Chasewood Apartments is a 300-unit complex near Fairway University that attracts
ID: 3351721 • Letter: C
Question
Chasewood Apartments is a 300-unit complex near Fairway University that attracts mostly university students. The manager has collected the following data and wants to project the number of units leased in Semester 9 using simple linear regression. Here is the information that has been collected:
Semester
University Enrollment
(in thousands)
Average Lease Price ($)
Number of Units Leased
1
7.2
450
291
2
6.3
460
228
3
6.7
450
252
4
7.0
470
265
5
6.9
440
270
6
6.4
430
240
7
7.1
460
288
8
6.7
440
246
In answering these questions, you must identify and use the correct independent and dependent variables.
a) The apartment manager wants to forecast the Number of Units Leased as a function of time. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9?
b) Suppose the manager believes that the Number of Units Leased is a function only of University Enrollment. It is believed that there will be a one semester lag between the enrollment and the units leased. In other words, the number of units leased in a semester is a function of the university enrollment in the prior semester. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9?
c) Suppose the manager believes that the Number of Units Leased is a function only of the Average Lease Price for that semester. What is the linear regression relationship the manager should use and what is the forecast for the Number of Units Leased for Semester 9 if the average lease price for that semester is $450?
d) Considering the strength of each of the relationships that you found in parts a) through c), would you use any of these to forecast the Number of Units Leased for Semester 9? Explain your answer.
Semester
University Enrollment
(in thousands)
Average Lease Price ($)
Number of Units Leased
1
7.2
450
291
2
6.3
460
228
3
6.7
450
252
4
7.0
470
265
5
6.9
440
270
6
6.4
430
240
7
7.1
460
288
8
6.7
440
246
Explanation / Answer
a) The apartment manager wants to forecast the Number of Units Leased as a function of time. In this we can assume that Number of Units Leased may be dependent on time, enrollment as well as Average Lease Price. Then regression model is
Semester = t
assume Number of Units Leased = NU
University Enrollment = UE
Average Lease Price = ALP
Then, regression model is
NU = a0 + a1 t+e
Using excel, we get the estimated coefficient value.
NU = 262.4643 -0.5476 t
the forecast for the Number of Units Leased for Semester 9 is
NU = 262.4643 -0.5476*9 = 257.53
(b) Suppose the manager believes that the Number of Units Leased is a function only of University Enrollment.
Then, regression model is
NU = a0 + a1 UE+e
Using excel, we get the estimated coefficient value.
NU= -196.382+67.2384UE
(c) Suppose the manager believes that the Number of Units Leased is a function only of the Average Lease Price for that semester.
Then, regression model is
NU = a0 + a1 ALP+e
Using excel, we get the estimated coefficient value.
NU = 72.5+0.4166ALP
the forecast for the Number of Units Leased for Semester 9 if the average lease price for that semester is $450
NU = 72.5 +0.4166*450 = 259.97
(d) Based on R-square, we can see that university enrollment will define the linear regression is this data set.
SUMMARY OUTPUT Regression Statistics Multiple R 0.059531 R Square 0.003544 Adjusted R Square -0.16253 Standard Error 24.29473 Observations 8 ANOVA df SS MS F Significance F Regression 1 12.59524 12.59524 0.021339 0.888642 Residual 6 3541.405 590.2341 Total 7 3554 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 262.4643 18.9303 13.86477 8.77E-06 216.1435 308.7851 t -0.54762 3.748759 -0.14608 0.888642 -9.7205 8.625264