EVALUATING THE IMPACT OF ENERGY
SAVINGS TECHNOLOGIES IN THE
STATLER HOTEL
A Master of Engineering Research Project
Presented to the Faculty of the Graduate School
of Cornell University
In Partial Fulfillment of the Requirements for the Degree of
Master of Engineering
by
Khadeejah Sani
August 2012
© 2012 Khadeejah Sani
ABSTRACT
Evaluating the Impact of Energy Savings Technologies in The Statler Hotel
Khadeejah Sani
Department of Biological and Environmental Engineering
Cornell University
August 2012
On average, hotels in America spend $2,196 per available room yearly on energy. In efforts to
reduce energy costs, The Statler Hotel permitted Schneider Electric to test Cassia™, its energy
management system. Cassia™ is an in-room energy solution based on sensors that detects room
status and triggers temperature setbacks in heating and cooling units. In this study, a four-room
test bed was used to evaluate potential energy savings associated with Cassia™. Statistical
analyses were conducted to determine parameters’ influence in reducing energy units’ runtime.
Results show that Cassia™ reduced runtime by 18%. While the average energy savings reported
by Schneider Electric is 25-44%, this range includes savings from lighting, which was out of the
scope of this study. By extrapolating savings from August-February 2012, a total of $7,829
would have been saved given a Cassia™ installation throughout the Hotel, while $3,003 saved
solely based on vacancies during an unrented status.
BIOGRAPHICAL SKETCH
Khadeejah Sani attained her bachelor’s degree in Industrial and Operations Engineering from the
University of Michigan in 2010. At Cornell University, she focused her master’s degree
coursework on classes related to renewable energy. In September 2012, Ms. Sani will begin her
doctoral studies in Chemical and Environmental Engineering at the University of California,
Riverside, with a research focus on renewable energy.
iii
ACKNOWLEDGEMENTS
I would like to express my gratitude to Lindsay Anderson, research advisor and personal
mentor, for her guidance and supervision throughout the duration of this research project.
I would also like to state my appreciation to my family and friends for their constant support
and encouragement in my pursuit in achieving my educational and personal ambitions. Thank
you!
iv
TABLE OF CONTENTS
Biographical Sketch ....................................................................................................................... iii
Acknowledgments.......................................................................................................................... iv
Chapter 1: Introduction ................................................................................................................... 1
Chapter 2: Methodology ................................................................................................................. 2
2.1 Test Environment ............................................................................................................. 2
2.2 Definitions of Measures ................................................................................................... 3
2.3 Assumptions ..................................................................................................................... 4
2.4 Data .................................................................................................................................. 5
2.5 Procedure .......................................................................................................................... 6
Chapter 3: Results and Discussion .................................................................................................. 7
3.1 Saved Runtime Percentage Analysis ................................................................................ 7
3.2 Basic Statistical Analysis ................................................................................................. 8
3.3 Scatter Plot Analysis ...................................................................................................... 10
3.4 Correlation Analysis ....................................................................................................... 15
3.5 Linear Regression Analysis ............................................................................................ 18
3.6 Multiple Regression Analysis ........................................................................................ 19
3.7 Expected Energy Savings Analysis ................................................................................ 22
3.8 Expected Cost Savings Analysis .................................................................................... 23
3.9 Cost Savings Analysis of Deep Setback Affect ............................................................. 24
Chapter 4: Conclusion................................................................................................................... 25
REFERENCES ............................................................................................................................. 28
Appendix A: Photographs of Standard Double and King Rooms ................................................ 29
Appendix B: Sample Extraction of Data ...................................................................................... 30
Appendix C: Basic Statistical Results........................................................................................... 32
Appendix D: Correlation Matrices................................................................................................ 34
Chapter 1: Introduction
The Statler Hotel, located in the midst of Cornell University, is being considered for a fullscale guest room implementation of the new energy management system, Cassia™. Built in
1987, The Statler Hotel is a nine-story structure with a total of 153 guest rooms. Cassia™, which
was developed late 2010 by the global energy management specialist company, Schneider
Electric, is estimated to achieve 25-44% energy savings per installed guest room (Schneider
Electric, 2010).
According to the U.S. Environmental Protection Agency (EPA), the average hotel in
America spends $2,196 per available room each year on energy, an amount that represents about
6% of all hotel operating costs (EPA, 2006). Hence, thousands of hotels have not only started to
measure their energy use, but have also began turning to energy management systems (EMSs)
such as Cassia™ to manage and reduce their hotel carbon footprints. The EPA encourages hotels
and hotel companies to establish partnerships to jointly reduce the effect of greenhouse gas
emissions produced by American hotels. Through programs such as EnergyStar developed by the
EPA, many hotels are seeking the EPA rating to gain recognition of operating according to
energy efficient building standards.
This project evaluates the impact of Cassia™ by analyzing the significance of its influence
on two rooms with the full-scale Cassia™ EMS installation compared against two similar rooms
without the EMS in order to assess the potential savings that could result from installing
Cassia™ in all rooms in The Statler Hotel.
1
Chapter 2: Methodology
Cassia™ is a wireless in-room set of technologies that reduces energy usage by determining
a room’s real-time occupancy status and automatically triggering temperature setbacks in
heating, ventilation, and air conditioning (HVAC) units both during vacancy periods while a
room is rented to a guest as well as vacancy periods while a room is unrented. The system also
has the ability to control electrical loads, though this is not implemented in this study.
2.1
Test Environment
The Cassia™ EMS was installed in four rooms that are all western-facing and located on the
same floor. All rooms in The Statler Hotel are 315 square feet and utilize a General Electric
#977S HVAC unit. In order to assess possible discrepancies due to room layout, two standard
double rooms (Rooms 612 and 616) as well as two standard king rooms (Rooms 614 and 618)
were selected for this analysis (see Appendix A for photographs of The Statler Hotel’s standard
double and king rooms). Rooms 612 and 614, referred to as the “Cassia Rooms”, have the fully
enabled Cassia™ EMS, while Rooms 616 and 618, referred to as the “Control Rooms,” only
have the occupancy sensors enabled without ties to automatic temperature setpoint adjustments.
At check-in, Cassia Rooms are set at a default temperature of 70°F. During room occupancy,
guests have complete control over temperature settings. When a vacancy is detected while a
room is rented, Cassia™ initiates a 3°F “simple” temperature setback. While a room is unrented,
Cassia™ initiates a 6°F “deep” temperature setback. Schneider Electric and The Statler Hotel
selected August 1, 2011 as the official start date for data collection. For the purpose of this
analysis, data recorded from the period of August 1, 2011 to February 29, 2012 was considered.
2
2.2
Definitions of Measures
Cassia™ records data to calculate 20 measures on a daily basis. The definitions and units of
these measures are provided by Schneider Electric and listed in Table 2.1 below, in the order of
their appearance in the extract data file from Cassia™.
Table 2.1: List of measures and their definitions
Measure
Runtime %
Avg Setpoint (°F)
Avg Temp (°F)
Avg Outside Temp (°F)
Cooling (Hours)
2nd Stg Cooling (Hours)
Heating (Hours)
2nd Stg Heating (Hours)
Idle (Hours)
Occupied (Hours)
Vacant (Hours)
Difference (°F)
Saved (Hours)
Saved Runtime %
Runtime Occupied
Cooling (Hours)
Runtime Vacant
Cooling(Hours)
Runtime Occupied
Heating(Hours)
Runtime Vacant
Heating (Hours)
Total Runtime
Occupied Runtime
Definition
Number of hours of HVAC runtime divided by the total number of
hours in the period
Average setpoint of the thermostat for the entire period
Average actual temperature in the guest room for the period
Average outside temperature
Number of runtime hours in 'Cooling' for the period
Number of runtime hours in '2nd Stage Cooling' for the period
Number of runtime hours in 'Heating' for the period
Number of runtime hours in '2nd Stage Heating' for the period
Number of hours the unit was not running during the period
Number of hours the room was occupied during the period
Number of hours the room was vacant during the period
Difference between the 'Average Setpoint' and 'Average Temperature'
during the period – This is a general indication of demand.
Calculation of saved runtime hours for a particular room for the
period
Calculation of the percentage savings in runtime over the period
Cooling runtime in hours only during the 'Occupied' periods
Cooling runtime in hours only during the 'Vacant' periods
Heating runtime in hours only during the 'Occupied' periods
Heating runtime in hours only during the 'Vacant' periods
Heating and Cooling runtime for the period
Heating and Cooling runtime for ‘Occupied’ periods
3
Saved Runtime Percentage, the definition of which is highlighted in Table 2.1, is the metric
created by Schneider Electric that is used to determine the impact of Cassia™ on energy usage.
Saved Runtime Percentage is based on three intermediary equations consisting of measures that
were either collected or computed based on the Table 2.1 measures. The metric of the Saved
Runtime Percentage and its intermediary equations are calculated as follows:
𝑆𝑎𝑣𝑒𝑑 𝑅𝑢𝑛𝑡𝑖𝑚𝑒 % =
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑇𝑜𝑡𝑎𝑙 𝑅𝑢𝑛𝑡𝑖𝑚𝑒−𝐴𝑐𝑡𝑢𝑎𝑙 𝑅𝑢𝑛𝑡𝑖𝑚𝑒
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑇𝑜𝑡𝑎𝑙 𝑅𝑢𝑛𝑡𝑖𝑚𝑒
𝐴𝑐𝑡𝑢𝑎𝑙 𝑅𝑢𝑛𝑡𝑖𝑚𝑒 = 𝐶𝑜𝑜𝑙𝑖𝑛𝑔 (ℎ𝑜𝑢𝑟𝑠) + 𝐻𝑒𝑎𝑡𝑖𝑛𝑔 (ℎ𝑜𝑢𝑟𝑠)
(2.1)
(2.2)
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑇𝑜𝑡𝑎𝑙 𝑅𝑢𝑛𝑡𝑖𝑚𝑒 = [𝑅𝑢𝑛𝑡𝑖𝑚𝑒 𝑂𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝐶𝑜𝑜𝑙𝑖𝑛𝑔 (ℎ𝑜𝑢𝑟𝑠) +
(2.3)
𝑅𝑢𝑛𝑡𝑖𝑚𝑒 𝑂𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝐻𝑒𝑎𝑡𝑖𝑛𝑔 (ℎ𝑜𝑢𝑟𝑠)] + [% 𝑅𝑢𝑛𝑡𝑖𝑚𝑒 𝑂𝑐𝑐𝑢𝑝𝑖𝑒𝑑 × 𝑉𝑎𝑐𝑎𝑛𝑡 (ℎ𝑜𝑢𝑟𝑠)]
% 𝑅𝑢𝑛𝑡𝑖𝑚𝑒 𝑂𝑐𝑐𝑢𝑝𝑖𝑒𝑑 =
2.3
𝑅𝑢𝑛𝑡𝑖𝑚𝑒 𝑂𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝐶𝑜𝑜𝑙𝑖𝑛𝑔 (ℎ𝑜𝑢𝑟𝑠)+ 𝑅𝑢𝑛𝑡𝑖𝑚𝑒 𝑂𝑐𝑐𝑢𝑝𝑖𝑒𝑑 𝐻𝑒𝑎𝑡𝑖𝑛𝑔 (ℎ𝑜𝑢𝑟𝑠)
𝑂𝑐𝑐𝑢𝑝𝑖𝑒𝑑 (ℎ𝑜𝑢𝑟𝑠)
(2.4)
Assumptions
There are a number of assumptions made for these calculations. The most significant
assumption Schneider Electric made in the calculation of the Saved Runtime Percentage
(Equation 2.1) is in determining Equation 2.3, Estimated Total Runtime. As shown above, this is
accomplished by taking the total number of Vacant hours and multiplying it by Percentage
Runtime Occupied. This assumption implies that if the HVAC unit ran, for example 30% of the
time while the room was occupied, then it would also run 30% of the time during the vacant
period since there is no control in place. Hence, if the setpoint was left at 68°F and the guest left
the room, then the HVAC unit would continue to try and deliver 68°F during the vacant period.
4
2.4
Data
For this study, 12 measures were utilized. One of these measures was gathered from an
external source, another was computed from the extracted data, eight measures were directly
extracted from the Cassia™ extract data file, and the remaining two measures were provided by
The Statler Hotel management. Table 2.2 shows the 12 measures as well as their origin and
corresponding values/formulas (see Appendix B for a sample extraction).
Table 2.2 List of measures and their origin and value
Origin
Value/Formula
Degree Days.net
‘Heating Degree Days’ in results analysis file
Computed
=1 if ‘Rented Duration’ > 12 hours; else =0
Occupied Duration
Cassia™ records
‘Occupied’ in extract data file
Vacant Duration
Cassia™ records
‘Vacant’ in extract data file
Rented Duration
The Statler Hotel
Provided by The Statler Hotel management
Unrented Duration
The Statler Hotel
= 24 – ‘Rented Duration’
Idle Hours
Cassia™ records
‘Idle’ in extract data file
Actual Runtime (Cooling)
Cassia™ records
‘Cooling’ in extract data file
Actual Runtime (Heating)
Cassia™ records
‘Heating’ in extract data file
Actual Runtime
Cassia™ records
= ‘Cooling’ + ‘Heating’
Occupied Runtime
Cassia™ records
‘Occupied Runtime’ in extract data file
Total Runtime
Cassia™ records
‘Total Runtime' in extract data file
Measure
Heating Degree Days
Rented?
In order to determine the impact of the Cassia™ EMS based on the temperature setback
feature and occupancy sensors technologies, two ‘primary parameters’ were selected. These
parameters are based on the objectives of the Cassia™ EMS to reduce the overall runtime of
HVAC units based on the detection of a room’s vacancy.
5
The primary parameters are:

Duration of rented vacancy: the period that a room is rented and vacant

Duration of unrented vacancy: the period that a room is unrented and vacant
Total Runtime is the dependent or response variable, while the primary parameters are the
independent variables, also called predictor variables or input variables.
2.5
Procedure
The below procedure was followed in this analysis:
1. Validate Cassia™ EMS records by implementing Equations 2.2-2.4 for extract file data
2. Compute Equation 2.1, Saved Runtime Percentage, for Cassia Rooms
3. Obtain vacancy data for Control Rooms
4. Compute rented/unrented durations for all rooms
5. Perform statistical analyses for all rooms:
a. Basic – mean and standard deviation for Total Runtime and primary parameters
b. Scatter Plot – graphs of Total Runtime against each of the two primary parameters
c. Correlation – Total Runtime against the first 11 measures from Table 2.2
d. Linear Regression – Total Runtime against each of the two primary parameters
e. Multiple Regression – Total Runtime against both of the primary parameters
6. Conduct an expected energy savings analysis for Cassia Rooms
7. Conduct an expected cost savings analysis for Cassia Rooms
8. Investigate affect of Deep Setback feature via energy and cost analyses for Cassia Rooms
The main challenges in this study were the constraint in the provision of precise
rented/unrented durations and the duration of vacancies for the Control Rooms. Hence, vacancy
durations for the Control Rooms were determined based on recorded motion sequences.
6
Chapter 3: Results and Discussion
For this study, the computation of Saved Runtime Percentage was initially analyzed followed
by five statistical analyses in order to evaluate the influence of the Cassia™ EMS on the total
runtime of the energy units. Also computed was the expected energy and cost savings associated
with the saved runtime.
3.1
Saved Runtime Percentage Analysis
Schneider Electric evaluates the energy savings of the Cassia™ EMS by calculating Equation
2.1, the Saved Runtime Percentage. This metric, the equation of which is provided again below,
was validated with data provided by Cassia™ and confirmed to be equivalent with slight
differences due to rounding errors.
𝑆𝑎𝑣𝑒𝑑 𝑅𝑢𝑛𝑡𝑖𝑚𝑒 % =
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑇𝑜𝑡𝑎𝑙 𝑅𝑢𝑛𝑡𝑖𝑚𝑒 − 𝐴𝑐𝑡𝑢𝑎𝑙 𝑅𝑢𝑛𝑡𝑖𝑚𝑒
𝐸𝑠𝑡𝑖𝑚𝑎𝑡𝑒𝑑 𝑇𝑜𝑡𝑎𝑙 𝑅𝑢𝑛𝑡𝑖𝑚𝑒
(2.1)
Table 3.1 shows the results of the Percentage Runtime Occupied measure as well as the
Estimated Total Runtime measure which are used to arrive at the Saved Runtime Percentage
metric. Results from computing the Saved Runtime Percentage metric based on the same
Cassia™ EMS extract data file used by Schneider Electric are also shown. Additionally, Table
3.1 displays the averages for all of the seven months considered and overall the Cassia Room
averages.
7
Table 3.1: Calculated results of the Saved Runtime Percentage metric and results provided by
Schneider Electric
% Runtime
Occupied
(calculated)
Cassia Room
Estimated Total
Runtime
(calculated)
Saved Runtime %
(calculated)
Saved Runtime %
(from Schneider Electric)
612
614
612
614
612
614
612
614
August
50%
26%
373.40
190.42
26%
32%
26%
33%
September
42%
17%
182.81
55.21
17%
28%
17%
28%
October
11%
24%
78.56
54.59
24%
1%
24%
0%
November
11%
11%
82.30
89.74
11%
12%
11%
12%
December
9%
7%
55.43
33.11
7%
8%
7%
8%
January
12%
5%
25.95
18.78
5%
9%
4%
9%
February
23%
27%
161.12
115.61
27%
41%
27%
41%
23%
13%
137.08
79.64
17%
19%
17%
19%
Average
Overall
Average
3.2
18%
108.36
18%
18%
Basic Statistical Analysis
At first, basic statistics including the mean and standard deviation for all four rooms were
computed to bring to light any obviously unusual data (see Appendix C for results from this
analysis). The averages of the measures under consideration are plotted as follows:

Total Runtime per month in Figure 3.1

The duration of rented vacancy per month in Figure 3.2

The duration of unrented vacancy per month in Figure 3.3
8
Total Runtime vs. Month
10
9
Room 612
Room 614
Room 616
Room 618
Runtime (hours)
8
7
6
5
4
3
2
1
0
Figure 3.1: Plot of total runtime for the seven months under analysis
Figure 3.1 shows that, overall, the HVAC units were used most frequently during the month of
August and least frequently in October.
24
Duration of Vacancy vs. Month
Room 612
20
Vacancy (hours)
Room 614
16
Room 616
Room 618
12
8
4
0
Figure 3.2: Plot of duration of rented vacancy for the seven months under analysis
9
The zero hour rented vacancy duration during October in Room 614 and the low rented vacancy
duration during January in Room 616 appear peculiar in Figure 3.2. This could be attributed to
an error in data recording, but no such information has been reported. Alternatively, Figure 3.3
shows the least questionable trend out of all of the three plots.
Duration of Unrented Status vs. Month
24
Room 612
Unrented Status (hours)
20
Room 614
Room 616
16
Room 618
12
8
4
0
Figure 3.3: Plot of duration of unrented vacancy for the seven months under analysis
3.3
Scatter Plot Analysis
Scatter plots are an important preliminary step prior to undertaking a formal statistical
analysis of the relationship between two variables (Johnson & Bhattacharyya, 1996). All eight
scatter plots, a plot of Total Runtime against each of the two primary parameters for each of the
four rooms, are displayed below in Figures 3.4-3.11. Also displayed on the graphs is the
regression equation and regression line, a straight line established through a data set that best
represents a relationship between two variables. These scatter plots show that a strong correlation
does not appear to exist between Total Runtime and either of the two parameters in all rooms.
10
Room 612: Total Runtime vs. Duration of Rented Vacancy
y = -0.1526x + 6.2727
r² = 0.0528
Runtime (hours)
24
20
16
12
8
4
0
0
4
8
12
16
20
24
Vacancy (hours)
Figure 3.4: Plot of total runtime against the duration of rented vacancy for Room 612
Runtime (hours)
Room 614: Total Runtime vs. Duration of Rented Vacancy
24
y = -0.087x + 2.9869
r² = 0.07
20
16
12
8
4
0
0
4
8
12
16
20
Vacant (hours)
Figure 3.5: Plot of total runtime against the duration of rented vacancy for Room 614
11
24
Room 616: Total Runtime vs. Duration of Rented Vacancy
y = -0.0914x + 4.2308
r² = 0.0245
25
Runtime (hours)
20
15
10
5
0
0
4
8
12
16
20
24
Vacant (hours)
Figure 3.6: Plot of total runtime against the duration of rented vacancy for Room 616
Room 618: Total Runtime vs. Duration of Rented Vacancy
y = -0.1088x + 5.7811
r² = 0.0228
30
Runtime (hours)
25
20
15
10
5
0
0
4
8
12
16
20
Vacant (hours)
Figure 3.7: Plot of total runtime against the duration of rented vacancy for Room 618
12
24
Room 612: Total Runtime vs. Duration of Unrented Vacancy
y = -0.2021x + 7.02
r² = 0.145
25
Runtime (hours)
20
15
10
5
0
0
4
8
12
16
20
24
Unrented (hours)
Figure 3.8: Plot of total runtime against the duration of unrented vacancy for Room 612
Room 614: Total Runtime vs. Duration of Unrented Vacancy
y = -0.0875x + 3.0625
r² = 0.0791
25
Runtime (hours)
20
15
10
5
0
0
4
8
12
16
20
Unrented (hours)
Figure 3.9: Plot of total runtime against the duration of unrented vacancy for Room 614
13
24
Room 616: Total Runtime vs. Duration of Unrented Vacancy
y = -0.0504x + 3.378
r² = 0.0163
25
Runtime (hours)
20
15
10
5
0
0
4
8
12
16
20
24
Unrented (hours)
Figure 3.10: Plot of total runtime against the duration of unrented vacancy for Room 616
Room 618: Total Runtime vs. Duration of Unrented Vacancy
y = -0.0678x + 4.8086
r² = 0.0205
30
Runtime (hours)
25
20
15
10
5
0
0
4
8
12
16
20
Unrented (hours)
Figure 3.11: Plot of total runtime against the duration of unrented vacancy for Room 618
14
24
Statistical ideas must be introduced into the study of relation when the points in a scatter plot do
not lie perfectly on the regression line (Johnson & Bhattacharyya, 1996).
3.4
Correlation Analysis
In order to analyze the relationship between Total Runtime and the primary parameters as
well as determine the possible influence of any additional parameters, a correlation analysis was
conducted. In addition to the primary parameters, also considered were the potential relationships
between Total Runtime and each of the secondary parameters:

Heating Degree Days

Rented?
The latter parameter was coded as a binary variable, based on the assumption that a room
was considered rented for the day if Rented Duration was greater than 12 hours and unrented if
Rented Duration was less than 12 hours. The former parameter, Heating Degree Days, is a
measure of how much (in degrees) outside air temperature was lower than a specific base
temperature. Heating Degree Days data was retrieved from Degree Days.net and utilized 70°F as
the base temperature as opposed to the original base temperature of 65°F which is the standard
base temperature in the Heating Degree Days equation. The original base temperature of 65°F
represents houses of the early twentieth century in the United States when insulation was
minimal and indoor air temperatures were approximately 75°F (Vanek & Albright, 2008).
According to Vanek and Albright, today’s homes are generally insulated to a higher level with
control temperatures lower than 75°F. For this reason, a base temperature of 70°F was selected
for this study which also matches the Cassia™ EMS default temperature at check-in.
The correlation coefficient, denoted as r, is a measure of strength of the linear relationship
between the dependent and independent variables (Johnson & Bhattacharyya, 1996). The
15
correlation coefficient determines how closely the points in the scatter plot approximate a
straight-line pattern, i.e. the regression line. Johnson and Bhattacharyya’s textbook, Statistics:
Principles and Methods, summarizes the important features of the correlation coefficient:
1. The value of r is always between -1 and +1.
2. The magnitude of r indicates the strength of a linear relation, whereas its sign indicates the
direction. More specifically,
a. r > 0
if the pattern of the scatter plot is a band that runs from lower left to upper right.
b. r < 0
if the pattern of the scatter plot is a band that runs from upper left to lower right.
c. r = +1 if all values on the scatter plot lie exactly on the regression line with a positive
slope (perfect positive linear relation)
d. r = -1 if all values on the scatter plot lie exactly on the regression line with a negative
slope (perfect negative linear relation)
3. A high numerical value of r, that is, a value close to +1 or -1, represents a strong linear
relation.
The correlation coefficient values for the primary and secondary parameters are highlighted
in Table 3.2. The complete correlation matrices for all four rooms are provided in Appendix D.
The primary parameters and the first secondary parameter are depicted on a color scale with dark
green (r closest to -1) coded as the strongest inverse relationship and dark red (r closest to 1)
coded as the strongest direct relationship. A value of r close to zero means that the linear
association is very weak. As shown via the color scale, a strong inverse relationship explains that
as the parameter increases (i.e. duration of rented or unrented vacancy), Total Runtime
decreases. Alternatively, a strong direct relationship explains that as the parameter increases,
Total Runtime also increases.
16
Table 3.2: Summary of r values for the primary and secondary parameters in all four rooms
Cassia Rooms
Room
Total Runtime &
Duration of
Rented Vacancy
Primary
Parameters Total Runtime &
Duration of
Unrented Vacancy
Total Runtime vs.
Heating Degree
Secondary Days
Parameters
Total Runtime vs.
Rented?
Control Rooms
612
614
616
618
-0.23
-0.26
-0.16
-0.15
-0.38
-0.28
-0.13
-0.14
-0.33
-0.16
-0.36
-0.13
0.33
0.29
0.10
0.11
There are two main two conclusions can be drawn from the Correlation Analysis: (1) there is
a stronger inverse relationship between Total Runtime and each of the two primary parameters in
the Cassia Rooms than there is in the Control Rooms and (2) one primary parameter, the duration
of unrented vacancy, shows a stronger inverse relationship with Total Runtime than the duration
of rented vacancy in the Cassia Rooms. As for the secondary parameters, there is an apparently
stronger inverse correlation between Total Runtime and Heating Degree Days for the doublesized rooms, 612 and 616, than the king-sized rooms, 614 and 618. However, since only one
Cassia room and one Control room was selected for each room layout type, a relationship
between Heating Degree Days and Cassia™ cannot be drawn. Regarding the other secondary
parameter, Rented?, Total Runtime indeed has a stronger direct relationship (higher positive r
values) in the Cassia Rooms than in the Control Rooms on the basis of whether or not the room
is rented.
17
3.5
Linear Regression Analysis
Regression analysis concerns the study of relationships between variables with the object of
identifying, estimating, and validating the relationship (Johnson & Bhattacharyya, 1996). The
estimated relationship can then be used to predict one variable from the value of the other
variable. In this study, regression analysis was used to further analyze potential patterns in the
relationships between Total Runtime and each of the two primary parameters: the duration of
rented vacancy and the duration of unrented vacancy.
The square of the correlation coefficient or r2, namely the coefficient of determination,
represents the amount of the variation in the dependent variable that is explained by the
regression line (Triola, 2006).
The coefficient of determination is computed as follows:
𝑟2 =
𝑒𝑥𝑝𝑙𝑎𝑖𝑛𝑒𝑑 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛
𝑡𝑜𝑡𝑎𝑙 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛
(3.1)
Hence, r2 can be calculated by using Equation 3.1 or by simply squaring the correlation
coefficient, r. The coefficient of determination ranges from 0 to 1 inclusive (Montgomery &
Runger, 2003). When the value of r2 is small, it can only be concluded that a straight-line
relation does not give a good fit to the data (Johnson & Bhattacharyya, 1996).
Below, Table 3.3 summarizes the r2 values as percentages on a color scale, with dark green
(r2 closest to 100%) coded as the strongest relationship and dark red (r2 closest to 0%) as the
weakest relationship. The coefficient of determination values are also displayed as decimal
values on the previously depicted scatter plots in Figures 3.4-3.11.
18
Table 3.3: Summary of r2 values for the primary parameters in all four rooms
Cassia Rooms
Room
Primary
Parameters
Total Runtime vs.
Duration of
Rented Vacancy
Total Runtime vs.
Duration of
Unrented Vacancy
Control Rooms
612
614
616
618
5%
7%
2%
2%
15%
8%
2%
2%
As confirmed in the Correlation Analysis, the same two conclusions can be drawn from the
resulting r2 values: (1) there is a stronger relationship between Total Runtime and the duration of
rented vacancy as well as between Total Runtime and the duration of unrented vacancy for the
Cassia Rooms than there is for the Control Rooms and (2) the primary parameter of the duration
of unrented vacancy is a stronger predictor of Total Runtime in the Cassia Rooms.
3.6
Multiple Regression Analysis
The Correlation Analysis as well as the Linear Regression Analysis verified that, despite
considerable small, a relationship does exist between Total Runtime and each of the primary
parameters. In order to better evaluate the level of influence of the primary parameters in
determining Total Runtime, a Multiple Regression Analysis was conducted using the two
primary parameters as the input, independent variables. The name “multiple regression” refers to
a model of relationship where the response depends on two or more predictor variables (Johnson
& Bhattacharyya, 1996).
R2 denotes the multiple coefficient of determination, which is a measure of how well the
multiple regression equation fits the sample data (Triola, 2006). According to Triola’s textbook,
Elementary Statistics, a perfect fit would result in R2 = 1 and a very good fit results in a value
near 1. A very poor fit results in a value of R2 close to 0. But, as pointed out in the same text, the
19
multiple coefficient of determination has a serious flaw: “As more variables are included, R2
increases.” The largest R2 is obtained by simply including all of the available variables. However,
the best multiple regression equation does not necessarily use all of the available variables. Due
to the multiple coefficient of determination flaw, comparison of different multiple regression
equations is better accomplished with the adjusted coefficient of determination which is
R2adjusted for the number of variables and the sample size (Triola, 2006).
The equation for Adjusted R2is as follows:
𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑅 2 = 1 −
(n − 1)
× (1 − 𝑅 2 )
[n − (k + 1)]
(3.2)
where
n = sample size
k = number of predictor variables
R2 = the unadjusted multiple coefficient of determination
Source: Triola (2006)
The summary of results from the Multiple Regression Analysis is shown in Table 3.4. The
table displays the results of the Adjusted R2 values, the Significance F values and P-values and is
color coded to dark green representing the most favorable results, light green representing a
slight relationship/influence, orange representing almost no relationship/influence and dark red
representing the most unfavorable results. The Significance F value is the P-value of the F-test,
where the P-value is a measure of the overall significance of the multiple regression equation
(Triola, 2006). The P-values or level of significance for each of the two primary parameters are
also provided in Table 3.4. Significance F values and P-values equal to zero or below 0.05 are
classified as significant, with values greater than 0.05 classified as not significant.
20
Table 3.4: Results from the Multiple Regression Analysis for all four rooms
Cassia Rooms
Room
Control Rooms
612
614
616
618
Adjusted R2
14%
9%
2%
1%
Significance F
0.00
0.00
0.10
0.13
0.46
0.06
0.18
0.43
0.00
0.02
0.56
0.64
Rented
P-value
Unrented
There are three main conclusions that can be drawn from the Multiple Regression Analysis.
The first conclusion of the Multiple Regression Analysis supports the first conclusion in the
previous two analyses (Correlation and Linear Regression) in that there is a stronger correlation
between Total Runtime and each of the two primary parameters for the Cassia Rooms than there
is for the Control Rooms. This conclusion is evident by the higher Adjusted R2 value in the
Cassia Rooms. The second conclusion from the Multiple Regression Analysis relates to the
Significance F values which show that the Multiple Regression relationship is significant in the
Cassia Rooms and insignificant in the Control Rooms. The smaller the Significance F value, the
greater the probability that Total Runtime was not determined coincidentally. Lastly, as
confirmed in both the Correlation and Linear Regression analyses, the P-values show that there
is a higher significance in the relationship between Total Runtime and the duration of unrented
vacancy in the Cassia Rooms than there is between Total Runtime and the duration of rented
vacancy in the Cassia Rooms. The relationships between Total Runtime and each of the primary
parameters are extremely insignificant in the Control Rooms as shown by the low Adjusted R2
values (close to 0%) as well as the high Significance F values and P-values (far from zero).
21
3.7
Expected Energy Savings Analysis
Based on the results from the Saved Runtime Percentage metric presented in Section 3.1, the
expected energy saved in kilowatt-hours (kWh) was calculated per month by assuming a medium
speed set at 75 watts for the General Electric #977S HVAC unit. The generic equation for
expected energy saved (kWh) is:
Expected Energy Saved =
75 𝑘𝑖𝑙𝑜𝑤𝑎𝑡𝑡𝑠
× # 𝑜𝑓 𝑑𝑎𝑦𝑠 𝑖𝑛 𝑚𝑜𝑛𝑡ℎ × 𝑟𝑢𝑛𝑡𝑖𝑚𝑒 𝑝𝑒𝑟 𝑚𝑜𝑛𝑡ℎ × 𝑠𝑎𝑣𝑒𝑑 𝑟𝑢𝑛𝑡𝑖𝑚𝑒 %
1000
For Cassia Rooms, Table 3.5 shows the expected energy saved for each of the months
analyzed. Also included is the total expected energy saved in the Cassia Rooms as well as the
average expected energy saved for all of the months considered.
Table 3.5: Results from the Expected Energy Savings Analysis
Expected Energy Saved (in kWh)
Cassia Room
612
614
August
167.62
81.53
September
56.28
14.22
October
33.20
1.50
November
20.72
15.26
December
8.43
3.48
January
4.41
7.73
February
64.17
44.34
Total
354.83
168.05
Average
50.69
24.01
22
3.8
Expected Cost Savings Analysis
In order to further assess the impact of the Cassia™ EMS, the expected cost savings were
calculated based on the expected energy savings computed in the previous Section 3.6 and
extrapolated from the two Cassia Rooms to all 153 rooms in The Statler Hotel. The average
electricity prices per kilowatt-hour for the state of New York were gathered from a Bureau of
Labor Statistics release (U.S. Department of Labor, 2012). Table 3.6 shows the expected cost
savings on a monthly basis for the Cassia Rooms and the complete Statler Hotel as well as the
average monthly New York electricity prices. Also included in Table 3.6 are the total expected
cost savings in the two Cassia Rooms, 612 and 614, and in The Statler Hotel as well as the
average expected cost savings for all of the months considered.
Table 3.6: Results from Expected Cost Savings Analysis
Average Price for
Electricity ($/kWh)
Cassia Room
612
614
Cost Savings
Extrapolation for All
Rooms in Hotel
Expected Cost Savings (in $)
August
$0.200
$33.52
$16.31
$3,811.96
September
$0.205
$11.54
$2.91
$1,105.57
October
$0.191
$6.34
$0.29
$507.04
November
$0.188
$3.90
$2.87
$507.04
December
$0.184
$1.55
$0.64
$167.58
January
$0.189
$0.83
$1.46
$175.53
February
$0.186
$11.94
$8.25
$1,544.00
Total
$69.62
$32.72
$7,829.10
Average
$9.95
$4.67
$1,118.44
23
3.9
Cost Savings Analysis of Deep Setback Affect
Based on the Correlation, the Linear Regression and the Multiple Regression analyses, it is
apparent that the duration of unrented vacancy has the most significant influence on the Total
Runtime than the duration of rented vacancy. The increased reduction in Total Runtime during
the durations of unrented vacancies is due to the Deep Setback feature of 6°F as opposed to the
3°F Simple Setback feature during the durations of rented vacancies. For this reason, the
expected cost savings related only to the duration of unrented vacancy were calculated as the
final analysis in this study. Table 3.7 shows the results of the cost savings in the Cassia Rooms
based only on the influence of the Deep Setback feature as well as the cost savings extrapolation
for all rooms in The Statler Hotel. Also included in Table 3.7 is the total expected cost savings in
the Cassia Rooms, 612 and 614, and in The Statler Hotel as well as the average expected cost
savings for all of the months considered.
Table 3.7: Results from Expected Cost Savings Analysis based on the Deep Setback feature
612
612
Cost Savings
Extrapolation for All
Rooms in Hotel (in $)
August
$12.02
$0.69
$972.51
September
$2.99
$0.01
$229.25
October
$0.97
$0.00
$74.66
November
$10.38
$0.24
$812.33
December
$5.69
$0.32
$459.20
January
$1.53
$1.75
$250.92
February
$2.23
$0.44
$204.40
Total
$35.81
$35.81
$3,003.28
Average
$5.12
$5.12
$429.04
Expected Cost Savings (in $)
Cassia Rooms
24
Chapter 4: Conclusion
The energy savings in the Cassia Rooms are a result of the occupancy sensor technologies
that are components of the Cassia™ EMS. The EMS triggers a 3°F reduction in the Total
Runtime of the HVAC units which correspond to the measure of the primary parameter of the
duration of rented vacancy. On the other hand, the Deep Setback feature which reduces the Total
Runtime of the HVAC units by 6°F is triggered when a room is vacant and unrented. This latter
case corresponds to the measure of the duration of unrented vacancy.
Overall, the Cassia™ EMS does assist in reducing the Total Runtime of HVAC units, but not
within the range of the average energy savings reported by Schneider Electric (25-44%).
However, since energy savings from lighting were out of the scope of this study but included in
Schneider Electrics’ average energy savings range, the expected energy savings in the Cassia
Rooms of 18% may actually be highly gratifying depending on how much energy savings is
associated with lighting. Nonetheless, as a result of the Cassia™ EMS in the Cassia Rooms, the
Total Runtime of HVAC units is most strongly affected by the duration of unrented vacancy than
by other parameters of interest. This conclusion was confirmed in all three statistical analyses
conducted i.e. the Correlation Analysis, Linear Regression Analysis and Multiple Regression
Analysis.
The duration of unrented vacancy does not have a significant influence in reducing Total
Runtime as shown in the relatively low r2 values in the Linear Regression Analysis and low
Adjusted R2 values in the Multiple Regression Analysis. The Linear Regression Analysis reveals
that only 15% of the total runtimes can be predicted by the duration of unrented vacancy in
Room 612 and only 8% in Room 614. Compare that prediction to the Control Rooms, Rooms
616 and 618, in which for both rooms, only 2% of the total runtimes can be predicted by the
25
duration of unrented vacancy. The predictions from the Cassia Rooms are stronger, but not that
much greater than the Control Rooms and are far from a direct relationship between Total
Runtime and the parameter, which would have resulted in r2 values equal or close to100%. When
incorporating both primary parameters as predictors of Total Runtime, as conducted in the
Multiple Regression Analysis, the resulting Adjusted R2 values show just a slightly stronger
relationship of 15% in Room 612 and 10% in Room 614. However, again, these results are not
much greater than the Control Rooms in which the two parameters can predict Total Runtime
only 3% and 2% of the time for Room 616 and Room 618, respectively. These values are far
below an Adjusted R2 value near 100%, which would represent a strong correlation between
Total Runtime and the two parameters.
Cost savings are useful in determining the impact of the Cassia™ EMS. Based on expected
energy savings calculated from Schneider Electric’s Saved Runtime Percentage metric, from the
period between August 2011 and February 2012, about $70 would have been saved in Room 612
and $32 saved in Room 614 as a result of the complete enabling of all features of the Cassia™
EMS. That adds to a total savings of $102 for the seven months analyzed in the Cassia Rooms.
Based exclusively on the most influential parameter, the duration of unrented vacancy, the cost
savings would have been $36 in Room 612 and $3 in Room 614 for a total savings of $39 in the
Cassia Rooms for the seven months analyzed. These figures do not appear to make a significant
impact in cost savings when the savings in the two Cassia Rooms alone are analyzed. Hence,
cost savings from the Cassia Rooms over the span of seven months (from August 2011 to
February 2012) were extrapolated to all 153 rooms in The Statler Hotel which resulted in a total
savings of $7,829 based on the complete enabling of all Cassia™ features and a total of $3,003
26
based the enabling of only the Deep Setback feature. These results show that the Deep Setback
feature accounts for around 40% of the total cost savings.
In closing, this research study has allowed a better understanding of the impacts of the
Cassia™ EMS in The Statler Hotel. As a result of the conclusions drawn from the analyses
conducted in this study, it is advised that a final decision on the full-scale Cassia™ EMS
installation in all guest rooms is decided upon between one of three options: (1) install the
complete Cassia™ EMS with all occupancy sensors and temperature setback technologies, (2)
install only the components of the Cassia™ EMS that trigger the Deep Setback feature in the
HVAC units, or (3) continue as usual without installing any Cassia™ EMS components.
Ultimately, the tolerable amount of savings would need to be decided on by The Statler Hotel
management team and would depend on the management’s motives for energy savings, such as
achieving energy savings ratings like EnergyStar, and also on the cost of the Cassia™ EMS and
consequent payback requirements. Nonetheless, this study assists in projecting an anticipated
range in energy and cost savings and proves that a relationship between Cassia™ and a reduction
in Total Runtime does indeed exist.
Further studies incorporating more Cassia and Control rooms could be favorable in
confirming the results reached in this study.
27
REFERENCES
BizEE Software. Degree Days.net. Accessed: June 2012.
Johnson, R. A., & Bhattacharyya, G. K. (1996). Statistics: Principles and methods. Hoboken,
NJ: John Wiley & Sons.
Montgomery, D. C., & Runger, G. C. (2003). Applied statistics and probability for engineers.
Hoboken, NJ: Wiley.
Schneider Electric. (2010), The Cassia™ Energy Management System (EMS). White Paper,
Document 1280HO1001.
Triola, M. F. (2006). Elementary statistics. Boston: Pearson/Addison-Wesley.
U.S. Department of Labor. Average Energy Prices in New York-Northern New Jersey –
February 2012. Bureau of Labor Statistics, http://www.bls.gov/ro2/avgengny.pdf.
Accessed: April 2012.
U.S. Environmental Protection Agency. Hotels: An Overview of Energy Use and Energy
Efficiency Opportunities. ENERGY STAR fact sheet,
www.energystar.gov/ia/business/challenge/learn_more/Hotel.pdf . Accessed: May 2012.
Vanek, F. M., & Albright, L. D. (2008). Energy systems engineering: Evaluation and
implementation. New York: McGraw-Hill.
28
Appendix A: Photographs of Standard Double and King Rooms
Standard Double Room
Standard King Room
29
Appendix B: Sample Extraction of Data
Room 612
Day
Occupied
Duration
Vacant
Duration
Rented
Duration
Unrented
Duration
Heating
Degree
Days
Rented?
Actual
Runtime
(Cooling)
Actual
Runtime
(Heating)
Actual
Runtime
Idle
Hours
Occupied
Runtime
Total
Runtime
8/1/2011
20.5
3.5
10.56666667
13.43333333
1.6
0
11.4
0
11.4
12.6
1.39645
11.433333
8/2/2011
10.4
13.6
0
24
4.3
0
12.4
0
12.4
11.6
6.47266
12.383333
8/3/2011
2.4
21.6
0
24
4.1
0
4.5
0
4.5
19.5
2.428355
4.483333
8/4/2011
12.6
11.4
0
24
2.3
0
2.6
0
2.6
21.5
2.09156
2.55
8/5/2011
4.6
19.4
14.06666667
9.933333333
2.9
1
9.8
0
9.8
14.2
2.63127
9.8
8/6/2011
16.2
7.8
16.7
7.3
0.9
1
14.7
0
14.7
9.3
12.659158
14.7
8/7/2011
11.9
12.1
10.06666667
13.93333333
1.3
0
12.1
0
12.1
11.9
10.238606
12.066666
8/8/2011
4.4
19.6
4.5
19.5
1.4
0
7.3
0.2
7.5
16.5
2.73109
7.5
8/9/2011
14.9
9.1
24
0
3.3
1
13.8
0
13.8
10.2
9.137663
13.8
8/10/2011
15.7
8.3
24
0
3.9
1
14.6
0
14.6
9.4
10.53209
14.616666
8/11/2011
16.2
7.8
16.08333333
7.916666667
6.3
1
8.5
0
8.5
15.5
7.749831
8.466666
8/12/2011
14.8
9.2
13.98333333
10.01666667
7.2
1
5.7
0
5.7
18.3
4.816146
5.733333
8/13/2011
15.4
8.6
24
0
4.8
1
1.7
0
1.7
22.3
1.447228
1.683333
30
8/14/2011
11.6
12.4
11.76666667
12.23333333
2.6
0
5.2
0
5.2
18.8
4.218805
5.166666
8/15/2011
3.7
20.3
0
24
4.9
0
3.4
0
3.4
20.6
3.08752
3.383333
8/16/2011
11.6
12.4
12.11666667
11.88333333
4.3
1
9.5
1.2
10.7
13.3
10.558531
10.666666
8/17/2011
19.4
4.6
24
0
5.4
1
0.3
0.8
1.1
22.9
1.104096
1.1
8/18/2011
18.7
5.3
18.66666667
5.333333333
3.7
1
9.7
0
9.7
14.3
2.510453
9.716666
8/19/2011
19.4
4.6
24
0
5.3
1
20
0
20
4.1
9.714596
19.95
8/20/2011
19.4
4.6
24
0
4.9
1
18.2
0
18.2
5.9
12.915806
18.15
8/21/2011
12.9
11.1
12.48333333
11.51666667
2.6
1
13.1
0
13.1
10.9
12.039665
13.116666
8/22/2011
14.9
9.1
16.33333333
7.666666667
9
1
9.3
0
9.3
14.7
8.296473
9.316666
8/23/2011
11.5
12.5
10.5
13.5
8.9
0
6.4
0
6.4
17.6
4.809756
6.383333
8/24/2011
9
15
9.033333333
14.96666667
4.1
0
7.2
0
7.2
16.8
6.296518
7.2
8/25/2011
17.6
6.4
17.95
6.05
1.5
1
8.1
0.2
8.3
15.8
6.502306
8.266666
8/26/2011
18.6
5.4
19.2
4.8
3.3
1
12
0
12
12.1
11.401883
11.95
8/27/2011
13.3
10.7
13.81666667
10.18333333
4.3
1
10
0
10
14
7.624583
9.966666
8/28/2011
18.5
5.5
0
24
7.8
0
6.5
0
6.5
17.5
6.11639
6.516666
8/29/2011
23
1
16.13333333
7.866666667
11.2
1
12.4
1.3
13.7
10.3
13.638553
13.683333
8/30/2011
12
12
11.48333333
12.51666667
9.1
0
1.9
0.9
2.8
21.2
1.442583
2.85
8/31/2011
0
24
0
24
6.1
0
1.5
0
1.5
22.6
0
1.45
31
Appendix C: Basic Statistical Results
Cassia Rooms
Mean
Standard Deviation
Mean
Standard Deviation
Mean
Standard Deviation
Mean
Standard Deviation
Mean
Standard Deviation
Mean
Standard Deviation
Room 612
October
November
August
September
December
January
February
Average
Total
Runtime
8.97
8.30
1.93
2.88
1.91
4.63
3.84
4.64
4.90
6.93
2.91
3.61
3.06
8.09
3.44
Duration of
Rented
Vacancy
10.61
13.97
10.69
14.75
13.65
2.68
11.40
5.71
7.03
6.26
8.75
10.06
3.69
6.85
Duration of
Unrented
Vacancy
11.11
12.69
8.47
15.66
20.44
16.00
7.62
8.16
9.46
8.46
9.76
6.99
12.00
8.95
December
January
February
Average
2.11
Room 614
October
November
August
September
Total
Runtime
3.56
1.26
1.76
1.81
0.75
3.93
1.72
3.11
1.50
2.35
3.06
2.22
7.29
2.24
Duration of
Rented
Vacancy
13.67
13.37
0.00
9.01
20.80
9.00
14.78
5.62
8.81
0.00
10.18
5.92
9.77
5.82
Duration of
Unrented
Vacancy
7.44
12.06
8.31
14.19
19.69
16.00
11.57
9.32
10.21
8.81
9.27
7.81
12.00
8.29
32
11.11
13.14
11.52
12.75
Control Rooms
Mean
Standard Deviation
Mean
Standard Deviation
Mean
Standard Deviation
Mean
Standard Deviation
Mean
Standard Deviation
Mean
Standard Deviation
Room 616
October
November
August
September
December
January
February
Average
Total
Runtime
6.00
4.43
1.37
0.92
2.31
2.53
1.90
2.78
3.87
6.34
1.58
1.16
2.51
6.04
1.79
Duration of
Rented
Vacancy
12.91
16.27
13.27
18.88
20.89
22.58
15.70
5.44
6.01
4.38
6.73
5.47
3.23
5.76
Duration of
Unrented
Vacancy
9.06
10.99
7.58
16.44
19.19
22.22
12.41
7.28
10.28
7.51
9.74
8.07
3.59
8.41
August
September
December
January
February
Average
Total
Runtime
4.24
6.40
2.59
5.60
3.60
2.04
2.96
3.92
5.02
4.79
3.70
5.99
4.95
1.56
1.87
Duration of
Rented
Vacancy
17.07
15.54
12.42
16.70
21.89
20.90
14.62
6.77
6.48
5.86
6.27
3.84
5.20
4.61
Duration of
Unrented
Vacancy
14.17
9.45
7.62
13.51
19.06
16.00
7.97
9.81
10.05
7.52
8.83
8.52
12.00
8.28
Room 618
October
November
33
17.21
13.98
17.02
12.54
Appendix D: Correlation Matrices
Room 612
Occupied
Duration
Vacant
Duration
Rented
Duration
Unrented
Duration
Heating
Degree
Days
Rented?
Actual
Runtime
(Cooling)
Vacant
Duration
-1
Rented
Duration
0.48
-0.48
-0.48
0.48
-1
0.10
-0.10
-0.05
0.05
0.44
-0.44
0.90
-0.90
-0.06
Actual
Runtime
(Cooling)
0.15
-0.15
0.38
-0.38
-0.42
0.32
Actual
Runtime
(Heating)
0.20
-0.20
0.05
-0.05
0.17
0.04
-0.12
Unrented
Duration
Heating
Degree
Days
Rented?
Actual
Runtime
(Heating)
Actual
Runtime
Idle
Hours
Actual
Runtime
Idle Hours
Occupied
Runtime
0.23
-0.23
0.38
-0.38
-0.33
0.33
0.91
0.29
-0.23
0.23
-0.38
0.38
0.33
-0.33
-0.91
-0.29
-1
0.33
-0.33
0.48
-0.48
-0.26
0.44
0.81
0.21
0.87
-0.87
Total
Runtime
0.23
-0.23
0.38
-0.38
-0.33
0.33
0.91
0.29
1
-1
34
Occupied
Runtime
0.87
Room 614
Occupied
Duration
Vacant
Duration
Rented
Duration
Unrented
Duration
Heating
Degree
Days
Rented?
Actual
Runtime
(Cooling)
Actual
Runtime
(Heating)
Actual
Runtime
Idle
Hours
Vacant
Duration
-1
Rented
Duration
0.53
-0.53
Unrented
Duration
Heating
Degree
Days
-0.53
0.53
-1
-0.13
0.13
-0.24
0.24
0.51
-0.51
0.90
-0.90
-0.21
0.13
-0.13
0.29
-0.29
-0.35
0.30
0.22
-0.22
0.09
-0.09
0.14
0.10
-0.10
0.27
-0.27
0.28
-0.28
-0.16
0.30
0.67
0.67
-0.26
0.26
-0.28
0.28
0.16
-0.30
-0.67
-0.67
-1
0.28
-0.28
0.36
-0.36
-0.17
0.37
0.76
0.38
0.85
-0.85
0.26
-0.26
0.28
-0.28
-0.16
0.29
0.67
0.67
1
-1
Rented?
Actual
Runtime
(Cooling)
Actual
Runtime
(Heating)
Actual
Runtime
Idle
Hours
Occupied
Runtime
Total
Runtime
35
Occupied
Runtime
0.85
Room 616
Motion
Duration
Vacant
Duration
Rented
Duration
Unrented
Duration
Heating
Degree
Days
Rented?
Actual
Runtime
(Cooling)
Actual
Runtime
(Heating)
Actual
Runtime
Idle
Hours
Vacant
Duration
-1
Rented
Duration
0.92
-0.92
Unrented
Duration
Heating
Degree
Days
-0.92
0.92
-1
-0.24
0.24
-0.22
0.22
0.84
-0.84
0.88
-0.88
-0.23
0.19
-0.19
0.16
-0.16
-0.54
0.14
-0.05
0.05
-0.04
0.04
0.30
-0.06
-0.19
0.16
-0.16
0.13
-0.13
-0.36
0.10
0.86
0.33
-0.16
0.16
-0.13
0.13
0.36
-0.10
-0.86
-0.34
-1
0.49
-0.49
0.44
-0.44
-0.36
0.40
0.79
-0.02
0.75
-0.75
0.16
-0.16
0.13
-0.13
-0.36
0.10
0.86
0.34
1
-1
Rented?
Actual
Runtime
(Cooling)
Actual
Runtime
(Heating)
Actual
Runtime
Idle
Hours
Occupied
Runtime
Total
Runtime
36
Occupied
Runtime
0.75
Room 618
Motion
Duration
Vacant
Duration
Rented
Duration
Unrented
Duration
Heating
Degree
Days
Rented?
Actual
Runtime
(Cooling)
Actual
Runtime
(Heating)
Actual
Runtime
Idle
Hours
Vacant
Duration
-1
Rented
Duration
0.81
-0.81
Unrented
Duration
Heating
Degree
Days
-0.81
0.81
-1
-0.13
0.13
-0.03
0.03
0.72
-0.72
0.89
-0.89
-0.04
0.18
-0.18
0.16
-0.16
-0.32
0.13
-0.11
0.11
-0.05
0.05
0.53
-0.07
-0.32
0.15
-0.15
0.14
-0.14
-0.13
0.11
0.92
0.07
-0.15
0.15
-0.14
0.14
0.13
-0.11
-0.92
-0.07
-1
0.47
-0.47
0.42
-0.42
-0.16
0.36
0.81
-0.02
0.85
-0.85
0.15
-0.15
0.14
-0.14
-0.13
0.11
0.92
0.07
1
-1
Rented?
Actual
Runtime
(Cooling)
Actual
Runtime
(Heating)
Actual
Runtime
Idle
Hours
Occupied
Runtime
Total
Runtime
37
Occupied
Runtime
0.85