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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 data below
Apartment: Monthly Rent: Size:
1 950 850
2 1600 1450
3 1200 1085
4 1500 1232
5 950 718
6 1700 1485
7 1650 1136
8 935 726
9 875 700
10 1150 956
11 1400 1100
12 1650 1285
13 2300 1985
14 1800 1369
15 1400 1175
16 1450 1225
17 1100 1245
18 1700 1259
19 1200 1150
20 1150 896
21 1600 1361
22 1650 1040
23 1200 755
24 800 1000
25 1750 1200
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?
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