Introduction to Statistics and Data Analysis
5th Edition
ISBN: 9781305445963
Author: PECK
Publisher: Cengage
expand_more
expand_more
format_list_bulleted
Concept explainers
Videos
Question
Chapter 14.4, Problem 51E
To determine
Explain the reasons that might have arrived at the particular model.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solution
Students have asked these similar questions
Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of thecompany wants to know how different variables affect the sales of his vehicles. A random sample ofyearly data was taken with the view to testing the model:SALES=?+?AGE+?MIL+?ENGWhere SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the totalmileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data wasprocessed using MINITAB and the following is an extract of the output obtained:The regression equation is *****PredictorCoef StDev t-ratio p-valueConstant1.7586 0.2525 6.9648 0.0000AGE 0.2124 0.3175 * 0.5042MIL -0.75270.3586 -2.0991 **ENG 4.8124 0.6196 7.7664 0.0000Analysis of VarianceSource DF SS MS F pRegression3 413.1291 138.7097*** 0.00Error 50 457.7607 2.2888Total 53a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ‘*’, ‘**’, ‘***’and ‘***’. d) Hence…
Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of thecompany wants to know how different variables affect the sales of his vehicles. A random sample ofyearly data was taken with the view to testing the model:SALES=?+?AGE+?MIL+?ENGWhere SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the totalmileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data wasprocessed using MINITAB and the following is an extract of the output obtained:
a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ‘*’, ‘**’, and ‘***’. d) Hence test whether ? is significant. Give reasons for your answer. e) 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.
What is the relationship between diamond price and carat size? 307 diamonds were sampled and a straight-line relationship was hypothesized between y = diamond price (in dollars) and x = size of the diamond (in carats). The simple linear regression for the analysis is shown below:
Least Squares Linear Regression of PRICE
Interpret the standard deviation of the regression model.
a) We expect most of the sampled diamond prices to fall within $1117.56 of their least squares predicted values.
b) We can explain 89.25% of the variation in the sampled diamond prices around their mean using the size of the diamond in a linear model.
c) For every 1-carat increase in the size of a diamond, we estimate that the price of the diamond will increase by $1117.56.
d) We expect most of the sampled diamond prices to fall within $2235.12 of their least squares predicted values.
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 - Prob. 38ECh. 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
- Find the equation of the regression line for the following data set. x 1 2 3 y 0 3 4arrow_forwardThe data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. ..... (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. y=x+O Data for licensed drivers by age and gender. (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Find the least-squares regression line for females. x + Number of Number of Number of Male Fatal Number of Female Fatal (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Licensed Drivers Crashes Licensed Drivers Crashes (b) Interpret the slope of the least-squares regression line for each gender, if appropriate. How might an insurance…arrow_forwardThe attached results are for a multiple regression study of smartphone addiction (SSA-SV) proneness in relation to 1) Gender 2)Age 3) Anxiety (GAD-7). I just want to clarify what the F-statistic means and the effects of AGE on the F-statistic; given that AGE is statistically significant compared to the other predictor variables.arrow_forward
- Zagat’s publishes restaurant ratings for various locations in the United States. The following table contains the Zagat rating for food, décor, service, and the cost per person for a sample of 100 restaurants located in New York City and in a suburb of New York City. Develop a regression model to predict the cost per person, based on a variable that represents the sum of the ratings for food, décor, and service. Predict the mean cost per person for a restaurant with a sum-mated rating of 50. What should you tell the owner of a group of restaurants in this geographical area about the relationship between the summated rating and the cost of a meal? Location Food Décor Service Summated Rating Coded Location Cost Bins Midpoints City 22 14 19 55 0 33 19.99 25 City 20 15 20 55 0 26 29.99 35 City 23 19 21 63 0 43 39.99 45 City 19 18 18 55 0 32 49.99 55 City 24 16 18 58 0 44 59.99 65 City 22 22 21 65 0 44 69.99 75 City 22 20 20 62 0 50 79.99 85 City 20 19…arrow_forwardA survey conducted by a research team was to investigate how the education level, tenure in current employment, and age, are related to annual income. A sample 20 emloyees is selected and the data is given below. 1. Which variable has significant relationship with income at 0.05 level of significance?arrow_forwardBeachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALES=?+?AGE+?MIL+?ENG Where SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: d) Hence test whether ? is significant. Give reasons for your answer. e) 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_forward
- Beachcomber Ltd in a local car dealership that sells used and new vehicles. The manager of the company wants to know how different variables affect the sales of his vehicles. A random sample of yearly data was taken with the view to testing the model: SALES=?+?AGE+?MIL+?ENG Where SALES= amount that a vehicle is sold for($000’s), AGE = age of the vehicle, MIL= the total mileage of the vehicle at the point of sale and ENG = the size of the engine. The sample of data was processed using MINITAB and the following is an extract of the output obtained: a) What is dependent and independent variables? b) Fully write out the regression equation c) Fill in the missing values ‘*’, ‘**’, and ‘***’.arrow_forwardAn article on the cost of housing in California† included the following statement: "In Northern California, people from the San Francisco Bay area pushed into the Central Valley, benefiting from home prices that dropped on average $4,000 for every mile traveled east of the Bay." If this statement is correct, what is the slope of the least-squares regression line, ŷ = a + bx, where y = house price (in dollars) and x = distance east of the Bay (in miles)? Explain. This value is the change in the distance east of the bay, in miles, for each increase of $1 in average home price.This value is the change in the distance east of the bay, in miles, for each decrease of $1 in average home price. This value is the change in the average home price, in dollars, for each increase of 1 mile in the distance east of the bay.This value is the change in the average home price, in dollars, for each decrease of 1 mile in the distance east of the bay.arrow_forwardas hit (in miles per hour) and the distance it traveled (in feet) fo efficient. Data Table Speed (mph) 103.6 101.2 100.7 101.3 99.4 104.8 101.4 105.3 103.0 101.7 105.4 103.4 Print Distance (feet) 402 392 396 393 394 421 399 420 393 411 418 394 Done X Cancel Critical Values for the Correlation Coefficient Critical Values for Correlation Coefficient n 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 0.997 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576 0.553 0.532 0.514 0.497 0.482 0.468 0.456 0.444 0.433 0.423 0.413arrow_forward
- The data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. Click the icon to view the data table. C... (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for female Find the least-squares regression line for males. ŷ=0x+0 (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Data for licensed drivers by age and gender. 21-24 25-34 35-44 45-54 55-64 65-74 > 74 Number of Male Fatal Licensed Age Drivers (000s) < 16 12 16-20 6,424 6,914 18,068 20,406 Number of Number of Female Fatal Crashes Licensed (Males) Drivers (000s) 227 12 6,139 Crashes (Females) 77 2,113 1,534 5,180 5,016 6,816 8,567 17,664 2,780 7,990 20,047 2,742 19,984 14,441 8,386 5,375 19,898 14,328 8,194…arrow_forwardThe relationship between total cholesterol (milligrams per deciliter) and BMI (Ratio of weight in kilograms to height in metres squared) of 20 participants is shown in the scatterplot below along with the least squares regression line. Which of the following statements is correct? a) The relationship between total cholesterol and BMI is linear as can be seen by the random scatter of the data above and below the least squares regression line. Both variables are metric and therefore it is appropriate to use Pearson's correlation to measure the linear association between the two variables. b) The relationship between total cholesterol and BMI is non-linear and since both variables are metric it is appropriate to use Pearson's correlation to measure the linear association between the two variables. c) The relationship between total cholesterol and BMI is non-linear as can be seen by the patterning of points around the least squares regression line and therefore it is not…arrow_forwardThe data in the table represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender. Complete parts (a) to (c) below. Click the icon to view the data table. (a) Find the least-squares regression line for males treating the number of licensed drivers as the explanatory variable, x, and the number of fatal crashes, y, as the response variable. Repeat this procedure for females. Find the least-squares regression line for males. Data for licensed drivers by age and gender. y = x+ (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Find the least-squares regression line for females. y =x+ Number of Number of (Round the slope to three decimal places and round the constant to the nearest integer as needed.) Number of Male Fatal Number of Female Fatal Licensed Drivers Crashes Licensed Drivers Crashes (b) Interpret the slope of the least-squares regression line for each gender, if…arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
Linear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
Elementary Linear Algebra (MindTap Course List)AlgebraISBN:9781305658004Author:Ron LarsonPublisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...AlgebraISBN:9781680331141Author:HOUGHTON MIFFLIN HARCOURTPublisher:Houghton Mifflin Harcourt
Linear Algebra: A Modern Introduction
Algebra
ISBN:9781285463247
Author:David Poole
Publisher:Cengage Learning
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Elementary Linear Algebra (MindTap Course List)
Algebra
ISBN:9781305658004
Author:Ron Larson
Publisher:Cengage Learning
Functions and Change: A Modeling Approach to Coll...
Algebra
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Cengage Learning
Big Ideas Math A Bridge To Success Algebra 1: Stu...
Algebra
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:Houghton Mifflin Harcourt
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