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

Using Excel<data>megastat<correlation/regression<scatterplot

a)

b) Using Excel<data>megastat<correlation/regression<Regression

Regression Analysis
	r²	0.723
	r	0.850
	Std. Error	194.595
	n	25
	k	1
	Dep. Var.	Rent ($) y
ANOVA table
Source	SS	df	MS	F	p-value
Regression	22,68,776.5453	1	22,68,776.5453	59.91	7.52E-08
Residual	8,70,949.4547	23	37,867.3676
Total	31,39,726.0000	24
Regression output					confidence interval
variables	coefficients	std. error	t (df=23)	p-value	95% lower	95% upper
Intercept	1,177.1208	161.00	7.31	0.00	844.06	1510.18
Size (square feet) x	1.0651	0.1376	7.740	7.52E-08	0.7805	1.3498

Intercept(b0) 1177.1208

Slope(b1) 1.0651

c) Interpretation:

b0: There is no meaning.

b1: When b1 increases one unit, the regression line increases

d)1177.1208+1.0651*1000 =2242.2208

e) An apartment with 500 square feet is out of the range for the independent variable.

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