Calculus: Graphical, Numerical, Algebraic

3rd Edition

ISBN: 9780133688399

Author: Finney, Ross L.

Publisher: Pearson/Prentice Hall

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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

Chapter 1.1, Problem 45E

(a)

To determine

To find:The linear regression equation for the given data.

(a)

Expert Solution

Answer to Problem 45E

The linear regression equation for the given data is y=2216.2x−4387470.6 .

Explanation of Solution

Given information:The table given below the mean annual compensation of construction workers for different years:

Construction Workers’ Average Annual Compensation
Year	Annual Total Compensation (dollars)
1999	42,598
2000	44,764
2001	47,822
2002	48,966

Calculation:

To find the linear regression equation of the given data, use graphing calculator.

Step 1: Press STAT1 keys to enter the given data.

Step 2: List the input values 1999, 2000, 2001 and 2002 in the L1 column.

Step 3: List the input values 42598, 44764, 47822 and 48966 in the L2 column.

Step 4: Press the keystrokes STAT⇒4ENTER to find line of regression and again press ENTER key. So, the linear regression equation for the given data is:

y=2216.2x−4387470.6

Therefore, thelinear regression equation for the given data is y=2216.2x−4387470.6 .

(b)

To determine

To find: The slope of the regression line for the given data and describe the representation of the slope.

(b)

Expert Solution

Answer to Problem 45E

The slope of the regression line for the given data is 2216.2 and it represents the increasing rate in earning rate of workers in dollars per year.

Explanation of Solution

Given information:The table given below the mean annual compensation of construction workers for different years:

Construction Workers’ Average Annual Compensation
Year	Annual Total Compensation (dollars)
1999	42,598
2000	44,764
2001	47,822
2002	48,966

Calculation:

From part (a), the linear regression equation for the given data is y=2216.2x−4387470.6 .

It is known that slope-form of a line is y=mx+c . Compare the above equation with this equation.

m=2216.2

Therefore, the slope of the regression line for the given data is 2216.2 and it represents the increasing rate in earning rate of workers in dollars per year.

(c)

To determine

To plot: The graph of the linear regression equation on a scatter plot for the given data.

(c)

Expert Solution

Explanation of Solution

Given information:The table given below the mean annual compensation of construction workers for different years:

Construction Workers’ Average Annual Compensation
Year	Annual Total Compensation (dollars)
1999	42,598
2000	44,764
2001	47,822
2002	48,966

Graph:

From part (a), the linear regression equation for the given data is y=2216.2x−4387470.6 .

Now, to make the scatter plot, follow the steps using graphing calculator.

Step 1: Press 2ndY= and make sure that Plot 1 is ON. Choose the scatter plot icon in type.

Step 2: Press GRAPH key. Set the window at [1998, 2003] with scale 1000 by [42000, 50000] with scale 2000.

Step 3: Press the keystrokes STAT⇒42nd1,2nd2,VARS⇒11ENTER . Now, press GRAPH and TRACE key to plot the graph as shown below.

Calculus: Graphical, Numerical, Algebraic, Chapter 1.1, Problem 45E

Figure (1)

Interpretation:From the graph it can be interpreted that the Annual Total Compensation in dollars of construction worker in year 2003 will be about 51578 dollars.

(d)

To determine

To find: The annual average compensation of construction workers in the year 2008 by using the regression equation.

(d)

Expert Solution

Answer to Problem 45E

The annual average compensation of construction workers in the year 2008 is $62,659.

Explanation of Solution

Given information:The table given below the mean annual compensation of construction workers for different years:

Construction Workers’ Average Annual Compensation
Year	Annual Total Compensation (dollars)
1999	42,598
2000	44,764
2001	47,822
2002	48,966

Calculation:

From part (a), the linear regression equation for the given data is y=2216.2x−4387470.6 .

To find the annual average compensation, substitute 2008 for x in the above equation.

y=2216.2(2008)−4387470.6=4450129.6−4387470.6=62659

Therefore, the annual average compensation of construction workers in the year 2008 is $62,659.

Chapter 1.1, Problem 44E

Chapter 1.1, Problem 46E

Chapter 1 Solutions

Calculus: Graphical, Numerical, Algebraic

Ch. 1.1 - Prob. 1QR Ch. 1.1 - Prob. 2QR Ch. 1.1 - Prob. 3QR Ch. 1.1 - Prob. 4QR Ch. 1.1 - Prob. 5QR Ch. 1.1 - Prob. 6QR Ch. 1.1 - Prob. 7QR Ch. 1.1 - Prob. 8QR Ch. 1.1 - Prob. 9QR Ch. 1.1 - Prob. 10QR

Ch. 1.1 - Prob. 1E Ch. 1.1 - Prob. 2E Ch. 1.1 - Prob. 3E Ch. 1.1 - Prob. 4E Ch. 1.1 - Prob. 5E Ch. 1.1 - Prob. 6E Ch. 1.1 - Prob. 7E Ch. 1.1 - Prob. 8E Ch. 1.1 - Prob. 9E Ch. 1.1 - Prob. 10E Ch. 1.1 - Prob. 11E Ch. 1.1 - Prob. 12E Ch. 1.1 - Prob. 13E Ch. 1.1 - Prob. 14E Ch. 1.1 - Prob. 15E Ch. 1.1 - Prob. 16E Ch. 1.1 - Prob. 17E Ch. 1.1 - Prob. 18E Ch. 1.1 - Prob. 19E Ch. 1.1 - Prob. 20E Ch. 1.1 - Prob. 21E Ch. 1.1 - Prob. 22E Ch. 1.1 - Prob. 23E Ch. 1.1 - Prob. 24E Ch. 1.1 - Prob. 25E Ch. 1.1 - Prob. 26E Ch. 1.1 - Prob. 27E Ch. 1.1 - Prob. 28E Ch. 1.1 - Prob. 29E Ch. 1.1 - Prob. 30E Ch. 1.1 - Prob. 31E Ch. 1.1 - Prob. 32E Ch. 1.1 - Prob. 33E Ch. 1.1 - Prob. 34E Ch. 1.1 - Prob. 35E Ch. 1.1 - Prob. 36E Ch. 1.1 - Prob. 37E Ch. 1.1 - Prob. 38E Ch. 1.1 - Prob. 39E Ch. 1.1 - Prob. 40E Ch. 1.1 - Prob. 41E Ch. 1.1 - Prob. 42E Ch. 1.1 - Prob. 43E Ch. 1.1 - Prob. 44E Ch. 1.1 - Prob. 45E Ch. 1.1 - Prob. 46E Ch. 1.1 - Prob. 47E Ch. 1.1 - Prob. 48E Ch. 1.1 - Prob. 49E Ch. 1.1 - Prob. 50E Ch. 1.1 - 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