed the following estimated...Ch. 15.2 - The owner of Showtime Movie Theaters, Inc., would...Ch. 15.2 - The National Football League (NFL) records a...Ch. 15.2 - PC Magazine provided ratings for several...Ch. 15.2 - The Cond Nast Traveler Gold List provides ratings...Ch. 15.2 - The Professional Golfers Association (PGA)...Ch. 15.2 - Prob. 10E
Ch. 15.3 - In exercise 1, the following estimated regression...Ch. 15.3 - Prob. 12ECh. 15.3 - In exercise 3, the following estimated regression...Ch. 15.3 - In exercise 4, the following estimated regression...Ch. 15.3 - In exercise 5, the owner of Showtime Movie...Ch. 15.3 - In exercise 6, data were given on the average...Ch. 15.3 - Prob. 17ECh. 15.3 - Refer to exercise 10, where Major League Baseball...Ch. 15.5 - In exercise 1, the following estimated regression...Ch. 15.5 - Refer to the data presented in exercise 2. The...Ch. 15.5 - The following estimated regression equation was...Ch. 15.5 - In exercise 4, the following estimated regression...Ch. 15.5 - Prob. 23ECh. 15.5 - Prob. 24ECh. 15.5 - The Cond Nast Traveler Gold List for 2012 provided...Ch. 15.5 - In exercise 10, data showing the values of several...Ch. 15.6 - In exercise 1, the following estimated regression...Ch. 15.6 - Refer to the data in exercise 2. The estimated...Ch. 15.6 - In exercise 5, the owner of Showtime Movie...Ch. 15.6 - In exercise 24, an estimated regression equation...Ch. 15.6 - The American Association of Individual Investors...Ch. 15.7 - Consider a regression study involving a dependent...Ch. 15.7 - Consider a regression study involving a dependent...Ch. 15.7 - Management proposed the following regression model...Ch. 15.7 - Refer to the Johnson Filtration problem introduced...Ch. 15.7 - This problem is an extension of the situation...Ch. 15.7 - The Consumer Reports Restaurant Customer...Ch. 15.7 - A 10-year study conducted by the American Heart...Ch. 15.8 - Data for two variables, x and y, follow. xi 1 2 3...Ch. 15.8 - Data for two variables, x and y, follow. xi 22 24...Ch. 15.8 - Exercise 5 gave the following data on weekly gross...Ch. 15.8 - The following data show the curb weight,...Ch. 15.8 - The Ladies Professional Golfers Association (LPGA)...Ch. 15.9 - Refer to the Simmons Stores example introduced in...Ch. 15.9 - In Table 15.12 we provided estimates of the...Ch. 15.9 - Community Bank would like to increase the number...Ch. 15.9 - Over the past few years the percentage of students...Ch. 15.9 - The Tire Rack maintains an independent consumer...Ch. 15 - The admissions officer for Clearwater College...Ch. 15 - The personnel director for Electronics Associates...Ch. 15 - A partial computer output from a regression...Ch. 15 - Recall that in exercise 49, the admissions officer...Ch. 15 - Recall that in exercise 50 the personnel director...Ch. 15 - The Tire Rack, Americas leading online distributor...Ch. 15 - The Department of Energy and the U.S....Ch. 15 - A portion of a data set containing information for...Ch. 15 - Fortune magazine publishes an annual list of the...Ch. 15 - Consumer Research, Inc., is an independent agency...Ch. 15 - Matt Kenseth won the 2012 Daytona 500, the most...Ch. 15 - Finding the Best Car Value When trying to decide...
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
- Cellular Phone Subscribers The table shows the numbers of cellular phone subscribers y in millions in the United States from 2008 through 2013. Source: CTIA- The Wireless Association Year200820092010201120122013Number,y270286296316326336 (a) Find the least squares regression line for the data. Let x represent the year, with x=8 corresponding to 2008. (b) Use the linear regression capabilities of a graphing utility to find a linear model for the data. How does this model compare with the model obtained in part a? (c) Use the linear model to create a table of estimated values for y. Compare the estimated values with the actual data.arrow_forwardThe relationship between a number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: ?̂ = -0.0127 + 0.0180x The above equation implies that: each beer consumed increases blood alcohol by 1.27% on average it takes 1.8 beers to increase blood alcohol content by 1% each beer consumed increases blood alcohol by an average of the amount of 1.8% each beer consumed increases blood alcohol by exactly 0.018arrow_forwardSherry rents long boards. She records the height in cm and length of the board in cm that the customers rented. She notices a fairly linear relationship so she calculates a least squares regression equation for predicting board length from customer height: y=1/3x+1/3 What is the residual of a customer with a height of 155 cm who rents a 51 cm board?arrow_forward
- The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x+ 41.337. A twelfth car weighs 3,425 pounds and gets 12 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Click the icon to view the data table. Data Table ..... Weight (pounds), x Miles per (a) The coefficient of determination of the expanded data set is R = %. Gallon, y (Round to one decimal place as needed.) Car 1 3,771 22 Car 2 ,990 19 Car 3 3,534 20 Car 4 3,172 24 Car 5 2,579 27 Car 6 3,730 20 Car 7 2,605 25 Car 8 3,777 19 Car 9 3,308 19 Car 10 2,997 26 Car 11 2,751 27arrow_forwardThe relationship between number of beers consumed (x) and blood alcohol content (y) was studied in 16 male college students by using least squares regression. The following regression equation was obtained from this study: y-hat = -0.0127 + 0.0180x The above equation implies that: each beer consumed increases blood alcohol by .0127 on average it takes 1.8 beers to increase blood alcohol content by .01 After consuming 1 beer, blood alcohol equals .0180. each beer consumed increases blood alcohol by 0.018arrow_forwardThe data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x + 43.875. A twelfth car weighs 3,425 pounds and gets 13 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Data Table Click the icon to view the data table. ..... (a) The coefficient of determination of the expanded data set is R = %. Weight (pounds), x Miles per (Round to one decimal place as needed.) Gallon, y Car 1 3,770 20 Car 2 3,980 19 Car 3 3,530 19 Car 4 3,175 22 Car 5 2,580 27 Car 6 3,729 20 Car 7 2,607 26 Car 8 3,776 19 Car 9 3,311 22 Car 10 2,999 27 Car 11 2,755 27arrow_forward
- The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y = - 0.006x + 43.875. A twelfth car weighs 3,425 pounds and gets 13 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R2? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Data Table Click the icon to view the data table. Weight |(pounds), x Miles per Gallon, y Car 1 3,770 20 Car 2 3,980 19 Car 3 3,530 19 Car 4 3,175 22 Car 5 2,580 27 Car 6 3,729 20 Car 7 2,607 26 Car 8 3,776 19 Car 9 3,311 22 Car 10 2,999 27 Car 11 2,755 27arrow_forwardAn independent mail delivery service wants to study factors that affect the daily gas usage of its delivery trucks. Using data collected from different trucks on various days, a company analyst uses software to fit a regression model of the following form. y = 13 +8x, -1.1x, + 2x3 +0.04.x, In this model are the following variables. y= volume of gasoline used (in gallons) X1 weight of truck (in tons) x, = tire pressure (in psi, pounds per square inch) weight of initial pačkage load (in hundreds of pounds) X4 total distance driven while delivering packages (in miles) Answer the questions below for the interpretation of the coefficient of x, in this model. (a) Holding the other variables fixed, what is the average change in daily fuel used for each additional ton that a truck weighs? gallon(s) (b) Is this change an increase or a decrease? O increase O decrease Activate Windoarrow_forwardPlease help me better understand proble and how to calculate predicted vale of Allen's final exam. In a accounting course, a linear regression equation was computed to predict the final exam score from the score on the midterm exam. The equation of the least-squares regression line was Y= 10 + 0.85X. Y represents the final exam score, and X is the midterm exam score. QUESTION: Suppose Allen scores 83 on the midterm exam. What would be the predicted value of his score on the final exam (assuming no extrapolation error)?arrow_forward
- The relationship between the number of beers consumed and the blood alcohol content was studied in 16 male college students by using the least squares regression. The following regression equation was obtained from the study: y ̂= -0.0127+0.0180x The above equation implies that:A. each beer consumed increases blood alcohol by 1.27%.B. on the average, it takes 1.8 beers to increase blood alcohol content by 1%.C. Each beer consumed increases blood alcohol by an average amount of 1.8%.D. Each beer consumed increases blood alcohol by exactly 0.018 units.arrow_forwardA study investigated how the content of vitamin A in carrots is affected by the time being cooked. In this example: X represents the amount of time, in minutes, that the carrot slices were cooked Y represents the content of vitamin A (in milligrams) in the carrot slices The least-squares regression equation for this relationship is: Y = 23.4 – 0.55X In this study, which variable is the explanatory variable?arrow_forwardSuppose Tatiyana is interested in the relationship between language ability and time spent reading. She randomly selects a sample of 30 students from the local high school and collects their scores from a language aptitude test. She surveys the sample asking each student how many hours per month he or she spends reading. Using the sample data, Tatiyana produces a scatterplot with reading time on the horizontal axis and language test scores on the vertical axis. She develops a least squares regression equation where ? is the amount of time spent reading during the month and ?̂ is the predicted value of the language test score. ?̂=3.251x+31.237 Compute the value of ?̂ when a student spends 42 hours reading. Give your answer precise to one decimal place. Avoid rounding until the last step. ?̂= ? points Identify all of the true statements regarding the interpretation of ?̂ when ?=42. The value of ?̂ is ? a. the predicted number of students that read for 42 hours. b. the language test…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
Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
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