An agent for a residential real estate company in a suburb located outside a maj
ID: 3247548 • Letter: A
Question
An agent for a residential real estate company in a suburb located outside a major city has the business objective of developing more accurate estimates of the monthly rental cost for apartments. Toward the 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 8 one-bedroom apartments and the data are shown. Complete parts (a) through (f).
Monthly Rent ($) Size (Square Feet)
925 900
1,450 1,200
825 900
1,450 1,200
1,900 2,000
925 750
1,700 1,350
1,400 1,050
a. Construct a scatter plot.?
b. Use the least-squares method to determine the regression coefficients b0 and b1.
b0 = ___? (Round to one decimal place as needed.)
b1 = ___? (Round to one decimal place as needed.)
c. Interpret the meaning of b0 and b1 in this problem. (Choose the correct answer below)
A. For each increase of 1 square foot in space, the monthly rent is expected to increase by b0 dollars. Apartments in this neighborhood cost at least b1 dollars.
B. For each increase of 1 square foot in space, the monthly rent is expected to increase by b1 dollars. Apartments in this neighborhood cost at least b0 dollars.
C. For each increase of 1 square foot in space, the monthly rent is expected to increase by b0 dollars. Since X cannot be zero, b1 has no practical interpretation.
D. For each increase of 1 square foot in space, the monthly rent is expected to increase by b1 dollars. Since X cannot be zero, b0 has no practical interpretation.
d. Predict the mean monthly rent for an apartment that has 1,000 square feet.
(Fill in the Blank)
The predicted mean monthly rent for such an apartment is $___? (Round to the nearest cent as needed.)
e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 500 square feet? (Choose Below)
A. The size of an apartment has no effect on the monthly rent, according to this model. There must be another factor that contributes to the rent price.
B. The correlation between an apartment's size and its monthly rent is too weak to use this model for such a prediction.
C. An apartment with 500 square feet is outside the relevant range for the independent variable.
D. The model predicts that the monthly rent for an apartment that has 500 square feet would be unrealistically low.
f. Two people are considering signing a lease for an apartment in this 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 $1,425. Based on (a) through (d), which apartment is a better deal? (Choose Below)
Based on (a) through (d), the apartment with (1,200, 1,000) square feet is the better deal.
Explanation / Answer
Regression Analysis: Monthly Rent ($) versus Size (Square Feet)
Analysis of Variance
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Regression
1
859247
859247
23.56
0.003
Size (Square Feet)
1
859247
859247
23.56
0.003
Error
6
218800
36467
Lack-of-Fit
4
213800
53450
21.38
0.045
Pure Error
2
5000
2500
Total
7
1078047
Model Summary
S
R-sq
R-sq(adj)
R-sq(pred)
190.962
79.70%
76.32%
20.35%
Coefficients
Term
Coef
SE Coef
T-Value
P-Value
VIF
Constant
269
227
1.19
0.280
Size (Square Feet)
0.900
0.186
4.85
0.003
1.00
Regression Equation
Monthly Rent ($)
=
269 + 0.900 Size (Square Feet)
a] Scatter Plot
b]
bo = 269
b1 = 0.9
c] Interpret the meaning of b0 and b1 in this problem
B. For each increase of 1 square foot in space, the monthly rent is expected to increase by b1 dollars. Apartments in this neighborhood cost at least b0 dollars.
d]
The predicted mean monthly rent for such an apartment is $ 1169 when space is 1000 square feet.
Source
DF
Adj SS
Adj MS
F-Value
P-Value
Regression
1
859247
859247
23.56
0.003
Size (Square Feet)
1
859247
859247
23.56
0.003
Error
6
218800
36467
Lack-of-Fit
4
213800
53450
21.38
0.045
Pure Error
2
5000
2500
Total
7
1078047
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