Concept explainers
(a)
To find:The linear regression equation for the given data.
(a)
Answer to Problem 45E
The linear regression equation for the given data is
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
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
Therefore, thelinear regression equation for the given data is
(b)
To find: The slope of the regression line for the given data and describe the representation of the slope.
(b)
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
It is known that slope-form of a line is
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 plot: The graph of the linear regression equation on a
(c)
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
Now, to make the scatter plot, follow the steps using graphing calculator.
Step 1: Press
Step 2: Press
Step 3: Press the keystrokes
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 find: The annual average compensation of construction workers in the year 2008 by using the regression equation.
(d)
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
To find the annual average compensation, substitute 2008 for
Therefore, the annual average compensation of construction workers in the year 2008 is $62,659.
Chapter 1 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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