Question

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?

Answer 1

Y = Rent

X = size

a)

b)

Computational Table:

	Size (square feet) (X)	Rent ($) (Y)	X2	Y2	XY
	850	1950	722500	3802500	1657500
	1450	2600	2102500	6760000	3770000
	1085	2200	1177225	4840000	2387000
	1232	2500	1517824	6250000	3080000
	718	1950	515524	3802500	1400100
	1485	2700	2205225	7290000	4009500
	1136	2650	1290496	7022500	3010400
	726	1935	527076	3744225	1404810
	700	1875	490000	3515625	1312500
	956	2150	913936	4622500	2055400
	1100	2400	1210000	5760000	2640000
	1285	2650	1651225	7022500	3405250
	1985	3300	3940225	10890000	6550500
	1369	2800	1874161	7840000	3833200
	1175	2400	1380625	5760000	2820000
	1225	2450	1500625	6002500	3001250
	1245	2100	1550025	4410000	2614500
	1259	2700	1585081	7290000	3399300
	1150	2200	1322500	4840000	2530000
	896	2150	802816	4622500	1926400
	1361	2600	1852321	6760000	3538600
	1040	2650	1081600	7022500	2756000
	755	2200	570025	4840000	1661000
	1000	1800	1000000	3240000	1800000
	1200	2750	1440000	7562500	3300000
Total	28383	59660	34223535	145512350	69863210

Calculation:

For Slope:

b = 1.07

For Intercept:

a = 2386.4 - 1.07*1135.32

a = 1177.12

Therefore, the least square regression line would be,

C)

Interpret the slope: If the size (square feet) is increase by 1 feet then We predict the monthly Rental Cost will increased by approximately 1.07 ($)

Interpret the Intercept: If the size (square feet) is 0 feet then We predict the monthly Rental Cost is 1177.12 ($)

d)

The least square regression line would be,

For X = 1000 square feet