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 the square footage to predict the monthly rental cost. The agent selects a sample of one-bedroom apartments and collects and stores the data.

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 mean 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 1,500 square feet?

f. Your friends Jim and Jennifer are considering signing a lease for a one-bedroom apartment in this residential neighborhood. They are trying to decide between two apartments, one with 800 square feet for a monthly rent of $1,130 and the other with 830 square feet for a monthly rent of $1,410. Based on (a) through (d), which apartment do you think is a better deal?

X (Rent)	Y (Sq Ft)
950	850
1600	1450
1200	1085
1500	1232
950	718
1700	1485
1650	1185
935	726
875	700
1150	956
1400	1100
1650	1285
2300	1985
1800	1985
1400	1369
1450	1175
1450	1225
1100	1245
1700	1259
1200	1150
1150	896
1600	1361
1650	1040
1200	755
800	1000
1750	1200

Answer 1

a)

Following is the scatter plot:

(b)

Following table shows the calculations

	X	Y	X^2	Y^2	XY
	950	850	902500	722500	807500
	1600	1450	2560000	2102500	2320000
	1200	1085	1440000	1177225	1302000
	1500	1232	2250000	1517824	1848000
	950	718	902500	515524	682100
	1700	1485	2890000	2205225	2524500
	1650	1185	2722500	1404225	1955250
	935	726	874225	527076	678810
	875	700	765625	490000	612500
	1150	956	1322500	913936	1099400
	1400	1100	1960000	1210000	1540000
	1650	1285	2722500	1651225	2120250
	2300	1985	5290000	3940225	4565500
	1800	1985	3240000	3940225	3573000
	1400	1369	1960000	1874161	1916600
	1450	1175	2102500	1380625	1703750
	1450	1225	2102500	1500625	1776250
	1100	1245	1210000	1550025	1369500
	1700	1259	2890000	1585081	2140300
	1200	1150	1440000	1322500	1380000
	1150	896	1322500	802816	1030400
	1600	1361	2560000	1852321	2177600
	1650	1040	2722500	1081600	1716000
	1200	755	1440000	570025	906000
	800	1000	640000	1000000	800000
	1750	1200	3062500	1440000	2100000
Total	36110	30417	53294850	38277489	44645210

(c)

Slope shows that for each additional sq.ft., rent is increased by $0.7637.

Intercept shows that for apartment with 0 sq. ft. rent is $109.2228. It is meaningless in this case.

(d)

(e)

It should be useful to predict he monthly rent for apartments that have 1,500 square feet because 1500 is in the range of X used to make the model.

(f)

Residual for X =800 :

$1,130 - $720.18 = $409.82

----------------------

Residual for X =830 :

$1410 - $743.09 = $666.91

Since residual is small for 800 so 800 square feet apartment seems to be a better deal.