Introduction To Statistics And Data Analysis
6th Edition
ISBN: 9781337793612
Author: PECK, Roxy.
Publisher: Cengage Learning,
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Textbook Question
Chapter 14.4, Problem 53E
The article “The Analysis and Selection of Variables in Linear Regression” (Biometrics [1976]: 1–49) reports on an analysis of data taken from issues of Motor Trend magazine. The dependent variable y was gas mileage and there were n = 32 observations. The independent variables were x1 = Engine type (1 = straight, 0 = V), x2 = number of cylinders, x3 = Transmission type (1 = manual, 0 = automatic), x4 = Number of transmission speeds, x5 = Engine size, x6 = Horsepower, x1 = Number of carburetor barrels, x8 = Final drive ratio, x9 = Weight, and x10 = Quarter-mile time. The R2 and adjusted R2 values are given in the accompanying table for the best model using k predictors for k = 1,…, 10.
Which model would you select? Explain your choice and the criteria used to reach your decision.
![Chapter 14.4, Problem 53E, The article The Analysis and Selection of Variables in Linear Regression (Biometrics [1976]: 149)](https://content.bartleby.com/tbms-images/9781337793612/Chapter-14/images/93612-14.4-53e-question-digital_image_001.png)
Expert Solution & Answer
Trending nowThis is a popular solution!
Students have asked these similar questions
Q2) Find the regression line for the following data, then predict the value of y
when x is 5:
X
0
2
4
6
8
y
2
4
3
8
10
Corvette, Ferrari, and Jaguar produced a variety of classic cars that continue to increase in value. The data showing the rarity rating (1–20) and the high price ($1000s) for 15 classic cars is contained in the Excel Online file below. Construct a spreadsheet to answer the following questions.
You work as a data scientist for a real estate company in a seaside resort town. Your boss has asked you to discover if it's possible to predict how much a
home's distance from the water affects its selling price. You are going to collect a random sample of 7 recently sold homes in your town. You will note the
distance each home is from the water (denoted by x, in km) and each home's selling price (denoted by y, in hundreds of thousands of dollars). You will also note
the product x.y of the distance from the water and selling price for each home. (These products are written in the row labeled "xy").
(a) Click on "Take Sample" to see the results for your random sample.
Distance from the
water, .x
(in km)
Take Sample
Selling price, y
(in hundreds of thousands
of dollars)
xy
Send data to calculator
Based on the data from your sample, enter the indicated values in the column on the left below. Round decimal values to three decimal places. When
you are done, select "Compute". (In the table…
Chapter 14 Solutions
Introduction To Statistics And Data Analysis
Ch. 14.1 - Prob. 1ECh. 14.1 - The authors of the paper Weight-Bearing Activity...Ch. 14.1 - Prob. 3ECh. 14.1 - Prob. 4ECh. 14.1 - Prob. 5ECh. 14.1 - Prob. 6ECh. 14.1 - Prob. 7ECh. 14.1 - Prob. 8ECh. 14.1 - Prob. 9ECh. 14.1 - The relationship between yield of maize (a type of...
Ch. 14.1 - Prob. 11ECh. 14.1 - A manufacturer of wood stoves collected data on y...Ch. 14.1 - Prob. 13ECh. 14.1 - Prob. 14ECh. 14.1 - Prob. 15ECh. 14.2 - Prob. 16ECh. 14.2 - State as much information as you can about the...Ch. 14.2 - Prob. 18ECh. 14.2 - Prob. 19ECh. 14.2 - Prob. 20ECh. 14.2 - The ability of ecologists to identify regions of...Ch. 14.2 - Prob. 22ECh. 14.2 - Prob. 23ECh. 14.2 - Prob. 24ECh. 14.2 - Prob. 25ECh. 14.2 - Prob. 26ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - Prob. 28ECh. 14.2 - The article The Undrained Strength of Some Thawed...Ch. 14.2 - Prob. 30ECh. 14.2 - Prob. 31ECh. 14.2 - Prob. 32ECh. 14.2 - Prob. 33ECh. 14.2 - This exercise requires the use of a statistical...Ch. 14.2 - This exercise requires the use of a statistical...Ch. 14.3 - Prob. 36ECh. 14.3 - Prob. 37ECh. 14.3 - When Coastal power stations take in large amounts...Ch. 14.3 - Prob. 39ECh. 14.3 - The article first introduced in Exercise 14.28 of...Ch. 14.3 - Data from a random sample of 107 students taking a...Ch. 14.3 - Benevolence payments are monies collected by a...Ch. 14.3 - Prob. 43ECh. 14.3 - Prob. 44ECh. 14.3 - Prob. 45ECh. 14.3 - Prob. 46ECh. 14.3 - Exercise 14.26 gave data on fish weight, length,...Ch. 14.3 - Prob. 48ECh. 14.3 - Prob. 49ECh. 14.3 - Prob. 50ECh. 14.4 - Prob. 51ECh. 14.4 - Prob. 52ECh. 14.4 - The article The Analysis and Selection of...Ch. 14.4 - Prob. 54ECh. 14.4 - Prob. 55ECh. 14.4 - Prob. 57ECh. 14.4 - Prob. 58ECh. 14.4 - Prob. 59ECh. 14.4 - Prob. 60ECh. 14.4 - This exercise requires use of a statistical...Ch. 14.4 - Prob. 62ECh. 14 - Prob. 63CRCh. 14 - Prob. 64CRCh. 14 - The accompanying data on y = Glucose concentration...Ch. 14 - Much interest in management circles has focused on...Ch. 14 - Prob. 67CRCh. 14 - Prob. 68CRCh. 14 - Prob. 69CRCh. 14 - A study of pregnant grey seals resulted in n = 25...Ch. 14 - Prob. 71CRCh. 14 - Prob. 72CRCh. 14 - This exercise requires the use of a statistical...
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
- MR In Dave Eggers’ novel The Circle, a mysteri-ous technology company has developed a strangely data-driven work environment in which employees are assigned a performance score that seems to be the product of factors in their social activities and environment, such as the extent of their engagement in work community and the number of times they post on the company’s social media site. Using the fictional data below, compute r and r2 for each com-bination of two variables from this novel and test the correlations for their significance. Write a paragraph interpreting the relationships between these vari-ables, and what they might mean for the companyarrow_forwardr. Lyte wishes to study speed of Reaction Time to press a button in response to the onset of a lamp. The independent variable (IV) is the color of the light produced by the lamp (red, orange, yellow, green, or blue). Since only 10 participants are available, she elects to administer the IV within-subjects with all 10 participants being exposed to all five levels of the color variable. The order of the color of the light presentation is to be counterbalanced. Using concepts from the textbook, why would Dr. Lyte need to use counterbalancing in this scenario?arrow_forwardQ: The dataset posted below lists a sample of months and the advertising budget (in hundreds of dollars) for TV, radio and newspaper advertisements. Also included is whether a coupon was published for that month and the resulting sales (in thousands of dollars). a) Develop a multiple regression model predicting the sales based off the four predictor variables: TV, radio, and newspaper advertising budget and whether a coupon is used. Recode Coupon as 0 = No and 1 = Yes. Report the estimated regression equation (Solve in Excel) TV ($100) radio ($100) newspaper ($100) Coupon sales ($1000) 0.7 39.6 8.7 No 1.6 230.1 37.8 69.2 No 22.1 4.1 11.6 5.7 Yes 3.2 44.5 39.3 45.1 No 10.4 250.9 36.5 72.3 No 22.2 8.6 2.1 1 No 4.8 17.2 45.9 69.3 Yes 9.3 104.6 5.7 34.4 No 10.4 216.8 43.9 27.2 Yes 22.3 5.4 29.9 9.4 No 5.3 69 9.3 0.9 No 9.3 70.6 16 40.8 No 10.5 151.5 41.3 58.5 No 18.5 195.4 47.7 52.9 Yes 22.4 13.1 0.4 25.6 Yes 5.3 76.4 0.8…arrow_forward
- A statistical program is recommended. Car manufacturers produced a variety of classic cars that continue to increase in value. Suppose the following data is based upon the Martin Rating System for Collectible Cars, and shows the rarity rating (1–20) and the high price ($1,000) for 15 classic cars. (b) Develop an estimated multiple regression equation with x = rarity rating and x2 as the two independent variables. (Round b0 and b1 to the nearest integer and b2 to one decimal place.) (c) Consider the nonlinear relationship shown by equation (16.7): E(y) = β0β1x Use logarithms to develop an estimated regression equation for this model. (Round b0 to three decimal places and b1 to four decimal places.)arrow_forwardSam Jones has 2 years of historical sales data for his company. He is applyingfor a business loan and must supply his projections of sales by month for thenext 2 years to the bank. a. Using the data from Table 6–12, provide a regression forecast for timeperiods 25 through 48.b. Does Sam’s sales data show a seasonal pattern?arrow_forwardA highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow(y) Vehicle Speed(x) 1,258 35 1,329 40 1,227 30 1,336 45 1,348 50 1,125 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2.(Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = ?? (b) Use ? = 0.01 to test for a significant relationship. State the null and alternative hypotheses. -H0: One or more of the parameters is not equal to zero.Ha: b0 = b1 = b2 = 0 -H0: b0 = b1 = b2 = 0Ha: One or more…arrow_forward
- Ten cars between 1 and 6 years old were randomly selected from the classified ads. The data were obtained, where x denotes age, in years, and y denotes price, in hundreds of dollars. Develop a scatterplot and describe the relationship between the price and the age of the cars. b) Find and interpret the correlation coefficient. c) d) At 5% level, test whether the age and the price of the cars are linearly related. D Find the regression equation and interpret the regression coefficients.arrow_forwardA special education teacher did research on whether or not there is a relationship between the number of students in his class and the number incidents of “acting out” behaviors exhibited by the autistic students in the classroom. He collects data for a year and aggregates them by month. He obtained the statistics below, r= -.863 R2=.74 b= -1.212294 a= 131.176598 10.) How does the presence of more students affect the incidents in the class? a) as students are added the incidences increase b) as students are added the incidences decrease c) the number of students does not affect acting out d) the number of students caused more incidents How much of the variability of acting out is explained by the number of students in the class?___________arrow_forwardConsider the following five data points: X -1 0 1 2 3 Y -1 1 2 4 5 a. Use regression analysis to calculate by hand the estimated coefficients of the equation Y = B + aX. b. Compute the standard error and the t-statistics for the coefficient of X.arrow_forward
- A highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow(y) Vehicle Speed(x) 1,254 35 1,330 40 1,228 30 1,334 45 1,351 50 1,126 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = (b) Use ? = 0.01 to test for a significant relationship. Find the value of the test statistic. (Round your answer to two decimal places.) Find the p-value. (Round your answer to three decimal places.) p-value = (c)…arrow_forwardA highway department is studying the relationship between traffic flow and speed. The following model has been hypothesized: y = ?0 + ?1x + ? where y = traffic flow in vehicles per hour x = vehicle speed in miles per hour. The following data were collected during rush hour for six highways leading out of the city. Traffic Flow(y) Vehicle Speed(x) 1,254 35 1,330 40 1,228 30 1,334 45 1,351 50 1,126 25 In working further with this problem, statisticians suggested the use of the following curvilinear estimated regression equation. ŷ = b0 + b1x + b2x2 (a) Develop an estimated regression equation for the data of the form ŷ = b0 + b1x + b2x2. (Round b0 to the nearest integer and b1 to two decimal places and b2 to three decimal places.) ŷ = (b) Use ? = 0.01 to test for a significant relationship. State the null and alternative hypotheses. H0: b0 = b1 = b2 = 0Ha: One or more of the parameters is not equal to zero.H0: One or more of the parameters is…arrow_forwardThank you for helping with this question.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
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