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) Construct a scatter plot.
(b) Use the least-squares method to determine the regression coefficients (intercept and slope).
(c) Interpret the meaning of the intercept and slope in this problem.
(d) Predict the monthly rent for an apartment that has 1000 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?
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