Question

A regression analysis of 117 homes for sale produced the following model, where price is in thousands of dollars and size in square feet. Price = 47.87+0.062(size)

A) Explain what the slope of the line says about housing prices and house size
B) What price would you predict for a 2500 square foot house in the market?
C) A real estate agent shows a potential buyer 1100 square foot house, saying that the asking price is $6000 less than what one would expect to pay for a house of this size. What is the asking price, and what is the $6000 called?

Answer 1

A) m = 0.062

B) 202.87 thousand dollars

C) Original price = 116.07 thousand dollars. $6000 is called the error term.

Explanation:

We are given the following in the question:

Price = 47.87+0.062(size)

The above equation is regression equation where price is in thousand dollars and size in square feet.

Let p be the prize and s be the size.

`p(s) = 47.87 + 0.062s`

Comparing it to linear equation, we have,

`y= mx + c`

where m is the slope and c is the y-intercept.

m = 0.062

c = 47.87

A) slope of the line

The slope of line tells the rate of change. Thus, it tells the change in price if the size of house is increased by 1 square feet.

The price of house increases by 0.062 thousand dollars if the size of house is increased by 1 square feet.

B) Price of house

We are given s = 2500. Putting this value in the equation.

`p(2500) = 47.87 + 0.062(2500) =202.87`

Thus, the price of a 2500 square feet house is 202.87 thousand dollars.

C) We are given s = 1100

Putting the value in the equation:

`p(1100) = 47.87 + 0.062(1100) =116.07`

Original price = 116.07 thousand dollars

Asking price =

`116.07 - 6 = 110.07`

The buyer is asking for 110.07 thousand dollars.

$6000 is called the error term.