Precalculus with Limits
Precalculus with Limits
3rd Edition
ISBN: 9781133947202
Author: Ron Larson
Publisher: Cengage Learning
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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 3, Problem 26PS

a

To determine

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

a

Expert Solution
Check Mark

Answer to Problem 26PS

  Precalculus with 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.

  Precalculus with Limits, Chapter 3, Problem 26PS , additional homework tip 2

Hence the result is shown in plot.

b

To determine

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

b

Expert Solution
Check Mark

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.

c.

To determine

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

c.

Expert Solution
Check Mark

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.

d.

To determine

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

d.

Expert Solution
Check Mark

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,

  Precalculus with Limits, Chapter 3, Problem 26PS , additional homework tip 3

Hence the required model is,

  y=5.1+1.92ln(x)

e.

To determine

Determine how well the model you chose fits the data.

e.

Expert Solution
Check Mark

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:

  Precalculus with Limits, Chapter 3, Problem 26PS , additional homework tip 4

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

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Chapter 3, Problem 25PS
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Chapter 4.1, Problem 1E

Chapter 3 Solutions

Precalculus with Limits

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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