Question

a regression analysis of 117 homes for sale produced the following model, where price is in thousands of dollars and size is in square feet. price = 47.82+0.063(size) a) explain what the slope of the line says about housing prices and house size. b) what price would you predict for a 3000 - square - foot house in this market? c) a real estate agent shows a potential buyer a 1200 - square - foot house, saying that the asking price is $5500 less than what one would expect to pay for a house of this size. what is the asking price, and what is the $5500 called? a) for every $1000 increase in price of a house, the size is predicted to increase by 0.063 square feet. b. for every $1 increase in price of a house, the size is predicted to increase by 63 square feet. c. for every additional square foot of area of a house, the price is predicted to increase by $63. d. for every additional square foot of area of a house, the price is predicted to increase by $0.063. b) what price would you predict for a 3000 - square - foot house in this market?

Explanation:

Step1: Identify the regression equation

The regression model is $\text{Price}=47.82 + 0.063(\text{Size})$, where Price is in thousands of dollars and Size is in square - feet.

Step2: Interpret the slope

The slope of the regression line is 0.063. This means that for every additional square - foot of area of a house, the price is predicted to increase by $0.063\times1000 = 63$ dollars. So the answer to part a) is that for every additional square - foot of area of a house, the price is predicted to increase by $63$.

Step3: Predict the price for a 3000 - square - foot house

Substitute Size = 3000 into the regression equation:
$\text{Price}=47.82+0.063\times3000$
$=47.82 + 189$
$=236.82$ (in thousands of dollars)
So the predicted price for a 3000 - square - foot house is $236820$ dollars.

Step4: Analyze the $5500$ difference

The $5500$ less than the asking price is called the residual. The residual is the difference between the observed value (asking price) and the predicted value from the regression model.

Answer:

a) For every additional square - foot of area of a house, the price is predicted to increase by $63$.
b) $236820$ dollars
c) Residual