Question

An agent for a residential real estate company in a large city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward that goal, the agent would like to use the size of an apartment, as defined by square footage to predict the monthly rental cost. The agent selects a sample of 25 apartments in a particular residential neighborhood and collects the following data:

Size (square feet) Rent ($)

850, 1950

1450, 2600

1085, 2200

1232, 2500

718, 1950

1485, 2700

1136, 2650

726, 1935

700, 1875

956, 2150

1100, 2400

1285, 2650

1985, 3300

1369, 2800

1175, 2400

1225, 2450

1245, 2100

1259, 2700

1150, 2200

896, 2150

1361, 2600

1040, 2650

755, 2200

1000, 1800

1200, 2750

(A) Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?

(B) Determine the coefficient of determination , r^2, and interpret its meaning.

(C) Determine the standard error of estimate.(syx)

(D) How useful do you think this regression model is for predicting the monthly rent?

(E) Can you think of other variables that might explain the variation in the monthly rent?

Answer 1

Dear student, please comment in the case of any doubt and I would love to clarify it.

A)

It would not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet because the data doesn't include any value near to 500 square feet for size. The size ranges from 700 to 2700 square feet and hence, accuracy will go down in the case of predicting price for 500 square feet.

B)

The coefficient of determination is interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.

The coefficient of determination comes out to be 0.7226(have shown in excel), which means that 72.26% of the change in rent is due to the size of the apartment.

C)

The standard error of estimate(rent) comes out to be 161.0043(shown in excel).

D)

The accuracy of the model comes out to be 72.26% as well(which is also the coefficient of determination).

E)

The other factors in predicting the price of apartments can be the number of bedrooms, number of washrooms, whether it is sea faced or not, the floor, etc.

I have used the function =LINEST(y_value, x_value, TRUE, TRUE) here. The y_value will be rent here and x_value will be the size of the apartment. Select 2 columns and 5 rows and type this formula into first cell and press Shift + Ctrl + Enter.