Question

An agent for a residential real estate company in a suburb located outside of Washington,DC, 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 48 apartments in a particular residential neighborhood and collects the following data:

RENT SIZE
950 850
1600 1450
1200 1085
1500 1232
950 718
1700 1485
1650 1136
935 726
875 700
1150 956
1400 1100
1650 1285
2300 1985
1800 1369
1400 1175
1450 1225
1100 1245
1700 1259
1200 1150
1150 896
1600 1361
1650 1040
1200 755
800 1000
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 800 square feet.

e. Why would it not be appropriate to use the model to predict the monthly rent for apartments that have 1500 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 800 square feet for a monthly rent of $1130 and the other with 830 square feet for a monthly rent of $1410. Based on (a) through (d), which apartment do you think is a better deal?

Answer 1

a)

b)

using minitab

Regression Analysis: RENT versus SIZE

Analysis of Variance

Source      DF   Adj SS   Adj MS F-Value P-Value
Regression   1 2268777 2268777    59.91    0.000
SIZE       1 2268777 2268777    59.91    0.000
Error       23   870949    37867
Total       24 3139726

Model Summary

      S    R-sq R-sq(adj) R-sq(pred)
194.595 72.26%     71.05%      69.12%

Coefficients

Term       Coef SE Coef T-Value P-Value   VIF
Constant    177      161     1.10    0.283
SIZE      1.065    0.138     7.74    0.000 1.00

Regression Equation

RENT = 177 + 1.065 SIZE

c) b1 = 1.065

this mean on average rent increase by 1.065 unit when size increase by 1 unit

b0 = 177

it means on average the rent will be 177 when size =0

here it has no practical meaning

d)

y^ = 177 + 1.065 * 800

= 1029