Question

In: Statistics and Probability

ABC Apartments is a 300-unit complex near Fairway University that attracts mostly university students. The manager...

ABC 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.

Expert Solution

a)

independent variable = time/Semester
dependent variable = number of Units lease

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.059531178
R Square	0.003543961
Adjusted R Square	-0.162532045
Standard Error	24.29473455
Observations	8

ANOVA
	df	SS	MS	F	Significance F
Regression	1	12.5952381	12.5952381	0.02133939	0.88864248
Residual	6	3541.40476	590.234127
Total	7	3554

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	262.4642857	18.9303047	13.8647682	8.7655E-06	216.143499	308.785073
Semester	-0.547619048	3.74875893	-0.14608009	0.88864248	-9.7205017	8.6252636

y^ = 262.4643 -0.5476* Semester

= 262.4643 -0.5476* 9

= 257.5357

b)

independent variable = University Enrollment
dependent variable = number of Units lease

y	x
228	7.2
252	6.3
265	6.7
270	7
240	6.9
288	6.4
246	7.1

SUMMARY OUTPUT

Regression Statistics
Multiple R	0.58741061
R Square	0.34505122
Adjusted R Square	0.21406147
Standard Error	17.9352561
Observations	7

ANOVA
	df	SS	MS	F	Significance F
Regression	1	847.347222	847.3472222	2.63418482	0.16551305
Residual	5	1608.36706	321.6734127
Total	6	2455.71429

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	488.849206	143.890704	3.397364752	0.0193062	118.966376	858.732037
X Variable 1	-34.3055556	21.1369021	-1.623017198	0.16551305	-88.6396921	20.0285809

x = 6.7

y^ = 259.002

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