Predictive Models for Estimating Metabolic and Physical Workload ...

Predictive Models for Estimating Metabolic Workload

based on Heart Rate and Physical Characteristics

B. Kamalakannan 1, W. Groves 2*, and A. Freivalds 1

1 Industrial Engineering Program, Department of Industrial & Manufacturing Engineering, The

Pennsylvania State University, University Park, PA 16802-5000

2 Industrial Health and Safety Program, Department of Energy and Geo-Environmental

Engineering, The Pennsylvania State University, University Park, PA 16802-5000

* Corresponding Author: Assistant Professor of Industrial Health and Safety, 223 Hosler

Building, Penn State University, University Park, PA 16802-5000, 814-863-1618, 814-865-3248

(FAX), [email protected].

mailto:[email protected]

Journal of SH&E Vol. 4, Num. 1 of 26

AUTHORS

Balaji Kamalakannan, M.S., is currently employed by Algonquin Industries, Guilford,

CT. He holds an M.S. degree in Industrial Engineering from the Pennsylvania State University.

William A. Groves, Ph.D., CSP, CIH, is an assistant professor in the Industrial Health

and Safety program at Pennsylvania State University, University Park. He holds a B.S. in

Chemical Engineering from Case Western Reserve University, and M.P.H. and Ph.D. degrees in

Industrial Health from the University of Michigan. Groves is a member of ASSE and AIHA and

serves on the editorial boards of the Journal of Occupational and Environmental Hygiene

(JOEH) and the Journal of the International Society for Respiratory Protection (JISRP).

Andris Freivalds, Ph.D. is a professor in the department of Industrial and Manufacturing

Engineering at Pennsylvania State University, University Park. He holds degrees in

Bioengineering (Ph.D., M.S.), Computer, Information and Control Engineering (M.S.), and

Science Engineering (B.S.E.) from the University of Michigan. Professor Freivalds initiated the

Human Factors/Ergonomics Engineering program at Penn State and developed a human factors

teaching and research laboratory. He is Fellow of the Ergonomics Society and is on the editorial

boards for the International Journal of Industrial Ergonomics and for Applied Ergonomics.


1. ABSTRACT

Predictive equations were developed to estimate metabolic work rate (MWR) as a

function of heart rate and physical characteristics. Thirteen subjects (5-Female, 8-Male) spanning

a range of age (22-55 yrs) and physical characteristics performed a series of “step” tests in which

oxygen consumption and heart rate were recorded. Three stepping frequencies and two runs were

considered. Physical workload was calculated for each subject based on the step height, stepping

frequencies, and weight with results ranging from 14-84 Watts (W). Corresponding estimates of

MWR based on oxygen consumption ranged from 120-745 W. Predictors considered for

modeling were: heart rate (HR), resting heart rate (RHR), age (A), gender (G), height (H), weight

(W), and body mass index (BMI). Four models were developed and evaluated using linear

regression. The best results were achieved with a model that included predictor variable

interactions and quadratic terms and the results of a single “calibration” step-test conducted prior

to the sampling period to develop a simple linear prediction of workload as a function of heart

rate specific to an individual. Validation through bootstrapping of residuals and Chow Tests

suggest that the model can be generalized for prediction of MWR without the need for collecting

metabolic work data.

Key Words: energy expenditure, work rate, pulse, hear rate, modeling


2. INTRODUCTION

2.1 Workplace Protection Factors (WPFs)

In the Final Rule of the Respiratory Protection Standard, the Occupational Safety and

Health Administration (OSHA) estimates that approximately 3-5 million workers, representing

roughly 20% of all establishments, wear respirators at some time for protection from airborne

contaminants (OSHA, 1988). Given such widespread use it is important to have sufficient

information to characterize respirator performance so that workers can be assured of adequate

protection. However, there is limited data available for evaluating the performance of

respiratory protection under actual workplace conditions. To address this problem, the National

Institute for Occupational Safety and Health (NIOSH) funded this research project to develop a

sampling system to measure contaminant concentrations inside respirators while worn.

Myers et al. (1983) defined workplace protection factor (WPF) as a measure of the actual

protection provided in the workplace under the conditions of that workplace by a properly

functioning respirator when correctly worn and used:

WPF = Co/Ci Eq-1

where Co is ambient contaminant concentration and Ci is the concentration inside the respirator

face piece. Workplace performance of respirators is assessed by determining workplace

protection factors. One of the factors likely to influence the effectiveness of respiratory

protection is the work rate of the person wearing the respirator. Work rate is directly related to

respiration rate and may also be correlated with respirator leakage; however, very little data

exists on measurement of work rate while measuring WPF.


2.2 Heart Rate and Energy Expenditure

Energy expenditure can be defined as the amount of energy required by the body to

perform a particular task. McArdle et al. (1991) defined daily energy expenditure as the sum

total of the basal and resting metabolisms, thermogenic influences (particularly the thermic effect

of food), and energy generated during physical activity. Though various factors affect a person’s

metabolic rate, the greatest influence comes from physical activity. Several classification

systems have been proposed for rating sustained physical activity in terms of its strenuousness.

One recommendation is that work tasks be classified by the ratio of energy required for the task

to the resting energy requirement. One of the systems used is the physical activity ratio, or PAR,

to classify physical activities. Light work for men is defined as that eliciting an oxygen uptake

(or energy expenditure) as great as three times the resting requirement; heavy work is

categorized as that requiring six to eight times the resting metabolism; whereas maximal work is

any task requiring an increase in metabolism to nine times or more above rest. As a frame of

reference, most industrial tasks require less than three times the resting energy expenditure

(McArdle et al.).

Another commonly used method for rating physical activity is measuring energy

expenditure based on heart rate. For every individual, heart rate and oxygen uptake tend to be

linearly related throughout a wide range of aerobic exercises. If this relationship is known, the

exercise heart rate can be used to estimate oxygen uptake (and then to compute energy

expenditure) during similar forms of physical activity. This approach has been used when the

oxygen uptake could not be measured during the actual activity. It has been observed that of all

the physiological variables, heart rate (HR) is the easiest to measure in the field (Acheson, 1980).

The relationship between HR and energy expenditure was shown as early as 1907, when


Benedict reported that changes in pulse rate were correlated with changes in heat production in

any one individual. Bergen and Christensen (1950), and Booyens and Hervey (1960) have also

described the use of hear rate as an estimator of metabolic rate.

Kaudewitz (1998) studied the assessment of a work standard using heart rate monitoring.

The author performed heart rate analysis from data collected from a subject performing his

normal work shift in a hospital. According to the author, heart rate monitoring is an ergonomic

tool that can help assess the appropriateness of a work standard for jobs where energy

expenditure and whole-body fatigue are primary concerns. Based on the results he concluded that

the resting heart rate is critical to the validity of the work capacity calculation and work capacity

can be significantly underestimated or overestimated if the resting heart rate is not accurate. This

study underlines the importance of getting a good measure of the resting heart rate

Bot and Hollander (2000) conducted a study to validate the use of heart rate responses to

estimate oxygen uptake (VO2) during varying non-steady state activities. Dynamic and static

exercises engaging large and small muscles masses were studied in four different experiments. In

the first experiment, 16 subjects performed an interval test on a cycle ergo meter, and 12 subjects

performed a field test consisting of various dynamic leg exercises. Simultaneous heart rate and

VO2 measurements were made. Linear regression analyses were done and the authors concluded

that there is very high correlation between heart rate and VO2 during both the interval test and the

field test.

These studies demonstrate the use of heart rate as a good measure of energy expenditure

and generally confirm the linear relationship between oxygen consumption and heart rate. The

objective of this research project was to identify an optimal protocol for estimating work rates

for individuals wearing respirators based on heart rate data and physical characteristics. Heart


rate was recorded by a multi-channel data-logging unit that is an integral part of a personal

sampling system developed for measuring WPF for gases and vapors. The complete system

consists of a sampling pump, a pressure transducer circuit designed to sense differential pressure

inside the respirator, and a multi-channel data-logging unit for recording the output from the

pressure transducer as well as a transducer for measuring heart rate. A “step-test” was used to

simulate work rates in an actual work environment and heart rate was recorded when the subjects

performed the step test. This heart rate, recorded after the subjects reached a steady state, was

used as a measure of energy expenditure based on the linear relationship between heart rate and

volume of oxygen consumption.

3. METHODS

3.1 Step Tests

Thirteen Subjects (5-Female,8-Male) spanning a range of age (22-55 yr) and physical

characteristics (Table 1) performed step tests at three levels of exertion. Oxygen consumption

and heart rate were recorded using a metabolic monitor and a commercially available heart rate

monitor (Polar Electro Inc., Lake Success, NY). Physical workload (PWL) was calculated based

on the step height (32.5 cm), stepping frequency (5, 10, and 15 steps/min), and body weight.

Metabolic work rate (MWR) was calculated from oxygen consumption (VO2) as determined by

the metabolic monitor. Two replicate runs per subject, for a total of 13 x 3 x 2 = 78 data points,

were conducted during the same day/session after a 30 minute rest period.

The subjects were asked to complete a medical screening questionnaire and signed an

informed consent form after being briefed about the experiment and the procedures involved.


Subjects were then asked to sit in a chair for a approximately 15 minutes and resting heart rate

was recorded with the help of the heart rate monitor. The metabolic monitor mask was donned

by the subjects who then performed the first run which included 3 stepping rates – 5, 10 and 15

steps per minute. The VO2 values were read from a strip-chart recorder and the digital display on

the metabolic monitor. Each stepping rate was performed until the subjects reached a steady state

that took a period of approximately 3 to 5 minutes depending on the age and physical fitness of

the subject. VO2 and heart rate were the variables recorded. At the end of each stepping rate, the

subjects were asked to rate their exertion using Borg’s RPE scale. This value was also recorded.

At the end of each stepping frequency, the subjects were asked to rest on a chair for 2 to 3

minutes to allow them to return back to their resting heart rate. After completion of the first set

of runs, the subjects were given a rest period of 30 minutes. At the end of this rest period, the

procedure was repeated.

3.2 Modeling

Seven variables (heart rate, resting heart rate, age, gender, height, weight, and body mass

index) were used to develop four regression models for predicting work rates (Table 2). Model I

was developed based on the significant variables obtained from stepwise regression of the seven

predictor variables. Predictive equations for Model II were developed based on stepwise

regression of predictor variables, interactions, and quadratic terms. Model III involved a single

calibration step test to estimate a linear relationship between heart rate and work rate for each

individual. Model IV is based on the stepwise regression of the variables obtained from Model II

and III. Models were subsequently validated.


3.2.1 Model Validation

Predictive equations were developed based on the data collected from the 13 subjects.

MINITAB 13.1, was used for developing the regression models and analysis of data. Models

were validated using statistical resampling methods (bootstrapping) and cross-validation tests

(Chow Test). Resampling methods are a class of statistical techniques for drawing inferences

based on the variability present within a dataset. They are typically used to calculate the

confidence intervals and p-values. The common concept underlying all resampling methods is

that variability can be assessed by drawing a large number of samples from the observed data

and then comparing the properties of the observed data to the properties of the resampled

datasets. There are various resampling methods – a bootstrapping technique was employed for

this study. Bootstrap methods are substantially more general than randomization methods, and

involve resampling with replacement, i.e. a value from the original data may occur more than

once in a resampled dataset (Efron 1979, 1983; Kohavi, 1995).

“Regressboot”, a bootstrapping macro in MINITAB was used to validate the models

(Butler, 2003). This macro is used to fit a multiple regression model. The significance of the

parameter for each predictor is computed, along with the overall significance of the regression.

Regressboot computes the p-values by bootstrapping of the residuals. The Chow test was used

for cross-validation of the predictive equations (Chow, 1960). This test determines if a

regression model can be generalized between a training and validation data set. The entire data

is split into two data sets and three separate regressions (complete, training, and validation sets)

test whether the model applies to both subsets. The confidence intervals of the three subsets are

compared and if there is no significant difference between the confidence intervals it is

concluded that the data set can be generalized i.e. the results from the Chow test can be used to


judge how well models developed based on the data collected from the subject population can

also be used to predict metabolic work rate in an industrial population having similar

characteristics.

4. RESULTS

4.1 Models for Predicting Work Rate

Heart rate (HR), resting heart rate (RHR), and the physical characteristics age (A), gender

(G), height (H), weight (W), and body mass index (BMI) were used as the predictor variables.

Data were used to develop four models for correlating heart rate and metabolic work rate

(MWR). A 5% level of significance was chosen as a criterion for statistical significance. A

stepwise linear regression approach was adopted for finding the significant set of variables for

the predictive equation. Models are summarized in Table 2.

4.1.1 Model I

Model I was developed to examine the correlation between work rate and predictor

variables: age, gender, body mass index, height, weight, heart rate and resting heart rate. This

regression model was developed based solely on the seven predictor variables. Interaction terms

of physical characteristics and quadratic terms were not considered. Results are shown in Figure

3 and the following regression equation resulted:

MWR = - 1967 + 8.58 HR + 25.1 HT + 4.50 A – 7.47 RHR + 67.8 G Eq-2


where MWR is metabolic work rate (W), HR is heart rate (bpm), HT is height (in.), A is age (yr),

RHR is resting heart rate (bpm), and G is gender (M=0, F=1). The regression equation was

significant (p<0.05) with an R2 value of 0.797.

4.1.2 Model II

This model included the original seven predictive variables as well as their interactions

and quadratic terms as input variables for predicting MWR. Stepwise regression was used to

select significant variables and a predictive equation was developed:

MWR = - 37614 – 17.9*B2 + 698*B – 0.00170*HR*RHR*HT + 0.571*HR*A +

0.0544*RHR*HT*B + 0.0158*HR*A*B – 8.02*HT2 + 0.778*HR*B*G + 969*HT +

0.0510*WT2 - 0.132*HR*WT*G + 0.00109*HR*WT*HT – 0.00220*RHR*A*WT –

2.83*RHR*B Eq-3

The resulting equation included 14 variables and was significant (p<0.05) with an R2 value of

0.9741.

4.1.3 Model III

Model III was based on a single calibration step test. The results from the first stepping

frequency (10 steps/min) were chosen for the 13 subjects and a slope (S) was calculated based on

the change in heart rate and work rate (ΔHR/MWR). S was then used to predict the work rate for

the remaining stepping frequencies (2 results from the first run and 3 results from the second run)

for each subject. This model considers the effect of performing a single calibration step test in a

workplace. There is no VO2 data and hence the metabolic work rate is calculated through an


indirect method. Metabolic work rate is estimated based on the efficiencies obtained during

laboratory experimentation. The efficiencies of the step test ranged from 7.29 % to 14.64%. The

average efficiency was calculated to be 11%. The physical workload readings were used along

with this overall efficiency to find the metabolic work rate, i.e., MWR = estimated physical work

load / efficiency (0.11). This metabolic work rate was used along with the change in heart rate

readings to estimate S. This value of the slope was then used to predict the metabolic work rate

for the remaining energy expenditure results for each subject:

MWR = S * HR-RHR Eq-4

This resulting regression equation was significant (p<0.05) with an R2 value of 0.886.

4.1.4 Model IV

Model IV is a combination of Models II and III. The slope and predicted work rate calculated

from Model III were used as input variables along with the variables from Model II and a

regression model was developed. A stepwise regression was performed to identify the

significant variables and the following equation resulted:

MWR = - 145 + 0.0249*RHR*PWR + 67.7*A*G*S – 0.172 A*G*RHR – 0.560*PWR +

0.230*A*G*B – 0.101*A2 + 0.0978*A*HT – 0.0288*W*S*PWR Eq-5

where PWR (W) and S (Δ bpm / W) are the predicted work rate and slope from Model III. The

equation was significant (p<0.05) with an R2 value of 0.9764 (Figure 3). A summary of all

modeling results is presented in Table 3.


4.2 Model Validation

The Regressboot Minitab macro fits a multiple regression model and the significance of

the parameter for each predictor is computed, along with the overall significance of the

regression. Regression p-values in these cases should be less than 0.05. In the case of the Chow

test, the null hypothesis is that these models could be generalized to predict metabolic work rate

without the actual collection of metabolic work data. If we obtain a p-value greater than 0.05, the

null hypothesis can be accepted. Validation tests were conducted for Model II and IV (Models I

and III were not validated due to the lower R2 and larger prediction errors). The validation tests

were run and the p-values for prediction of the metabolic work rate obtained. Tables 4 and 5

shows the results of the bootstrap evaluation of Models II and IV. All regression parameters and

the overall regression equations were found to be significant. Cross-Validation was done using

the Chow test. Fifteen runs of the Chow test were completed for each model to estimate the

range of p-values. In all cases, results were well over a p-value of 0.05 indicating that the

models could be generalized.

5. DISCUSSION

Model I is the simplest approach for estimating work rate and performs reasonably well

in terms of the percent of the variability explained. However the model exhibits a significant bias

as demonstrated by the slope of the regression line (Fig. 3a). The results obtained are dependent

on the subject population to a great extent and the results may vary when a different set of

subjects are used for experimentation. In an effort to reduce this bias and for better prediction,

interaction terms and quadratic terms were considered to develop the next Model II. Stepwise

linear regression was conducted and 14 significant variables were identified. The resulting model


had a higher R2 value and reduced errors (Table 3). However, the model is relatively

complicated in terms of the number of variables in the predictive equation and the ability to

generalize well to larger populations is uncertain.

The previous models considered heart rate and physical characteristics of the subjects.

Model III is based on the change in heart rate and a slope (S) calculated based on a single

calibration step test. The regression equations for this model gave R2 values of 0.886 and average

percentage error for predicting the metabolic work rate of 11.06%. Model III is computationally

simple and is likely to be the most robust in predicting work rate since it employs a “calibration”

step test and is not dependent on the characteristics of the 13 subject step-test. However, the

calculated slope (S) is based on an estimate of efficiency which is in turn based on the

characteristics of the step-test. If the characteristics of the calibration test employed do not

accurately reflect the actual work activities of the subject, the resulting model may not give a

good prediction of work rate. Though validation runs indicate that this model can be generalized

to predict metabolic work rate without collection of actual metabolic work data, error levels and

R2 values were superior for Model II.

Model II was developed based on predictor variables and their interactions and Model

III was based on a single calibration step test. To optimize the favorable results from these

models, Model IV was developed as a combination of these two models with the predictor

variables, interactions, and the slope and predicted work rate obtained from Model III as input

variables. Stepwise linear regression was conducted and eight significant variables were

identified. The regression equation based on these significant variables gave an R2 value of 0.976

for metabolic work rate.


Model IV has the best R2 value of all the four models and a low average percentage

error for predicting the metabolic work rate - 0.72%. Though slightly higher than Model II,

Model IV incorporates a calibration step test which eliminates potential bias and dependency on

the subject population shown by Models I and II. Model IV combines the features of Model II

and Model III resulting in a more accurate and less biased estimate of work rate. This approach is

expected to be more robust than Model II as a result of the calibration step test. Validation

techniques performed on Model IV yielded results that indicate that this model can be

generalized to predict metabolic work rate without actual collection of metabolic work data.

6. CONCLUSIONS

The results of this project suggest that work rates can be estimated without collection of

metabolic work data. Physical characteristics such as age, gender, height, and weight can be

used to improve the accuracy of predicted work rates. Model I is the simplest approach to

estimating MWR and performs reasonably well in terms of the portion of the variability

explained (~80%) and the percent error. However, the model exhibits a significant bias as

demonstrated by the slope of the regression line (Fig. 3a). Model II yields excellent, unbiased

results that explain 97% of the variability in MWR with the lowest average absolute % error.

However, the model contains 14 parameters and should be applied with caution. Models I and II

do not require the “calibration” step-test and would be easier to implement in a field protocol;

however, it is assumed that the subjects used to develop the models fully represent the industrial

workplace population. Model III is computationally simple and is likely to be the most robust in

predicting MWR for individuals since it employs a “calibration” step-test and is not dependent

on the characteristics of the 13 subject test-set. Model IV combines the features of Models II and


III resulting in an accurate, unbiased estimate of MWR (Fig 3b). This approach is expected to be

more robust than Model II as a result of including the “calibration” step test.

Directions for future research include an examination of the performance of the

predictive models and field protocols for their implementation using a larger industrial

population and an evaluation of model applicability for subjects who are in good physical shape

versus subjects who do not exercise regularly.

ACKNOWLEDGEMENTS

Support by the National Institute for Occupational Safety and Health (NIOSH) is

gratefully acknowledged (SERCA 5K01OH00177). This project was approved by the

Pennsylvania State University Institutional Review Board (IRB Approval # 15194).


REFERENCES

Acheson, K. J., Campbell, I. T., Edholm, O. G., Miller, D. S., and Stock, M. J., 1980. The

measurement of daily energy expenditures—an evaluation of some techniques. The

American Journal of Clinical Nutrition, 33:1155-1164.

Bergren, G., and Christensen, E. H., 1950, Hear rate and body temperature as indices of

metabolic rate during work, Arbeitsphysiologie, 14:255.

Booyens, J., and Hervey, G. R., 1960, The pulse rate as a means of measuring metabolic rate in

man, Can. J. Biochem Physiol, 38:1301-9.

Bot. S, D, M., Hollander, A. P., 2000, The relationship between heart rate and oxygen uptake

during non-steady state exercise, Ergonomics, Vol. 43, pp.1578-1592.

Butler, A., Rothery, P., and Roy, D., 2003, Minitab macros for resampling methods, Teaching

Statistics, 25:22.

G. C. Chow, 1960, Tests of Equality Between Sets of Coefficients in Two Linear Regressions,

Econometrica, 28, 591-605.

Davison, A.C., Hinkley, D.V., 1997, Introduction, Bootstrap methods and their applications,

Cambridge University Press Ch 1, pp. 1-10.


Efron, B., 1979, Bootstrap methods: Another look at the jackknife, Annals of Statistics, Vol. 7,

pp. 1-26.

Efron, B., 1983, Estimating the error rate of a prediction rule: improvement on cross-validation,

Journal of the American Statistical Association, Vol. 78 (382) pp.316-330.

Kaudewitz, H. R., 1998, Work Standard Assessment Using Heart Rate Monitoring, IIE

Solutions, pp. 37-43.

Kohavi, R., 1995, A Study of Cross-Validation and Bootstrap for Accuracy Estimation and

Model Selection, International Joint Conference on Artificial Intelligence (IJCAI).

McArdle, W. D., Katch, F. I, Katch V.L, 1991 Exercise Physiology, Fourth Edition, Williams &

Wilkins.

Myers WR, Lenhart SW, Campbell K, Provost G, (1983), Letter to the Editor, Am. Ind. Hyg.

Assoc. J., 44:B25-B26.

The Occupational Safety and Health Administration (OSHA), 1988, "Respiratory Protection;

Final Rule". Federal Register 63:5 (8 January, 1998). pp. 1152-1300.


Figure 1. Personal sampling system for measuring workplace protection factors (WPFs) - a) respirator, b) heart rate transducer, c) data logger/sampling system, and d) sampling lines for measuring contaminant concentrations and in-mask pressure.


Figure 2. Subject performs step-test while oxygen consumption is monitored using the metabolic monitor.


FIGURE 3. Predicted MWR versus actual results for a) Model I, and b) Model IV

a) b)

Figure 3. Predicted MWR versus actual results for a) Model I, and b) Model IV


Table 1. Subject’s Physical Characteristics

SUBJECT AGE (years) Gender HEIGHT

(inches) WEIGHT

(lb) BMI

A 41 Male 76.0 203 25

B 55 Male 72.5 193 26

C 32 Male 69.0 127 19

D 22 Male 70.5 135 20

E 39 Female 65.0 143 24

F 52 Male 73.0 170 22

G 45 Male 74.0 187 24

H 33 Female 64.0 117 20

I 29 Male 72.5 234 31

J 50 Male 70.0 179 26

K 22 Female 68.5 168 25

L 22 Female 67.5 132 20

M 26 Female 65.5 154 25

Mean (SD) 36 (12) 69.8 (3.7) 165 (34) 23.6 (3.4)


Table 2. Model Descriptions

Model Description

I Stepwise regression of seven predictor variables vs. MWR

II Stepwise regression of predictor variables, interactions, and quadratic terms vs. MWR

III “Calibration” step test to establish relationship between heart rate and MWR for each individual

IV Models II and III combined, stepwise regression of variables vs. MWR


Table 3. Summary of Modeling Results for Prediction of MWR

Model Significant Terms R2 Average % Error Average

Absolute % Error

I 5 0.797 2.77 16.46

II 14 0.974 0.42 5.99

III 1 0.886 11.06 15.36

IV 8 0.976 0.72 6.96


Table 4. Bootstrap Results for Model II – Metabolic Work Rate

Row coef SE coef F normal p ran p 1 -17.936 1.622 122.340 0.0000000 0.0009990 2 698.004 60.597 132.683 0.0000000 0.0009990 3 -0.002 0.000 31.678 0.0000005 0.0009990 4 0.571 0.047 146.396 0.0000000 0.0009990 5 0.054 0.011 26.716 0.0000027 0.0009990 6 -0.016 0.002 70.487 0.0000000 0.0009990 7 -8.021 1.124 50.952 0.0000000 0.0009990 8 0.778 0.152 26.131 0.0000033 0.0009990 9 968.799 145.267 44.477 0.0000000 0.0009990 10 0.051 0.009 31.027 0.0000006 0.0009990 11 -0.132 0.023 32.086 0.0000004 0.0009990 12 0.001 0.000 94.460 0.0000000 0.0009990 13 -0.002 0.000 93.086 0.0000000 0.0009990 14 -2.827 0.699 16.361 0.0001473 0.0009990

Overall F-ratio for regression 166.24 P-value using normality 0.0000 P-value using randomization 0.0010

Table 5. Bootstrap Results for Model IV

Row coef SE coef F normal p ran p 1 0.0249 0.0023 114.955 0.0000000 0.0009990 2 67.7477 12.3878 29.909 0.0000011 0.0009990 3 -0.1724 0.0456 14.297 0.0003867 0.0029970 4 -0.5599 0.1386 16.310 0.0001682 0.0009990 5 0.2296 0.0952 5.820 0.0192113 0.0229770 6 -0.1008 0.0295 11.640 0.0012167 0.0009990 7 0.0978 0.0310 9.990 0.0025589 0.0039960 8 -0.0288 0.0065 19.351 0.0000504 0.0009990

Overall F-ratio for regression 284.47 P-value using normality 0.0000 P-value using randomization 0.0010

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