Chapter 8, Problem 21E

(a)

To determine

To explain what the slope of the line says about housing prices and house size.

Explanation of Solution

It is given in the question that, a random sample of records of sales of homes gives the price and size of homes. A regression to predict price from size has an R -squared of $\text{71}\text{.4\%}$ . The residual plot indicated that a linear model is appropriate. And the regression analysis gives the model:

  $\text{<mover accent="true"><mo>P</mo><mo>^</mo></mover> rice}=47.82+0.061\text{Size}$

Thus, the slope of the line says about housing prices and house size is that price of the house increases by about $\$0.061\times 1000\text{ or \$61}\text{.00}$ per additional square feet.

(b)

To determine

To find out what price would you predict for a $3000$ -square foot house in this market.

Answer to Problem 21E

The price of the house is $\$230.82\text{ thousands or }\$230820$ .

Explanation of Solution

It is given in the question that, a random sample of records of sales of homes gives the price and size of homes. A regression to predict price from size has an R -squared of $\text{71}\text{.4\%}$ . The residual plot indicated that a linear model is appropriate. And the regression analysis gives the model:

  $\text{<mover accent="true"><mo>P</mo><mo>^</mo></mover> rice}=47.82+0.061\text{Size}$

Thus, we want to predict the price for a $3000$ -square foot house in this market, that is by,

  $\begin{array}{l}\text{<mover accent="true"><mo>P</mo><mo>^</mo></mover> rice}=47.82+0.061\text{Size}\\ =47.82+0.061\times 3000\\ =230.82\end{array}$

Thus, the price of the house is $\$230.82\text{ thousands or }\$230820$ .

(c)

To determine

To find out what is the asking price and explain what is the $\$6000$ called.

Answer to Problem 21E

The asking price is $\$115020$ .

Explanation of Solution

It is given in the question that, a random sample of records of sales of homes gives the price and size of homes. A regression to predict price from size has an R -squared of $\text{71}\text{.4\%}$ . The residual plot indicated that a linear model is appropriate. And the regression analysis gives the model:

  $\text{<mover accent="true"><mo>P</mo><mo>^</mo></mover> rice}=47.82+0.061\text{Size}$

It is also given that a real estate agent shows a potential buyer a $1200$ square foot home, saying that the asking price is $\$6000$ less than what one would expect to pay for a house of this size. Thus, the asking price will be calculated as:

  $\begin{array}{l}\text{<mover accent="true"><mo>P</mo><mo>^</mo></mover> rice}=47.82+0.061\text{Size}\\ =47.82+0.061\times 1200\\ =121.02\\ \text{ or \$121020}\\ \text{Asking price}=\$121020-\$6000\\ =\$115020\end{array}$

Thus, the asking price is $\$115020$ . And $\$6000$ is the residual in this context.