Question

An agent for a real estate company in a large city would like to be able to predict the monthly rental cost for​ apartments, based on the size of the​ apartment, as defined by square footage. A sample of eight apartments in a neighborhood was​ selected, and the information gathered revealed the data shown below. For these​ data, the regression coefficients are b0 = 314.3583 and b1 = 0.8995. Complete parts​ (a) through​ (d).

Monthly Rent​ ($) 950 - 1,450 - 850 - 1,500 - 2,000 - 950 - 1,700 - 1,300 Size​ (Square Feet) 750 - 1,250 -  950 - 1,100 - 2,000 - 700 - 1,300 - 1,050 (Those are not negative signs but dashes to separate the values.

a. Determine the coefficient of​ determination, r squared​, and interpret its meaning.

r squared =  ? ​(Round to three decimal places as​ needed.)

What is the meaning of r squared​?

A. r squared measures the proportion of variation in apartment size that cannot be explained by the variation in monthly rent.

B. r squared measures the proportion of variation in apartment size that can be explained by the variation in monthly rent.

C. r squared measures the proportion of variation in monthly rent that can be explained by the variation in apartment size.

D. r squared measures the proportion of variation in monthly rent that cannot be explained by the variation in apartment size.

b. Determine the standard error of the​ estimate, Syx, and interpret its meaning.

Syx =  ? ​(Round to three decimal places as​ needed.)

What is the meaning of Syx​?

A. Syx measures the typical difference between an​ apartment's size and the size predicted by the regression equation.

B. Syx measures the typical difference between an​ apartment's actual rent and the rent predicted by the regression equation.

C. Syx measures the amount by which an​ apartment's rent is greater than the rent predicted by the regression equation.

D. Syx measures the amount by which an​ apartment's rent is less than the rent predicted by the regression equation.

c. How useful is this model for predicting the monthly​ rent?

A. It is very useful for predicting the monthly rent because r squared is close to 1 and Syx is fairly small compared to the actual rents.

B. It is very useful for predicting the monthly rent because r squared is close to 1. Syx does not indicate whether a regression model is useful.

C. It is not very useful for predicting the monthly rent because r squared is close to 0 and Syx is fairly small compared to the actual rents.

D. It is not very useful for predicting the monthly rent because although r squared is close to​ 1, Syx is fairly small compared to the actual rents.

d. What other variables might explain the variation in monthly​ rent? Select all that apply.

A. Whether tenants are allowed to keep pets

B. The condition of the apartment

C. Whether parking is available to tenants

D. The desirability of the apartment​ building's location

E. The presence or absence of carpeting in the apartment

Answer 1

a)

r squared = 0.823

C. r squared measures the proportion of variation in monthly rent that can be explained by the variation in apartment size.

b)

syx =184.023

B. Syx measures the typical difference between an​ apartment's actual rent and the rent predicted by the regression equation.

c)

A. It is very useful for predicting the monthly rent because r squared is close to 1 and Syx is fairly small compared to the actual rents.

d)

All are correct