In Problem, an agent for a real estate company wanted to predict the monthly rent for apartments, based on the size of the apartments. Perform a residual analysis for these data (stored in Rent). Based on these results, evaluate whether the assumptions of regression have been seriously violated.
Problem
An agent for a residential real estate company 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 (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
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?
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