Question

The following data represents the square footage and rent of apartments in the boroughs of Queens, New York.
Queens (New York City)

Square Footage	Rent Per Month
500	650
588	1215
1000	2000
688	1655
825	1250
460	1805
1259	2700
650	1200
560	1250
1073	2350
1452	3300
1305	3100

a. Find the least-squares regression line, treating square footage as the explanatory variable.
b. Interpret the slope and y-intercept, if appropriate.
c. Is the rent on the 825-square-foot apartment in the data above or below the average among 825-square-foot apartments?
d. Suppose a 900-square-foot apartment in Astoria (Queens) has a residual of −20. Interpret what this means.

Answer 1

using excel>data>data analsysis>Regression

we have

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.909287
R Square	0.826803
Adjusted R Square	0.809483
Standard Error	364.7004
Observations	12
ANOVA
	df	SS	MS	F	Significance F
Regression	1	6349409	6349409	47.73763	4.15E-05
Residual	10	1330064	133006.4
Total	11	7679473
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-34.3148	295.4357	-0.11615	0.909833	-692.587	623.9571	-692.587	623.9571
Square Footage	2.209148	0.319738	6.909243	4.15E-05	1.496727	2.921569	1.496727	2.921569

we have

a )the least-squares regression line, is

Rent = -34.315 +2.209 *Square footage

b. Interpret the slope : for every one feet increase in the square footage the rent will increase by $ 2.209

interpretation of intercept is not appropriate because rent cannot be negative

c) for square footage =  825-square-foot

Rent = -34.315 +2.209 *825 = 1788.11

Residual = 1250 -1788.11 = -538.11 so the rent on the 825-square-foot apartment in the data below the average among 825-square-foot
d. Suppose a 900-square-foot apartment in Astoria (Queens) has a residual of −20 , the rent of a 900-square-foot apartment in Astoria (Queens) is under estimated