Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Concept explainers

Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as p…
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Question
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Chapter 1.7, Problem 32E

a.

To determine

To calculate:

Equation and correlation coefficient for given graphs.

a.

Expert Solution
Check Mark

Answer to Problem 32E

Correlation coefficients that represents the graph (iii) is 0.973 , graph (ii) is 0.624 , and the graph (i) is −0.986 .

Explanation of Solution

Given information:

  Precalculus with Limits: A Graphing Approach, Chapter 1.7, Problem 32E , additional homework tip 1Precalculus with Limits: A Graphing Approach, Chapter 1.7, Problem 32E , additional homework tip 2

  y=0.68x+2.7y=0.41x+2.7y=−0.62x+10.0r=0.973r=−0.986r=0.624

Calculation:

Consider the first equation,

  y=0.68x+2.7

Now plot a scatter plot for the equation y=0.68x+2.7 ,

  Precalculus with Limits: A Graphing Approach, Chapter 1.7, Problem 32E , additional homework tip 3

From the above graph it is observed that the it is same as the graph in option (iii)

Thus, equation y=0.68x+2.7 represents the graph (iii)

Also, slope of the equation y=0.68x+2.7 is most positive, thus the correlation coefficients that represents the graph (iii) is 0.973 .

Now, consider the second equation,

  y=0.41x+2.7

Now plot a scatter plot for the equation y=0.41x+2.7 ,

  Precalculus with Limits: A Graphing Approach, Chapter 1.7, Problem 32E , additional homework tip 4

From the above graph it is observed that the it is same as the graph in option (ii)

Thus, equation y=0.41x+2.7 represents the graph (ii)

Also, slope of the equation y=0.41x+2.7 is second most positive, thus the correlation coefficients that represents the graph (ii) is 0.624 .

Now, consider the third equation,

  y=−0.62x+10.0

Now plot a scatter plot for the equation y=−0.62x+10.0 ,

  Precalculus with Limits: A Graphing Approach, Chapter 1.7, Problem 32E , additional homework tip 5

From the above graph it is observed that it is same as the graph in option (i)

Thus, equation y=−0.62x+10.0 represents the graph (i)

Also, slope of the equation y=−0.62x+10.0 is negative, thus the correlation coefficients that represents the graph (i) is −0.986

b.

To determine

To calculate:

Model that best fit for its data according to correlation coefficient.

b.

Expert Solution
Check Mark

Answer to Problem 32E

Model equation y=−0.62x+10.0 fits the data well.

Explanation of Solution

Given information:

  Precalculus with Limits: A Graphing Approach, Chapter 1.7, Problem 32E , additional homework tip 6Precalculus with Limits: A Graphing Approach, Chapter 1.7, Problem 32E , additional homework tip 7

  y=0.68x+2.7y=0.41x+2.7y=−0.62x+10.0r=0.973r=−0.986r=0.624

Calculation:

According to the correlation coefficient, model number 3 fits the data well which represents y=−0.62x+10.0 equation as it has closet |r|≤1

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Chapter 1.7, Problem 31E
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Chapter 1.7, Problem 33E

Chapter 1 Solutions

Precalculus with Limits: A Graphing Approach

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Prob. 15ECh. 1.6 - Prob. 16ECh. 1.6 - Prob. 17ECh. 1.6 - Prob. 18ECh. 1.6 - Prob. 19ECh. 1.6 - Prob. 20ECh. 1.6 - Prob. 21ECh. 1.6 - Prob. 22ECh. 1.6 - Prob. 23ECh. 1.6 - Prob. 24ECh. 1.6 - Prob. 25ECh. 1.6 - Prob. 26ECh. 1.6 - Prob. 27ECh. 1.6 - Prob. 28ECh. 1.6 - Prob. 29ECh. 1.6 - Prob. 30ECh. 1.6 - Prob. 31ECh. 1.6 - Prob. 32ECh. 1.6 - Prob. 33ECh. 1.6 - Prob. 34ECh. 1.6 - Prob. 35ECh. 1.6 - Prob. 36ECh. 1.6 - Prob. 37ECh. 1.6 - Prob. 38ECh. 1.6 - Prob. 39ECh. 1.6 - Prob. 40ECh. 1.6 - Prob. 41ECh. 1.6 - Prob. 42ECh. 1.6 - Prob. 43ECh. 1.6 - Prob. 44ECh. 1.6 - Prob. 45ECh. 1.6 - Prob. 46ECh. 1.6 - Prob. 47ECh. 1.6 - Prob. 48ECh. 1.6 - Prob. 49ECh. 1.6 - Prob. 50ECh. 1.6 - Prob. 51ECh. 1.6 - Prob. 52ECh. 1.6 - Prob. 53ECh. 1.6 - Prob. 54ECh. 1.6 - Prob. 55ECh. 1.6 - Prob. 56ECh. 1.6 - Prob. 57ECh. 1.6 - Prob. 58ECh. 1.6 - Prob. 59ECh. 1.6 - Prob. 60ECh. 1.6 - Prob. 61ECh. 1.6 - Prob. 62ECh. 1.6 - Prob. 63ECh. 1.6 - Prob. 64ECh. 1.6 - Prob. 65ECh. 1.6 - Prob. 66ECh. 1.6 - Prob. 67ECh. 1.6 - Prob. 68ECh. 1.6 - Prob. 69ECh. 1.6 - Prob. 70ECh. 1.6 - Prob. 71ECh. 1.6 - Prob. 72ECh. 1.6 - Prob. 73ECh. 1.6 - Prob. 74ECh. 1.6 - Prob. 75ECh. 1.6 - Prob. 76ECh. 1.6 - Prob. 77ECh. 1.6 - Prob. 78ECh. 1.6 - Prob. 79ECh. 1.6 - Prob. 80ECh. 1.6 - Prob. 81ECh. 1.6 - Prob. 82ECh. 1.6 - Prob. 83ECh. 1.6 - Prob. 84ECh. 1.6 - Prob. 85ECh. 1.6 - Prob. 86ECh. 1.6 - Prob. 87ECh. 1.6 - Prob. 88ECh. 1.6 - Prob. 89ECh. 1.6 - Prob. 90ECh. 1.6 - Prob. 91ECh. 1.6 - Prob. 92ECh. 1.6 - Prob. 93ECh. 1.6 - Prob. 94ECh. 1.6 - Prob. 95ECh. 1.6 - Prob. 96ECh. 1.6 - Prob. 97ECh. 1.6 - Prob. 98ECh. 1.6 - Prob. 99ECh. 1.6 - Prob. 100ECh. 1.6 - Prob. 101ECh. 1.6 - Prob. 102ECh. 1.6 - Prob. 103ECh. 1.6 - Prob. 104ECh. 1.6 - Prob. 105ECh. 1.6 - Prob. 106ECh. 1.6 - Prob. 107ECh. 1.6 - Prob. 108ECh. 1.6 - Prob. 109ECh. 1.6 - Prob. 110ECh. 1.6 - Prob. 111ECh. 1.6 - Prob. 112ECh. 1.6 - Prob. 113ECh. 1.6 - Prob. 114ECh. 1.6 - Prob. 115ECh. 1.6 - Prob. 116ECh. 1.6 - Prob. 117ECh. 1.6 - Prob. 118ECh. 1.6 - Prob. 119ECh. 1.6 - Prob. 120ECh. 1.6 - Prob. 121ECh. 1.6 - Prob. 122ECh. 1.6 - Prob. 123ECh. 1.6 - Prob. 124ECh. 1.6 - Prob. 125ECh. 1.6 - Prob. 126ECh. 1.6 - Prob. 127ECh. 1.6 - Prob. 128ECh. 1.6 - Prob. 129ECh. 1.6 - Prob. 130ECh. 1.6 - Prob. 131ECh. 1.6 - Prob. 132ECh. 1.6 - Prob. 133ECh. 1.6 - Prob. 134ECh. 1.6 - Prob. 135ECh. 1.6 - Prob. 136ECh. 1.6 - Prob. 137ECh. 1.6 - Prob. 138ECh. 1.6 - Prob. 139ECh. 1.6 - Prob. 140ECh. 1.7 - Prob. 1ECh. 1.7 - Prob. 2ECh. 1.7 - Prob. 3ECh. 1.7 - Prob. 4ECh. 1.7 - Prob. 5ECh. 1.7 - Prob. 6ECh. 1.7 - Prob. 7ECh. 1.7 - Prob. 8ECh. 1.7 - Prob. 9ECh. 1.7 - Prob. 10ECh. 1.7 - Prob. 11ECh. 1.7 - Prob. 12ECh. 1.7 - Prob. 13ECh. 1.7 - Prob. 14ECh. 1.7 - Prob. 15ECh. 1.7 - Prob. 16ECh. 1.7 - Prob. 17ECh. 1.7 - Prob. 18ECh. 1.7 - Prob. 19ECh. 1.7 - Prob. 20ECh. 1.7 - Prob. 21ECh. 1.7 - Prob. 22ECh. 1.7 - Prob. 23ECh. 1.7 - Prob. 24ECh. 1.7 - Prob. 25ECh. 1.7 - Prob. 26ECh. 1.7 - Prob. 27ECh. 1.7 - Prob. 28ECh. 1.7 - Prob. 29ECh. 1.7 - Prob. 30ECh. 1.7 - Prob. 31ECh. 1.7 - Prob. 32ECh. 1.7 - Prob. 33ECh. 1.7 - Prob. 34ECh. 1.7 - Prob. 35ECh. 1.7 - Prob. 36ECh. 1.7 - Prob. 37ECh. 1.7 - Prob. 38ECh. 1 - Prob. 1RECh. 1 - Prob. 2RECh. 1 - Prob. 3RECh. 1 - Prob. 4RECh. 1 - Prob. 5RECh. 1 - Prob. 6RECh. 1 - Prob. 7RECh. 1 - Prob. 8RECh. 1 - Prob. 9RECh. 1 - Prob. 10RECh. 1 - Prob. 11RECh. 1 - Prob. 12RECh. 1 - Prob. 13RECh. 1 - Prob. 14RECh. 1 - Prob. 15RECh. 1 - Prob. 16RECh. 1 - Prob. 17RECh. 1 - Prob. 18RECh. 1 - Prob. 19RECh. 1 - Prob. 20RECh. 1 - Prob. 21RECh. 1 - Prob. 22RECh. 1 - Prob. 23RECh. 1 - Prob. 24RECh. 1 - Prob. 25RECh. 1 - Prob. 26RECh. 1 - Prob. 27RECh. 1 - Prob. 28RECh. 1 - Prob. 29RECh. 1 - Prob. 30RECh. 1 - Prob. 31RECh. 1 - Prob. 32RECh. 1 - Prob. 33RECh. 1 - Prob. 34RECh. 1 - Prob. 35RECh. 1 - Prob. 36RECh. 1 - Prob. 37RECh. 1 - Prob. 38RECh. 1 - Prob. 39RECh. 1 - Prob. 40RECh. 1 - Prob. 41RECh. 1 - Prob. 42RECh. 1 - Prob. 43RECh. 1 - Prob. 44RECh. 1 - Prob. 45RECh. 1 - Prob. 46RECh. 1 - Prob. 47RECh. 1 - Prob. 48RECh. 1 - Prob. 49RECh. 1 - Prob. 50RECh. 1 - Prob. 51RECh. 1 - Prob. 52RECh. 1 - Prob. 53RECh. 1 - Prob. 54RECh. 1 - Prob. 55RECh. 1 - Prob. 56RECh. 1 - Prob. 57RECh. 1 - Prob. 58RECh. 1 - Prob. 59RECh. 1 - Prob. 60RECh. 1 - Prob. 61RECh. 1 - Prob. 62RECh. 1 - Prob. 63RECh. 1 - Prob. 64RECh. 1 - Prob. 65RECh. 1 - Prob. 66RECh. 1 - Prob. 67RECh. 1 - Prob. 68RECh. 1 - Prob. 69RECh. 1 - Prob. 70RECh. 1 - Prob. 71RECh. 1 - Prob. 72RECh. 1 - Prob. 73RECh. 1 - Prob. 74RECh. 1 - Prob. 75RECh. 1 - Prob. 76RECh. 1 - Prob. 77RECh. 1 - Prob. 78RECh. 1 - Prob. 79RECh. 1 - Prob. 80RECh. 1 - Prob. 81RECh. 1 - Prob. 82RECh. 1 - Prob. 83RECh. 1 - Prob. 84RECh. 1 - Prob. 85RECh. 1 - Prob. 86RECh. 1 - Prob. 87RECh. 1 - Prob. 88RECh. 1 - Prob. 89RECh. 1 - Prob. 90RECh. 1 - Prob. 91RECh. 1 - Prob. 92RECh. 1 - Prob. 93RECh. 1 - Prob. 94RECh. 1 - Prob. 95RECh. 1 - Prob. 96RECh. 1 - Prob. 97RECh. 1 - Prob. 98RECh. 1 - Prob. 99RECh. 1 - Prob. 100RECh. 1 - Prob. 101RECh. 1 - Prob. 102RECh. 1 - Prob. 103RECh. 1 - Prob. 104RECh. 1 - Prob. 105RECh. 1 - Prob. 106RECh. 1 - Prob. 107RECh. 1 - Prob. 108RECh. 1 - Prob. 109RECh. 1 - Prob. 110RECh. 1 - Prob. 111RECh. 1 - Prob. 112RECh. 1 - Prob. 113RECh. 1 - Prob. 114RECh. 1 - Prob. 115RECh. 1 - Prob. 116RECh. 1 - Prob. 117RECh. 1 - Prob. 118RECh. 1 - Prob. 119RECh. 1 - Prob. 120RECh. 1 - Prob. 121RECh. 1 - Prob. 122RECh. 1 - Prob. 123RECh. 1 - Prob. 124RECh. 1 - Prob. 125RECh. 1 - Prob. 126RECh. 1 - Prob. 127RECh. 1 - Prob. 128RECh. 1 - Prob. 129RECh. 1 - Prob. 130RECh. 1 - Prob. 131RECh. 1 - Prob. 132RECh. 1 - Prob. 133RECh. 1 - Prob. 134RECh. 1 - Prob. 135RECh. 1 - Prob. 136RECh. 1 - Prob. 137RECh. 1 - Prob. 138RECh. 1 - Prob. 139RECh. 1 - Prob. 140RECh. 1 - Prob. 141RECh. 1 - Prob. 142RECh. 1 - Prob. 143RECh. 1 - Prob. 144RECh. 1 - Prob. 145RECh. 1 - Prob. 146RECh. 1 - Prob. 147RECh. 1 - Prob. 148RECh. 1 - Prob. 149RECh. 1 - Prob. 150RECh. 1 - Prob. 151RECh. 1 - Prob. 1CTCh. 1 - Prob. 2CTCh. 1 - Prob. 3CTCh. 1 - Prob. 4CTCh. 1 - Prob. 5CTCh. 1 - Prob. 6CTCh. 1 - Prob. 7CTCh. 1 - Prob. 8CTCh. 1 - Prob. 9CTCh. 1 - Prob. 10CTCh. 1 - Prob. 11CTCh. 1 - Prob. 12CTCh. 1 - Prob. 13CTCh. 1 - Prob. 14CTCh. 1 - Prob. 15CTCh. 1 - Prob. 16CTCh. 1 - Prob. 17CTCh. 1 - Prob. 18CTCh. 1 - Prob. 19CTCh. 1 - Prob. 20CT
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