Question

Strip malls appear to popping up everywhere. The relationship between the actual price of a strip mall and the listing price is modeled in the least-squares regression line Ĉ = 0.2 + 1.011. Both amounts are in hundred-thousands of dollars. Let L represent the listing price and C represent the sales price. Which of the following is the best interpretation of the slope of the regression line?

A)For each hundred-thousand-dollar increase in the listing price, the sales price will increase by $1.01.
B)For each hundred-thousand-dollar increase in the listing price, the sales price will increase by $101,000,
C)For each hundred-thousand-dollar increase in the listing price, the sales price will decrease by $101,000.
D)For each hundred-thousand-dollar increase in the listing price, the sales price is predicted to increase by $1.01.
E)For each hundred-thousand dollar increase in the listing price, the sales price is predicted to increase by $101,000.​

Answer 1

The correct option is;

E) For each hundred-thousand dollar increase in the listing price, the sales price is predicted to increase by $101,000

Explanation:

Whereby the relationship between the actual price of a strip mall and the listing price is modeled according to the least squares regression line as follows;

C = 0.2 + 1.01·L

Where;

L = The listing price

C = The sales price

Where both amounts are in hundred-thousands of dollars;

Therefore, given that the slope is 1.01, we have that for an increase of $100,000 for the listing price, L, which is 1 unit increase the sale price increases as follows

C₁ = 0.2 + 1.01 × 1 = 1.21

While for an increase of an extra $100,000, to make the listing price. $200,000 or 2 units, we have;

C₂ = 0.2 + 1.01 × 2 = 2.22

The increase is C₂ - C₁ = 2.22 - 1.21 = 1.01

C₂ - C₁ = $100,000 × 1.01 = $101,000

The increase is C = $101,000

Whereby, the equation is a linear regression line which is a model for prediction, we have;

The predicted increase in the sale price is $101,000 for each $100,000 increase in the listing price.