4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

Concept explainers

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…

Videos

Question

Chapter 3, Problem 26PS

To determine

Use a graphing utility to create a scatter plot of the data.

Expert Solution

Answer to Problem 26PS

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 26PS , additional homework tip 1

Explanation of Solution

Given information:

Use a graphing utility to create a scatter plot of the data.

(1, 5.0), (1.5, 6.0), (2, 6.4), (4, 7.8), (6, 8.6), (8, 9.0)

Calculation:

The scatter plot of the data is as given.

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 26PS , additional homework tip 2

Hence the result is shown in plot.

To determine

Verify that the model is linear model, an exponential model, or a logarithmic model,

Expert Solution

Answer to Problem 26PS

logarithmic model

Explanation of Solution

Given information:

Decide whether the data could best be modelled by a linear model, an exponential model, or a logarithmic model.

(1, 5.0), (1.5, 6.0), (2, 6.4), (4, 7.8), (6, 8.6), (8, 9.0)

Calculation:

Let cosider the points,

(1, 5.0), (1.5, 6.0), (2, 6.4), (4, 7.8), (6, 8.6), (8, 9.0)

Hence, the best model is logarithmic model.

To determine

Explain why you chose the model you did in part (b)

Expert Solution

Answer to Problem 26PS

logarithmic model is best suited.

Explanation of Solution

Given information:

Explain why you chose the model you did in part (b) .

(1, 5.0), (1.5, 6.0), (2, 6.4), (4, 7.8), (6, 8.6), (8, 9.0)

Calculation:

Let cosider the graph is plotted in part (b) shows that the points are increasing non-linearly, thus we cannot use a linear model for this, also the points are not growing rapidly thus exponential model is not suitable . Hence logarithmic model is best suited.

Hence, the best model is logarithmic model.

To determine

Use the regression feature of the graphing utility to find the model you chose in part (b) .

Expert Solution

Answer to Problem 26PS

y=5.1+1.92ln(x)

Explanation of Solution

Given information:

Use the regression feature of the graphing utility to find the model you chose in part (b) for the data and graph the model with the scatter plot.

(1, 5.0), (1.5, 6.0), (2, 6.4), (4, 7.8), (6, 8.6), (8, 9.0)

Calculation:

Consider the x,y values from the data and utility we get,

X:−Vector[1,1.5,2,4,6,8],datatype=float;

>X:=[11.5000000000000002468]

Y:−Vector[5,6,6.4,7.8,8.6,9],datatype=float;

>Y:=[566.4000000000000347.9999999999999828.5999999999999649]

>Fit(a+bln(t),X,Y,t)5.099946313242485782+1.919920469100358ln(t)

The scatter plot of data is,

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 26PS , additional homework tip 3

Hence the required model is,

y=5.1+1.92ln(x)

To determine

Determine how well the model you chose fits the data.

Expert Solution

Answer to Problem 26PS

The graph shows that, the model fit for the data points.

Explanation of Solution

Given information:

Determine how well the model you chose fits the data.

Calculation:

EBK PRECALCULUS W/LIMITS, Chapter 3, Problem 26PS , additional homework tip 4

Hence, from the graph we get the model fit for the data points.

Chapter 3, Problem 25PS

Chapter 4.1, Problem 1E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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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