Statistics for Business & Economics
12th Edition
ISBN: 9781285528830
Author: David R. Anderson
Publisher: Cengage Learning US
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Chapter 14.2, Problem 5E
Elliptical trainers are becoming one of the more popular exercise machines. Their smooth and steady low-impact motion makes them a preferred choice for individuals with knee and ankle problems. But selecting the right trainer can be a difficult process. Price and quality are two important factors in any purchase decision. Are higher prices generally associated with higher quality elliptical trainers? Consumer Reports conducted extensive tests to develop an overall rating based on ease of use, ergonomics, construction, and exercise
| Brand and Model | Price ($) | Rating |
| Precor 5.31 | 3700 | 87 |
| Keys Fitness CG2 | 2500 | 84 |
| Octane Fitness Q37e | 2800 | 82 |
| LifeFitness X1 Basic | 1900 | 74 |
| NordicTrack AudioStrider 990 | 1000 | 73 |
| Schwinn 430 | 800 | 69 |
| Vision Fitness X6100 | 1700 | 68 |
| ProForm XP 520 Razor | 600 | 55 |
- a. Develop a
scatter diagram with price as the independent variable. - b. An exercise equipment store that sells primarily higher priced equipment has a sign over the display area that says “Quality: You Get What You Pay For.” Based upon your analysis of the data for ellipical trainers, do you think this sign fairly reflects the price-quality relationship for elliptical trainers?
- c. Use the least squares method to develop the estimated regression equation.
- d. Use the estimated regression equation to predict the rating for an ellipitical trainer with a price of $1500.
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Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I.
Woosley and A. J. McIntyre (University of New Mexico Press) provides data relating x =
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found at a prehistoric site. The following Minitab printout provides an analysis of the data.
Predictor
Coef
SE Coef
Constant
-0.221
2.429
-0.09
0.929
Diameter
0.8067
0.1524
5.33
0.001
S = 4.23750
R-Sq = 87.5%
(a) The standard error S. of the linear regression model is given in the printout as "S." What is the value ofS,?
e
(b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is SJVEX² - (1/n)(Ex). From the Minitab display, what is the
value of the standard error for the slope b?
(c) The formula for the margin of error E for…
Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data.
Predictor
Coef
SE Coef
T
P
Constant
-0.182
2.429
-0.09
0.929
Diameter
0.7824
0.1281
5.33
0.003
S = 3.92430
R-Sq = 71.4%
(a) The standard error Se of the linear regression model is given in the printout as "S." What is the value of Se?(b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is Se/√Σx2 – (1/n)(Σx)2. From the Minitab display, what is the value of the standard error for the slope b?(c) The formula for the…
Chapter 14 Solutions
Statistics for Business & Economics
Ch. 14.2 - Given are five observations for two variables, x...Ch. 14.2 - Given are five observations for two variables, x...Ch. 14.2 - Given are five observations collected in a...Ch. 14.2 - The following data give the percentage of women...Ch. 14.2 - Elliptical trainers are becoming one of the more...Ch. 14.2 - The National Football League (NFL) records a...Ch. 14.2 - A sales manager collected the following data on...Ch. 14.2 - The American Association of Individual Investors...Ch. 14.2 - Using a global-positioning-system (GPS)-based...Ch. 14.2 - On March 31, 2009, Ford Motor Companys shares were...
Ch. 14.2 - Sporty cars are designed to provide better...Ch. 14.2 - Concur Technologies, Inc., is a large...Ch. 14.2 - To the Internal Revenue Service, the...Ch. 14.2 - PCWorld rated four component characteristics for...Ch. 14.3 - The data from exercise 1 follow. xi 1 2 3 4 5 yi 3...Ch. 14.3 - The data from exercise 2 follow. xi 3 12 6 20 14...Ch. 14.3 - The data from exercise 3 follow. xi 2 6 9 13 20 yi...Ch. 14.3 - The following data show the brand, price (), and...Ch. 14.3 - In exercise 7 a sales manager collected the...Ch. 14.3 - Bicycling, the worlds leading cycling magazine,...Ch. 14.3 - An important application of regression analysis in...Ch. 14.3 - Refer to exercise 5 where the following data were...Ch. 14.5 - The data from exercise 1 follow. xi 1 2 3 4 5 yi 3...Ch. 14.5 - The data from exercise 2 follow. xi 3 12 6 20 14...Ch. 14.5 - The data from exercise 3 follow. xi 2 6 9 13 20 yi...Ch. 14.5 - In exercise 18 the data on price () and the...Ch. 14.5 - The number of megapixels in a digital camera is...Ch. 14.5 - In exercise 8 ratings data on x = the quality of...Ch. 14.5 - Refer to exercise 21, where data on production...Ch. 14.5 - Prob. 30ECh. 14.5 - In exercise 20, data on x = weight (pounds) and y...Ch. 14.6 - The data from exercise 1 follow. xi 1 2 3 4 5 yi 3...Ch. 14.6 - The data from exercise 2 follow. xi 3 12 6 20 14...Ch. 14.6 - The data from exercise 3 follow. xi 2 6 9 13 20 yi...Ch. 14.6 - The following data are the monthly salaries y and...Ch. 14.6 - In exercise 7, the data on y = annual sales (...Ch. 14.6 - In exercise 13, data were given on the adjusted...Ch. 14.6 - Refer to exercise 21, where data on the production...Ch. 14.6 - Almost all U.S. light-rail systems use electric...Ch. 14.7 - The commercial division of a real estate firm is...Ch. 14.7 - Following is a portion of the computer output for...Ch. 14.7 - A regression model relating x, number of...Ch. 14.7 - Out-of-state tuition and fees at the top graduate...Ch. 14.7 - Automobile racing, high-performance driving...Ch. 14.8 - Given are data for two variables, x and y. xi 6 11...Ch. 14.8 - The following data were used in a regression...Ch. 14.8 - Data on advertising expenditures and revenue (in...Ch. 14.8 - Refer to exercise 7, where an estimated regression...Ch. 14.8 - Recent family home sales in San Antonio provided...Ch. 14.9 - Consider the following data for two variables, x...Ch. 14.9 - Consider the following data for two variables, x...Ch. 14.9 - Charity Navigator is Americas leading independent...Ch. 14.9 - Many countries, especially those in Europe, have...Ch. 14.9 - Prob. 54ECh. 14 - Does a high value of r2 imply that two variables...Ch. 14 - In your own words, explain the difference between...Ch. 14 - What is the purpose of testing whether 1 = 0? If...Ch. 14 - The Dow Jones Industrial Average (DJIA) and the...Ch. 14 - The following data show Morningstars Fair Value...Ch. 14 - One of the biggest changes in higher education in...Ch. 14 - Jensen Tire Auto is in the process of deciding...Ch. 14 - In a manufacturing process the assembly line speed...Ch. 14 - A sociologist was hired by a large city hospital...Ch. 14 - The regional transit authority for a major...Ch. 14 - A marketing professor at Givens College is...Ch. 14 - The Transactional Records Access Clearinghouse at...Ch. 14 - The Toyota Camry is one of the best-selling cars...Ch. 14 - You have been assigned to analyze the risk...Ch. 14 - As part of a study on transportation safety, the...Ch. 14 - Consumer Reports tested 166 different...Ch. 14 - Finding the Best Car Value When trying to decide...
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- Prehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data. Predictor Constant Diameter S = 3.91620 Coef -0.185 0.7959 lower limit upper limit R-Sq= 70.75 SE Coef 2.429 0.1686 T 5.33 P 0.929 0.019 (a) The standard error Se of the linear regression model is given in the printout as "S." What is the value of Se? (b) The standard error of the coefficient of the predictor variable is found under "SE Coef." Recall that the standard error for b is S₂/Ex² - (1/n)(Ex)². From the Minitab display, what is the value of the standard error for the slope b? (c) The formula for the…arrow_forwardPrehistoric pottery vessels are usually found as sherds (broken pieces) and are carefully reconstructed if enough sherds can be found. Information taken from Mimbres Mogollon Archaeology by A. I. Woosley and A. J. McIntyre (University of New Mexico Press) provides data relating x = body diameter in centimeters and y = height in centimeters of prehistoric vessels reconstructed from sherds found at a prehistoric site. The following Minitab printout provides an analysis of the data. Predictor Coef SE Coef T P Constant -0.212 2.429 -0.09 0.929 Diameter 0.7527 0.1686 5.33 0.013 S = 4.16190 R-Sq = 81.2% (c) The formula for the margin of error E for a c% confidence interval for the slope ? can be written as E = tc(SE Coef). The Minitab display is based on n = 12 data pairs. Find the critical value tc for a 90% confidence interval in the relevant table. Then find a 90% confidence interval for the population slope ?. (Use 3 decimal places.) tc lower limit upper…arrow_forwardWhich one of the following cost estimation methods is the most accurate? Select one: a. The high-low method. b. Regression analysis. Of Subjective forecasting. Of. Scatter Grapharrow_forward
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