Concept explainers
(a)
To find:The linear regression equation forcost of home in south using the given data.
(a)
Answer to Problem 53E
The linear regression equation for cost of home in south is
Explanation of Solution
Given information:The table given below shows the data of dingle-family homes in various parts of the country:
Median Price of Single-Family Homes | ||
Year | South (dollars) | West (dollars) |
1999 | 145,900 | 173,700 |
2000 | 148,000 | 196,400 |
2001 | 155,400 | 213,600 |
2002 | 163,400 | 238,500 |
2003 | 168,100 | 260,900 |
Calculation:
Use the data for various years in South part of the country for the linear regression equation for home cost in the South.
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, 2002 and 2003 in the L1 column.
Step 3: List the input values 145900, 148000, 155400, 163400 and 168100 in the L2 column.
Step 4: Press the keystrokes
Therefore, thelinear regression equation for cost of home in south is
(b)
To explain: The meaning that the slope of the regression line represents.
(b)
Answer to Problem 53E
The slope represents the annual increment in the cost in dollars of single-homes in south region.
Explanation of Solution
Given information:The table given below shows the data of dingle-family homes in various parts of the country:
Median Price of Single-Family Homes | ||
Year | South (dollars) | West (dollars) |
1999 | 145,900 | 173,700 |
2000 | 148,000 | 196,400 |
2001 | 155,400 | 213,600 |
2002 | 163,400 | 238,500 |
2003 | 168,100 | 260,900 |
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 represents the annual increment in the cost in dollars of single-homes in south region.
(c)
To find:The linear regression equation for cost of home in west using the given data.
(c)
Answer to Problem 53E
The linear regression equation for cost of home in westis
Explanation of Solution
Given information:The table given below shows the data of dingle-family homes in various parts of the country:
Median Price of Single-Family Homes | ||
Year | South (dollars) | West (dollars) |
1999 | 145,900 | 173,700 |
2000 | 148,000 | 196,400 |
2001 | 155,400 | 213,600 |
2002 | 163,400 | 238,500 |
2003 | 168,100 | 260,900 |
Calculation:
Use the data for various years in South part of the country for the linear regression equation for home cost in the West.
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, 2002 and 2003 in the L1 column.
Step 3: List the input values 173700, 196400, 213600, 238500 and 260900 in the L2 column.
Step 4: Press the keystrokes
Therefore, the linear regression equation for cost of home in westis
(d)
To find: The median price is increasing more rapidly in South region or in West region.
(d)
Answer to Problem 53E
The median price is increasing more rapidly in West region.
Explanation of Solution
Given information:The table given below shows the data of dingle-family homes in various parts of the country:
Median Price of Single-Family Homes | ||
Year | South (dollars) | West (dollars) |
1999 | 145,900 | 173,700 |
2000 | 148,000 | 196,400 |
2001 | 155,400 | 213,600 |
2002 | 163,400 | 238,500 |
2003 | 168,100 | 260,900 |
Calculation:
From part (a), the linear regression equation for cost of single-home in South region is
From part (c), the linear regression equation for cost of single-home in West region is
It is known that the slop represents change in median price for single-home n the country.
The slope of regression line for South is
It can be observed that the slope of regression line for West is increasing more rapidly than the slope of regression line for South.
Therefore, the median price is increasing more rapidly in West region.
Chapter 1 Solutions
Calculus 2012 Student Edition (by Finney/Demana/Waits/Kennedy)
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