Chapter 1.1, Problem 53E

(a)

To determine

To find:The linear regression equation forcost of home in south using the given data.

Answer to Problem 53E

The linear regression equation for cost of home in south is $y=5980x-1.18098\times {10}^7$ .

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 $\boxed{\text{STAT}}\boxed{1}$ keys to enter the given data.

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 $\boxed{\text{STAT}}\boxed{\Rightarrow }\boxed{4}\boxed{\text{ENTER}}$ to find line of regression and again press $\boxed{\text{ENTER}}$ key. So, the linear regression equation for the given data is:

  $\begin{array}{l}y=5980x-11809820\\ y=5980x-1.18098\times {10}^7\end{array}$

Therefore, thelinear regression equation for cost of home in south is $y=5980x-1.18098\times {10}^7$ .

(b)

To determine

To explain: The meaning that the slope of the regression line represents.

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 $y=5980x-1.18098\times {10}^7$ . Here, $x$ represents the year and $y$ represent the median price of single family homes in South region.

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

  $m=5980$

Therefore, the slope represents the annual increment in the cost in dollars of single-homes in south region.

(c)

To determine

To find:The linear regression equation for cost of home in west using the given data.

Answer to Problem 53E

The linear regression equation for cost of home in westis $y=21650x-4.3105\times {10}^7$ .

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 $\boxed{\text{STAT}}\boxed{1}$ keys to enter the given data.

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 $\boxed{\text{STAT}}\boxed{\Rightarrow }\boxed{4}\boxed{\text{ENTER}}$ to find line of regression and again press $\boxed{\text{ENTER}}$ key. So, the linear regression equation for the given data is:

  $\begin{array}{l}y=21650x-43105030\\ y=21650x-4.3105\times {10}^7\end{array}$

Therefore, the linear regression equation for cost of home in westis $y=21650x-4.3105\times {10}^7$ .

(d)

To determine

To find: The median price is increasing more rapidly in South region or in West region.

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 $y=5980x-1.18098\times {10}^7$ .

From part (c), the linear regression equation for cost of single-home in West region is $y=21650x-4.3105\times {10}^7$ .

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 $m=5980$ and the slope of regression line for Westis $m=21650$ .

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.