Question

A real estate agent would like to know if the number of bedrooms in a house can be used to predict the selling price of the house. More​ specifically, he wants to know whether a larger number of bedrooms leads to a higher selling price. Records for 25 houses that recently sold in the area were selected at​ random, and data on the number of bedrooms​ (x) and the selling price y​ (in $000s) for each house were used to fit the model​ E(y) =​ β0 +​ β1x.

The results of the simple linear regression are provided below. Assume a​ 95% prediction interval for y when x​ = 4.00 is​ (645,721). Which of the following interpretations of the interval is​ correct?

A. We are​ 95% confident that the selling price of a house will fall between​ $645,000 and​ $721,000.

B. We are​ 95% confident that the selling price of a house with four bedrooms will fall between​ $645,000 and​ $721,000.

C. We are​ 95% confident that the selling price of a house will increase between​ $6,450 and​ $7,210 for every additional bedroom.

D. We are​ 95% confident that the mean selling price of houses with four bedrooms will fall between​ $645,000 and​ $721,000

Answer 1

Explanation: The prediction interval of the simple linear regression model is used to predict the future observation of the dependent variable(Y), for the particular value of the independent variable(x). The interpretation of the prediction interval: The correct interpretation of the prediction interval is that there is a 95% chance that the future observation will be contained within in the interval is between $645000 and $721000. Hence, we are 95% confident that the mean selling price of houses with the four bed rooms will fall between $645,000 and $721,000. The correct option to choose is (D).