Intro Stats + New Mylab Statistics With Pearson Etext:
Intro Stats + New Mylab Statistics With Pearson Etext:
5th Edition
ISBN: 9780134210230
Author: De Veaux, Richard D.
Publisher: Pearson College Div
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Chapter 7, Problem 1E

True or false If false, explain briefly.

  1. a) We choose the linear model that passes through the most data points on the scatterplot.
  2. b) The residuals are the observed y-values minus the y-values predicted by the linear model.
  3. c) Least squares means that the square of the largest residual is as small as it could possibly be.

a.

Expert Solution
Check Mark
To determine

Find whether the given statement is true or false.

Answer to Problem 1E

The given statement is false.

Explanation of Solution

Given info:

The linear model, which passes through the most data points on the scatterplot, are chosen.

Justification:

If the line passes through the most data points on the then that line won’t be straight line. The line touches some of the points or none of the points, but it minimize the sum of least squares.

Thus, the given statement is false.

Statistics Concept Introduction

The conditions for a scatterplot that is well fitted for the data are,

  • Straight Enough Condition: The relationship between y and x straight enough to proceed with a linear regression model.
  • Outlier Condition: No outlier must be there which influences the fit of the least square line.
  • Thickness Condition: The spread of the data around the generally straight relationship seem to be consistent for all values of predictor variable.

b.

Expert Solution
Check Mark
To determine

Find whether the given statement is true or false.

Answer to Problem 1E

The given statement is true.

Explanation of Solution

Given info:

The residuals are the observed y-values minus the predicted y-values by the linear model.

Justification:

The residual gives the difference between the observed value of the response variable and that of the predicted value.

Thus, the given statement is true.

Statistics Concept Introduction

Residual:

The residual is defined as Residual = Observed value  Predicted value or e=yy^ where y^ be the predicted value of the response variable and y be the actual value of the response variable.

c.

Expert Solution
Check Mark
To determine

Find whether the given statement is true or false.

Answer to Problem 1E

The given statement is false.

Explanation of Solution

Given info:

Least square defines the square of the largest residual is as small as it could possibly be.

Justification:

A least square criterion defines the unique line that minimize the variance of residuals or sum of squared of the residuals. It does not imply to minimize the largest residual is as small as it could possibly be.

Thus, the given statement is false.

Statistics Concept Introduction

Least-square criterion:

The least-square criterion is of a regression line that the best fits of a set of data points having the smallest possible sum of squares.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 7 Solutions

Intro Stats + New Mylab Statistics With Pearson Etext:

Ch. 7 - True or false II If false, explain briefly. a)...Ch. 7 - Prob. 3ECh. 7 - Prob. 4ECh. 7 - Bookstore sales revisited Recall the data we saw...Ch. 7 - Prob. 6ECh. 7 - Prob. 7ECh. 7 - Prob. 8ECh. 7 - Bookstore sales once more Here are the residuals...Ch. 7 - Prob. 10ECh. 7 - Prob. 11ECh. 7 - Prob. 12ECh. 7 - Prob. 13ECh. 7 - Prob. 14ECh. 7 - Prob. 15ECh. 7 - Prob. 16ECh. 7 - More cereal Exercise 15 describes a regression...Ch. 7 - Prob. 18ECh. 7 - Another bowl In Exercise 15, the regression model...Ch. 7 - More engine size In Exercise 16, the regression...Ch. 7 - Cereal again The correlation between a cereals...Ch. 7 - Prob. 22ECh. 7 - Prob. 23ECh. 7 - Prob. 24ECh. 7 - Prob. 25ECh. 7 - Prob. 26ECh. 7 - Prob. 27ECh. 7 - Residuals Tell what each of the residual plots...Ch. 7 - Real estate A random sample of records of home...Ch. 7 - Prob. 30ECh. 7 - Prob. 31ECh. 7 - Prob. 32ECh. 7 - Real estate again The regression of Price on Size...Ch. 7 - Prob. 34ECh. 7 - Prob. 35ECh. 7 - More misinterpretations A Sociology student...Ch. 7 - Real estate redux The regression of Price on Size...Ch. 7 - Prob. 38ECh. 7 - Prob. 39ECh. 7 - Prob. 40ECh. 7 - Prob. 41ECh. 7 - Last ride Consider the roller coasters (with the...Ch. 7 - Prob. 43ECh. 7 - Prob. 44ECh. 7 - Prob. 45ECh. 7 - Prob. 46ECh. 7 - Prob. 47ECh. 7 - Prob. 48ECh. 7 - Prob. 49ECh. 7 - Interest rates and mortgages 2015 again In Chapter...Ch. 7 - Online clothes An online clothing retailer keeps...Ch. 7 - Online clothes II For the online clothing retailer...Ch. 7 - Prob. 53ECh. 7 - Success in college Colleges use SAT scores in the...Ch. 7 - SAT, take 2 Suppose we wanted to use SAT math...Ch. 7 - Prob. 56ECh. 7 - Prob. 57ECh. 7 - Wildfires 2015sizes We saw in Exercise 57 that the...Ch. 7 - Used cars 2014 Carmax.com lists numerous Toyota...Ch. 7 - Drug abuse revisited Chapter 6, Exercise 42...Ch. 7 - Prob. 61ECh. 7 - Prob. 62ECh. 7 - Prob. 63ECh. 7 - Chicken Chicken sandwiches are often advertised as...Ch. 7 - Prob. 65ECh. 7 - Cost of living 2016 Numbeo.com lists the cost of...Ch. 7 - Prob. 67ECh. 7 - Prob. 68ECh. 7 - Prob. 69ECh. 7 - Climate change 2016, revisited In Exercise 69, we...Ch. 7 - Prob. 71ECh. 7 - Prob. 72ECh. 7 - Prob. 73ECh. 7 - Heptathlon revisited again We saw the data for the...Ch. 7 - Hard water In an investigation of environmental...Ch. 7 - Gators Wildlife researchers monitor many wildlife...Ch. 7 - Prob. 77ECh. 7 - Least squares Consider the four points (200,1950),...
Knowledge Booster
Statistics
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.
Recommended textbooks for you
  • Glencoe Algebra 1, Student Edition, 9780079039897...
    Algebra
    ISBN:9780079039897
    Author:Carter
    Publisher:McGraw Hill
    Linear Algebra: A Modern Introduction
    Algebra
    ISBN:9781285463247
    Author:David Poole
    Publisher:Cengage Learning
    Elementary Linear Algebra (MindTap Course List)
    Algebra
    ISBN:9781305658004
    Author:Ron Larson
    Publisher:Cengage Learning
  • Big Ideas Math A Bridge To Success Algebra 1: Stu...
    Algebra
    ISBN:9781680331141
    Author:HOUGHTON MIFFLIN HARCOURT
    Publisher:Houghton Mifflin Harcourt
  • Glencoe Algebra 1, Student Edition, 9780079039897...
    Algebra
    ISBN:9780079039897
    Author:Carter
    Publisher:McGraw Hill
    Linear Algebra: A Modern Introduction
    Algebra
    ISBN:9781285463247
    Author:David Poole
    Publisher:Cengage Learning
    Elementary Linear Algebra (MindTap Course List)
    Algebra
    ISBN:9781305658004
    Author:Ron Larson
    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