An agent for a residential 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 an apartment, as defined by square footage. The agent selects a sample of 25 apartments in a particular residential neighborhood and gathers the following data (stored in Rent).
Rent ($) Size (Square Feet)
950........................................850
1,600....................................1,450
1,200....................................1,085
1,500....................................1,232
950........................................718
1,700....................................1,485
1,650....................................1,136
935........................................726
875........................................700
1,150......................................956
1,400....................................1,100
1,650....................................1,285
2,300....................................1,985
1,800....................................1,369
1,400....................................1,175
1,450....................................1,225
1,100....................................1,245
1,700....................................1,259
1,200....................................1,150
1,150......................................896
1,600....................................1,361
1,650....................................1,040
1,200......................................755
800......................................1,000
1,750....................................1,200
a. Construct a scatter plot.
b. Use the least-squares method to determine the regression coefficients b0 and b1.
c. Interpret the meaning of b0 and b1 in this problem.
d. Predict the monthly rent for an apartment that has 1,000 square feet.
e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet?
f. Your friends Jim and Jennifer are considering signing a lease for an apartment in this residential neighborhood. They are trying to decide between two apartments, one with 1,000 square feet for a monthly rent of $1,275 and the other with 1,200 square feet for a monthly rent of $1,425. Based on (a) through (d), which apartment do you think is a better deal?