Question

In: Statistics and Probability

The following data represents the square footage and rent of apartments in the boroughs of Queens,...

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.

Solutions

Expert Solution

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

orchestra answered 2 years ago
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