3rd Edition

ISBN: 9781285607160

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…

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Question

Chapter 7, Problem 82RE

To determine

Find a linear model for the data.

Expert Solution

Answer to Problem 82RE

The linear equation is $y=240.58t−10.877$

Explanation of Solution

Given information:

The table shows the sales $y$ (in millions of dollars) for Aéropostale, Increase from $2003$ through $2010$ .

EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 82RE , additional homework tip 1

Use the regression feature of a graphing utility to find a linear model for the data. Let $t$ represent the year, with $t=3$ corresponding to $2003$ .

Calculation:

Enter the data in calculator.

Press button STAT and select EDIT and press enter.

Enter year in $L1$ and salary in $L2$ .

EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 82RE , additional homework tip 2

To find the linear function use regression in calculator, press STAT ans select CAL then press enter, the linear equation is $y=240.58t−10.877$

EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 82RE , additional homework tip 3

Hence, the linear equation is $y=240.58t−10.877$

To determine

Find the area of the trapezoid bounded by the linear model.

Expert Solution

Answer to Problem 82RE

EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 82RE , additional homework tip 4

Explanation of Solution

Given information:

The table shows the sales $y$ (in millions of dollars) for Aéropostale, Increase from $2003$ through $2010$ .

EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 82RE , additional homework tip 5

The total sales for Aéropostale during this eight-year period can be approximated by finding the area of the trapezoid bounded by the linear model you found in part $(a)$ and the lines $y=0$ , $t=2.5$ and $t=10.5$ Use the graphing utility to graph this region.

Calculation:

Area bounded by $y=0$ , $t=2.5$ and $t=10.5$ is shown as,

EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 82RE , additional homework tip 6

To determine

Find the area of the trapezoid bounded by the linear model.

Expert Solution

Answer to Problem 82RE

the total sale is $$7698.8million$

Explanation of Solution

Given information:

The table shows the sales $y$ (in millions of dollars) for Aéropostale, Increase from $2003$ through $2010$ .

EBK PRECALCULUS W/LIMITS, Chapter 7, Problem 82RE , additional homework tip 7

Use the formula for the area of a trapezoid to approximate the total sales for Aéropostale. Calculation:

We know that,

$y=240.58t−10.877y(2.5)=240.58×2.5−10.877=590.59y(10.5)=240.58×10.5−10.877=2515.29$

Area of a trapezoid is,

Area= $12$ (sum of length of parallel sides) (distance between them)

$Area=12(2515.29−590.59)(10.5−2.5)=962.35×8=7698.8$

Hence, the total sale is $$7698.8million$

Chapter 7, Problem 81RE

Chapter 7, Problem 83RE

Chapter 7 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - Prob. 9E Ch. 7.1 - Prob. 10E

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