can the usage and experimentation with illicit drugs and...

Can the usage and experimentation with illicit drugs and cigarettes explain the age variances with the usage of Cannabis?

QUME 436 - ECONOMETRICS

Prepared for Dr. Daniel Simons

TABLE OF CONTENTS

Executive Summary.................................................................................................................................................................................. 2

Introduction................................................................................................................................................................................................. 2

Purpose..................................................................................................................................................................................................... 2

Interest...................................................................................................................................................................................................... 2

Literature Review...................................................................................................................................................................................... 3

Specification of the Model......................................................................................................................................................................6

Dependent Variable.............................................................................................................................................................................6

INdependent Variables............................................................................................................................................................................7

B1 - Age at which started smoking cigarettes...........................................................................................................................7

B2 - Age at which tried/used cocaine or crack.........................................................................................................................7

B3 - Age at which tried/used MDMA, Ecstasy, Molly, etc.....................................................................................................8

B4 - Sex....................................................................................................................................................................................................... 9

B5 - Marital Status.................................................................................................................................................................................9

Data............................................................................................................................................................................................................... 10

Initial Regression.................................................................................................................................................................................... 11

Estimation............................................................................................................................................................................................. 11

Interpretation......................................................................................................................................................................................11

Data Analysis............................................................................................................................................................................................. 13

Testing for Violations of Classical Assumptions........................................................................................................................15

Multicollinearity.................................................................................................................................................................................15

Heteroskedasticity............................................................................................................................................................................ 16

Fixing Heterskedasticity.................................................................................................................................................................17

Serial Correlation...............................................................................................................................................................................18

Final Regression...................................................................................................................................................................................... 20

Conclusion.................................................................................................................................................................................................. 20

Recommendations for Further Research.....................................................................................................................................20

References....................................................................................................................................................................................................... 22

Appendices...................................................................................................................................................................................................... 23

Initial Regression...............................................................................................................................................................................23

Descriptive Statistics........................................................................................................................................................................23

Multicollinearity.................................................................................................................................................................................24

Heteroskedasticity............................................................................................................................................................................ 26

Serial (Auto) Correlation................................................................................................................................................................29

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EXECUTIVE SUMMARY

The research conducted for this report is based on finding evidence that concludes if consumption

of cannabis in teenage years can be linked to the usage of cigarettes and other illicit drugs.

Variables that were chosen to test this theory were the ages at which started smoking cannabis,

gender, marital status, ages at which started smoking cigarettes, ages at which tried/used cocaine

or crack, ages at which tried/used MDMA, Ecstasy, Molly, etc. The purpose of this paper is to

provide regression based analysis calculating the significance of variables and how they have an

effect on the age at which one first tries cannabis and importantly at what stage in life one is trying

this drug.

INTRODUCTION

PURPOSE

The purpose of this study is to determine if the age at which you try drugs like ecstasy, MDMA,

“Molly,” Cocaine, Crack contributes to the age at which one first tries cannabis. Due to popular

belief that Cannabis is a gateway drug, interest arose in testing the relationship between the age

one starts consuming cannabis and other factors such as: gender, marital status as well as the age

that one starts using cigarettes and illicit drugs. It is assumed that people will try cannabis as one of

their first drugs and later on in life will experiment with other illicit drugs. The purpose of this

research study is to see if the age at which people try cocaine or ecstasy, smoking cigarettes given

their gender and marital status can explain the age at which one first smokes cannabis.

INTEREST

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The main interest of this topic came by the amount of drug activity that occurs in and around

people at bars and clubs, in addition to exposure through education, work and volunteering. Due to

the common statement that, “cannabis is a gateway drug” it was felt that a regression analysis was

needed to test a similar theory that would be an engaging and educating topic. In the beginning

stages of research and data collection other variables including: alcohol, interest in drugs, and

employment income also could have been contributing factors to the age one first tries cannabis. As

the data collection proceeded, it became apparent that unfortunately the information involved

regarding certain variables was not easily accessible or available. Given what was available in

proper context, a regression analysis was developed and this report will discuss and interpret the

findings.

LITERATURE REVIEW

The first article was analyzed was from google scholar (VIU access). The article, “Reassessing the

cannabis gateway effect,” aims to show the strong association between cannabis use and the

initiation of using hard drugs. The estimates from this document were found from the US household

surveys of drug use which took place between 1982 and 1994. The ages conducted for this analysis

were from zero to twenty-two years old. They designed a model based of three parts which include:

“(1) individuals have a non-specific random propensity to use drugs that is normally distributed in

the population; (2) this propensity is correlated with the risk of having an opportunity to use drugs

and with the probability of using them given an opportunity, and (3) neither use nor opportunity to

use cannabis is associated with hard drug initiation after conditioning on drug use propensity.” In

conclusion to their methodology, “do not disapprove, demonstrates that each of the phenomena

that appear to support such an effect,” (Morral, A. R., McCaffrey, D. F., & Paddock, S. M. 2002, p.

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1503). The authors also proceed to say that smoking cannabis may increase the risk to some youth

to try illicit drugs or decrease the risk for others, not declaring a solid conclusion if cannabis is a

gateway drug or not.

The second article selected for review was “Cannabis Use & Other Illicit Drug Use: Testing the

Cannabis Gateway Hypothesis,” was developed from 3 authors, Ferguson D., Boden J., and Harwood

L., who also used a regression analysis to answer their research question using the following

formula: Yn = Bo + B1Xn + Ui +Et,, where Ui represents “non-observed systematic factors.” Looking at

the drug usage between cannabis, cocaine, methamphetamines, and heroin with some of the other

variables assessed include: socio-economic background, other drug dependence and abuse (and the

symptoms there of), drug diversity, family functioning and gender. Using their regression and tables

of frequency the authors were able to determine that cannabis users over the age of twenty five

represented 82% of those who had tried other drugs, in this case, MDMA and 20% was represented

by those who had done cocaine. The peak usage of cannabis happens in adolescence, and then

started to rapidly decline. The final conclusion is that those who had smoked cannabis had a

relation twenty times higher to other illicit drugs than to those who have never consumed cannabis

before.

The third reviews article, “Predictors of Cannabis Use in adolescents before & after Licit Drug Use:

Examination of the Gateway Hypothesis” was able to prove and test that from a sample of males

ages ten to twelve years old observed over twenty two years, compared on thirty five variables,

that only twenty eight, which is 22% did not experiment further with other drugs determining

cannabis was not a gateway for them. These subjects were observed by many doctors who

collectively used tables to demonstrate patterns, ANOVA tables, means, standard deviations,

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correlations, as well as z and p-values. The findings done by these doctors was something that

ideally this report would have been able to determine, however any data collected could have

produced a much different result given the extensive research and careful watching these following

doctors devoted to this experiment for twenty-two years.

After examining other researcher’s studies on cannabis and illicit drugs, current interest then lied

between the gender and the marital status and what type of relationships have already been

discovered. Even though this article used no data or formulas to prove a hypothesis, there were

many key points of significance through interviewing young teens from the ages of thirteen through

eighteen from two British Columbian communities in 2005 & 2006. The largest goal through the

series of interviews was situating descriptions of cannabis usage within social context of drug usage,

why these teens used, and how they were able to obtain. Throughout the research the study

proved reasons for smoking cannabis to be unsuccessful, however it was found that smoking can

provide a connection to adult identities because it is viewed as more masculine. In addition to being

more masculine, it was very apparent that those who smoke are seen as risk takers. There appeared

to be more gender dominance on this subject and that most males thought it was weird for females

to smoke cannabis.

Lastly, the connection between marital status and drug usage seemed significant enough to explore

findings that other researchers have studied and written about. An article by Robert Kaestner, “The

Effects of Cocaine & Cannabis use on Marriage & Marital Stability” explores what drug use can do to

a marriage. From empirical analysis, using many probability tables, calculating the estimates of the

effects of drug usage, and by using a “Flexible” proportional hazards model, using age at first use as

a dummy variable, Kaestner was able to come to the conclusion that for non-black adults that

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cocaine and cannabis usage lead to a significant probability of marriage dissolution. The author’s

consensus was that people may choose to marry just to experience self-gains, in this case by having

a partner. Ways one can gain when married can include the following: more wages, future earnings,

and power. However, due to the usage of drugs, in this case cannabis and cocaine indicated many

signs towards marriage dissolution. The largest dissolution factors including: poor health, leading to

more unattractive partners, lack of intellectual ability all pointed towards higher divorce rates.

Although there were no actual answers of how the use of these drugs could contribute to one

another, these findings to suggest that drug users will most likely be single as marriages within

users are not lasting. As this ties into this current research, that the theory that married people will

have a significant difference in age over single people when it comes to the age one first smokes

cannabis.

SPECIFICATION OF THE MODEL

DEPENDENT VARIABLE

Definition:

This regressions dependent variable (Y) is the age that one first tries cannabis. When it comes to a

drug like cannabis, there are quite a few different ways that someone can use it other than just

smoking the product. From this point forward, any mention to the usage or experimentation with

cannabis will include any possible way to consume the product. The refined data bases the age of

those who first try cannabis to range from the age nine to the age thirty-five.

Function:

For the analysis of this regression it is believed that the gender, marital status, age at which started

smoking cigarettes as well as, cocaine, crack, MDMA, Ecstasy, and Molly will provide a conclusion if

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the age at which you first consumed cannabis can be explained by other drugs and cigarettes that

have been tried.

INDEPENDENT VARIABLES

B1 - AGE AT WHICH STARTED SMOKING CIGARETTES

Definition

This independent variable represents the age one first smoked a cigarette, the refined data gives a

range within the ages of five to twenty-four years old.

Theory & Expectations

The theory behind this variable is that the earlier teenagers start smoking cigarettes, the earlier

they will try or experiment with the form of smoking other things. The main purpose of this

regression is to test if the age at which cigarettes were first smoked has an effect on the age that

cannabis was tried. It is a belief that the step before smoking cannabis will be smoking cigarettes

due to getting accustomed to smoking and inhaling a product, therefore will have a positive

relationship to trying cannabis. It is expected that the relationship between the ages of first

smoking cigarettes will have a large significance and a strong relationship to the age at which one

tries cannabis.

B2 - AGE AT WHICH TRIED/USED COCAINE OR CRACK

Definition

This variable represents the age at which one first tried cocaine or crack. For the purpose of this

report, from here on, this variable will only be referred to as “cocaine.” The refined data for this

variable provided an age range in this category from the age of twelve to forty years old.


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The theory for this variable is that the people who are likely to try/use cocaine will be a majority of

young-adults. This theory arose as cocaine is a more powerful and intimidating drug, compared to

cannabis, which can be considered as generally harder to obtain especially as a teenager due to cost

to acquire and having to get connected with a source. It is to be expected that a great majority of

people who have tried cocaine will have a positive relationship to the age at which one tries

cannabis. It is predicted that the relationship will be significant, but not quite as significant as the

relationship to smoking cigarettes.

B3 - AGE AT WHICH TRIED/USED MDMA, ECSTASY, MOLLY, ETC.

Definition

This variable represents the age at which one first tried a drug known as ecstasy, MDMA (which

stands for Methylenedioxymethamphetamine), molly, etc. As per refined data, this variable has a

provided age range from the ages of twelve to forty-eight years old. For the purpose of this report,

this will solely be referred to as “ecstasy.”


It is believed that the correlation between MDMA, ecstasy, and molly will be highly correlated to

trying cannabis. It is also believed that ecstasy, also used in the forms of MDMA and “Molly,” will

generally follow cannabis in a timeline of experimentation and then could potentially lead to

experimentation with cocaine. It is also commonly known that this strain of drug is gaining its

popularity among those who party, which may be contributing to a more broadened range of those

who have tried the product in comparison to some of the other variables.

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B4 - SEX

Definition

Gender was chosen as one of two dummy variables in this regression. If the drug user is male it shall

be represented as a one and if drug user is anything otherwise it will be represented as zero among

the data.


It is expected that gender will have an impact on the usage of cannabis. It is assumed that males will

be more commonly influenced or peer-pressured to try smoking cannabis, sooner than females

mainly because of the trend that, males can mainly be more easily influenced than females.

B5 - MARITAL STATUS

Definition

Marital status is the second, and last, dummy variable for this regression. Someone whom is

married, which includes not only legally married, but those also married by common-law

relationship and shall be represented as a value of one. Anyone else otherwise including: single,

divorced, separated, and widowed will be represented by the value of zero.


It is assumed that users of the more illicit drugs and more serious drugs will be users whom are

older and will be single, opposed to those who tried any of the listed drugs at younger ages and that

are now in a long term, committed relationships. The expectation is for there to be a relationship to

those of older ages to drug use while being single, because single people usually have more

freedom than those who are in long term committed relationships. The expectation is also due to

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the common knowledge that some single people feel lonelier without a partner and choose to

party, explore, and experiment more frequently.

DATA

For this regression, it was chosen to use cross-sectional data as the regression is mainly based on

ages of those who experimented with different drugs. The data was received from the survey

“Canadian Alcohol and Drug Use Monitoring Survey (CADUMS)” most recently from 2012, as it was

the closest available survey to today’s date. The survey presented a large variety of drugs including

pharmaceutical drugs, illicit drugs, and alcohol as well as many different demographic, socio-

economic, and geographic situations. This survey was selected and found through CHASS Microdata

Analysis and Subsetting with SDA Faculty of Arts & Sciences, courtesy through the University of

Toronto.

For this regression, the selected independent variables were chosen due to the fact that they are

used more commonly with “partying” with the exception to cigarettes. Through consideration, the

choice to include cigarettes in this analysis arose due to the fact that smoking cigarettes may create

a strong linkage to the desire of wanting to smoke cannabis. The statistical information of the

selected the variable of interest, when produced, originally included eleven thousand and ninety

one samples, which were then refined and eliminated reducing the data set to one hundred and

sixty three samples. The data had to be reduced and eliminated due to people who refused to

answer the question or left their answer blank. In doing so each variable was sorted in ascending

order and any invalid or null responses were removed for each variable. It is believed that this

sample size is a decent sample size; however, it would have been preferred to have a larger sample

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size to enhance the accuracy of this regression which was unobtainable due to the answers from

the survey.

In the initial stages of research, it was concluded to test the argument that alcohol could be

considered a gateway to experimentation with drugs, but then after further analysis came to the

realization that it was not an appropriate explanatory variable to base this regression on due to the

lack of correlation within the independent variables. Originally, at the beginning stages of research,

it was attempted to include income to test if there was a linkage to trying drugs dependent on how

much money one made, yet there was no current surveys that could produce all of the following

information. Thus, more recent surveys were browsed which lead to the current hypothesis that the

usage of cannabis could be explained by the ages at which people first try other drugs and smoking

cigarettes.

INITIAL REGRESSION

ESTIMATION

AgeCannabis= B0 + B1AgeSmoking +B2AgeCocaine + B3AgeEcstasy + B4Sex + B5Marital + E

INTERPRETATION

AgeCannabis= 3.5953 + 0.3868AgeSmoking + 0.3269AgeCocaine – 0.0274AgeEcstasy + 0.6103Sex +

0.4449Marital

B0: Is the constant of the equation. In the regression the value of 3.5953 represents the age one first

smokes cannabis if all other independent variables remain at zero. The intercept has been declared

not meaningful due to the fact that the age of 3.59 does not fall within the range of this data set.

B2: Cigarettes coefficient holds a value of 0.3868. Holding all other independent variables constant,

for every year increase at which the age that one first smoked a cigarette the age at which they will

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smoke cannabis will increase by 0.3868 per year of age. The original expectation was that the

sample or people would smoke cigarettes prior to smoking cannabis, whereas after interpreting the

data this theory was determined to be false. According to this regression, one will smoke cannabis

before they will try smoking cigarettes.

B2: The coefficient for cocaine is 0.3269. When all other independent variables are held constant,

for every year increase at which the age that one first used cocaine, the age at which they will

smoke cannabis will increase by 0.3269 per year of age. This initial data coincides with the

expectation that the age at which first tries cannabis could be explained by the age at which one

first tries cocaine.

B3: The coefficient for ecstasy is negative 0.0274. When all other independent variables are held

constant, for every year increase at which the age that one first tried ecstasy, the age at which they

will try cannabis will decrease by 0.0274 per year of age. This refined data coincides with the

expectation that trying ecstasy explains the age at which one tries cannabis, but almost is

considered realistic as when all other variables are held constant the age will be lower than that of

the constant, which is outside of the data range.

B4: The coefficient for sex is 0.6103. This demonstrates the difference between men and women

who smoke cannabis. Therefore, when all other independent variables are held constant, males will

try cannabis 0.6103 of a year sooner than females. This raw data also coincides with the

expectations as it was assumed that males will be more influenced to try cannabis before females

do.

B5: The coefficient for the marital status is 0.4449. When all other independent variables are held

constant, then the age at which someone first tries cannabis will increase by 0.4449 if you are

married. This refined data coincides with the assumption, to an extent, that the samples would first

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try cannabis later in their life if they were married. With everything in consideration however, it was

assumed that the coefficient would be much more significant and be demonstrated with a larger

value than 45% of a year for those who are married versus those who are single.

DATA ANALYSIS

The initial regression for this data, which is located in the Appendices, provided many significant

pieces of information pertaining to our regression. This included the following: R2, adjusted R2, P-

values, T and F statistics, and the correlation matrix.

To begin with the analysis the first thing examined was the R2. The R2 is otherwise referred to as the

coefficient of determination. It has been educated that R2 is the variation in the dependent variable

that can be explained by the variation of the independent variable. For the data that had been

selected, the calculated value of .3604 is interpreted as 36% of the variation of people who have

tried smoking cannabis can be explained by the independent variables. The range for R2 must lie

between the values of zero and one. Ideally, it was expected that this value would be closer to one

to explain the theory that the independent variables highly explain the age at which one first tries

cannabis. Given that, it has been learned that in a multiple regression equation one must adjust the

R2 due to having more than one independent variable; this is called adjusting for the degrees of

freedom. Moving forward, next thing assessed was the adjusted R2, for this regression, the

calculated adjusted R2 is 0.3400 which indicates that actually 34% of those who try smoking

cannabis can be explained by the independent variables.

The P-value for the regression demonstrates three variables which held values that were less than

five percent, which is an indicator that they are significant to this regression. The two that were

more than five percent in relation to the significance level happened to be the dummy variables.

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Thus with this information and knowledge it is determined that the dummy variables do not hold

significance in this regression.

If there was a hypothesis test conducted relating to the P-value, the following could be concluded:

Hypothesis Test P-values

Ho: B1 = 0 Ho: B2 = 0 Ho:B3 = 0 Ho:B4 = 0 Ho:B5 = 0

Ha: B1 ≠ 0 Ha: B2 ≠

0

Ha:B3 ≠

0

Ha:B4 ≠

0

Ha:B5 ≠

0

For the coefficients: B1, B2 and B3, the null hypothesis will be rejected which indicates that there is a

statistically significant relation. For B4 and B5, there will be failure to reject the null, otherwise

accepting the null hypothesis, determining that there is no statistically significant relationship.

Following the P-value test, the next step was to evaluate the T-Statistics from the initial regression

at the five percent significance level which produced a critical value of -/+1.96 with a sample size of

one hundred and sixty three. The test indicated for cocaine, holding a value of 5.26, and smoking,

holding a value of 5.09 we fail to reject the Null Hypothesis indicating they are the only variables

that are statistically insignificant. The remainder of the variables all fell within the acceptance zone

indicating that due to the associated t-statistic they indicate to accept the null hypothesis

concluding there is no significant relationship.

The correlation matrix, located in the appendices, provides a lot of information regarding the

relationship between each of the variables. Firstly, the relationships were examined to determine

which were non-existent or insignificant; these findings were determined by any value that was

negative. In this regression, the variables which lacked relationship are the connection between

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marital status compared to ecstasy, cocaine, and sex. The highest relationship found was between

ecstasy and cocaine that held a value of 0.59 or 59%. The lowest relationship was between the

variables cocaine and sex calculated at 0.0099 or at a mere 1%.

TESTING FOR VIOLATIONS OF CLASSICAL ASSUMPTIONS

MULTICOLLINEARITY

A problem with multicollinearity occurs when any of the independent variables are highly

correlated, thus the first step in testing for violations of the classical assumptions was to test if this

regression had a problem with multicollinearity.

Firstly, all the independent variables were ran using each X as the dependent variable against one

another using the program E-views. The next step was to proceed to examine all the regressions

created and evaluate the R2. It is known that if the R2 is greater than 0.80 than multicollinearity is

most likely going to be a problem. In this regression the variable results showed the highest R2 to be

0.476 which provides strong enough evidence under the benchmark of 0.80 to conclude that

multicollinearity is not a problem.

After analyzing the R2, the next step was to continue on with that given information and to calculate

as well as analyze the Variance Inflation Factors (VIF). The VIF is calculated by taking 1 and dividing

it by 1-R2, for each of the variables among others. In order to demonstrate that there is not a

problem with multicollinearity, the VIF should be less than or equal to five. Based on the calculated

values, which can be found in the appendices, the highest VIF was cocaine and had a value of 1.909.

The VIF, R2 , and the correlation matrix results all indicate that this regression does not have a

problem with multicollinearity.

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HETEROSKEDASTICITY

According to Hill, Griffiths, & Lim (2011), “Heteroskedasticity is often encountered when using

cross-sectional data,” ( p. 301). As the data for this regression is cross-sectional data, it became

apparent that there was most likely going to be a problem with heteroskedasticity for this data and

regression analysis. “The least squares estimator is still a linear and unbiased estimator, but is no

longer best. There is another estimator with a smaller variance,” (Hill, R. C, Griffiths, W. E., & Lim, G.

2011, p. 302) and when this occurs, tests may be misleading. In the search to determine if

heteroskedasticity was a problem, three different tests were performed, which included: The White

test, the Breusch-Pagan-Godfrey test, Harvey Test, and the Gleijer Test.

White test

Firstly, the residual diagnostic of the White test was performed using cross terms. The results of this

test provided a Chi-square value of 19.30 and a p-value of .3735 when interpreted concludes that

the p-value is greater than five percent which indicates it is significant however; according to the

Chi-square test at a critical value of 3.84 the data falls in the rejection zone. Due to the

contradictory results that had been provided, it has been determined that the validity of this test,

three others should be performed.

Breusch-Pagan-Godfrey Test

Upon running the Breusch-Pagan-Godfrey test for heteroskedasticity obtained a Chi-Squared value

of 11.54 and a P-value of .0416. Using the same Chi-squared test as used for the White test, it can

be confirmed that this time both of these values also fall within the rejection zone indicating a

problem with heteroskedasticity.

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Harvey Test

Thirdly, the next test performed was the Harvey Test. The results from this test demonstrated that

there was a Chi-squared value of 38.19 and a P-value of 0. Thus providing a second indicator that

their regression had a problem with heteroskedasticity.

Glejser Test

Lastly, the final test performed was the Glejser test. The results from this test were the same as the

previous two, indicating that with a Chi-Squared value of 35.80 and a p-value of zero that this regression

did in fact have a problem with heteroskedasticity. This indicates that there is an incorrect standard

error which proves all the tests to be unreliable.

FIXING HETERSKEDASTICITY

Once it was determined that heteroskedasticity was a problem, before moving forward the value of the

standard errors had to be corrected for the validity of this regression. The first step towards trying to fix

the issue of heteroskedasticity lies within detecting the nature of the problem. The nature of the

problem is determined by the coefficient with the highest t-statistic value. As the results from the White

test determined to be inconclusive, the test that was examined when determining the nature of the

problem was the Breusch-Pagan-Godfrey test. Looking at this test, reference in the appendices, the

variable cocaine had the highest t-statistic value at 2.48.

Knowing the nature of the problem, the regression was weighted in e-views by cocaine, as it was the

nature of the problem. The weight was applied using: inverse standard deviation, standard deviation,

inverse variance, and variance and none of these tests were able to solve the problem of

heteroskedasticity.

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The next step after trying to fix the issue manually, was to ask e-views to auto fix using the White test

with corrected errors. After the auto fix, the t-statistics were still outside of the range concluding that e-

views was unable to solve the problem of heteroskedasticity.

When dealing with problems of heteroskedasticity there are a few final options:

1. Increase Sample Size – as the data was refined down to 163 observations due to rejected

answers or sections left blank there was no option to increase the sample size.

2. Drop a Variable – even though only two of the variables, which are cocaine and smoking, hold

lots of significance, it did not seem like a logical choice to drop a variable in this regression.

3. Do nothing – leaving the final option to carry on with the final test of classical assumption

violation.

Choosing to do nothing as the problem with heteroskedasticity could not be fully resolved, the

regression used moving forward, will be that of the White Heteroskedasticity Test with Corrected Errors.

SERIAL CORRELATION

DURBAN WATSON TEST

Upon testing for serial correlation, otherwise known as auto correlation, the first step is to determine if

there is first order serial correlation. This can be determined by using the Durban Watson test, using the

Durban Watson statistic. The initial Durban Watson statistic, moving forward after the tests for

heteroskedasticity, was 2.085. At the 5% significance level, using n=150 for the distribution, as it was the

closest to 163 that could be provided, the value falls within the fail to reject zone indicating that this

regression has no first order serial correlation.

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CORRELOGRAM

After determining that first order correlation did not appear to be a problem, there then needed to be

more tests performed to determine other orders of serial correlation. By using the correlogram, it

allowed for visual inspection to determine where there was the potential for other orders of serial

correlation. By looking at the correlogram, the first three lags indicated that no serial correlation existed,

however the lags four through six indicated that there could be serial correlation. Using this information

from visual inspection, the violations could then proceed to run an LM test with six lags. Double

checking the results as findings were carried forward, it was felt it was important to look at the Durban

Watson statistic again. According to the correlogram it can be concluded that the statistic still fell in the

fail to reject zone.

LM TEST

The final test performed to conclude if serial correlation was a problem for this regression was to run an

LM test. According to the results of the LM test, it could be determined that both residuals four and five

could potentially have serial correlation as the t-statistic for these values were outside of the critical

value of +/- 1.96. In order to fix this problem, the equation had to be re-estimated using auto regressors

(AR), so (AR)4 and (AR) 5 were added into the equation.

Upon completion of re-running the equation with the auto regressors, all t-statistics for co-efficient,

residuals and ARs fell within the critical value zone, indicating that any problem of serial correlation had

now been solved. In order to finally verify these results, the Durban Watson statistic was examined one

last and final time with a produced value of 1.98 still falling in the fail to reject zone indicating that this

regression did not have a problem with serial correlation, thus producing a final equation.

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FINAL REGRESSION

Upon completing, and in some cases fixing, the tests for violations of the classical assumptions, using e-

views the regression was adjusted as per Ordinary Least Squares (OLS) rulings and guidelines. Due to the

fact that there were errors that had to be resolved as the progressions moved forward from the initial

regressions, the coefficients associated to the independent variables changed which then produced the

final equation of this regression:

AgeCannabis = 3.8786 + .3983AgeSmoking + 0.2829AgeCocaine – 0.0075AgeEcstasy

+0.6454Sex + 0.4908Marital

CONCLUSION

In conclusion, the age at which one smokes cigarettes, the age at which one first tries cocaine, one’s

gender and marital status will all increase the age at which they first try cannabis; concluding that those

independent variables explain the dependent variable. The age at which one tries ecstasy is the only

variable that decreases the age that one first tries cannabis. Given that the constant is so small, all

calculations and interpretation of the regression indicates that one will smoke cannabis in life before

trying or experimenting with any other drugs, which could lead to prove that the belief that cannabis is a

gateway drug, to be true.

RECOMMENDATIONS FOR FURTHER RESEARCH

As previously mentioned at the beginning, it could have been beneficial to include variables like: alcohol,

employment income, as well as one’s interest in drugs. With reference to interest could refer to one

enjoys using occasionally or have tried once and will never try again, and onwards. Another key piece

that would have been more beneficial to this regression was a newer survey as it is nearly 2015 and the

data provided was statistics from 2012. It would have been more interesting to see if the age at which

one first tries ecstasy would change with current data and have more of a significant effect on the age at

20

which one tries cannabis. It is personally believed that with a newer survey as popularity seems to grow

with a substance like MDMA and Molly it could change the regression significantly. Lastly, it could

provide interest to examine one’s household status which may provide questions and reasoning to if

people that are experimenting with drugs have children or revolve under an adult based household.

21

REFERENCES

Faculty of Arts & Science (2005). UT/DLS microdata analysis and subsetting. Retrieved from http://sda.chass.utoronto.ca/sdaweb/sda.htm

Ferguson, D. M., Boden, J. M., & Horwood, L. J. (2006).Cannabis use & other illicit drug use: testing the cannabis gateway hypothesis. Society for the Study of Addiction, 101, p.556-569. doi: 10.1111/j.1360-0443.2005.01322.x

Haines, R. J., Johnson, J. L., Carter, C., & Arora, K. (2009). "I couldn't say, I'm not a girl" adolescents talk about gender & cannabis use. Social Science & Medicine, 68, 2029-2036. doi: 10.1016/j.socscimed.2009.03.003

Hill, R. C, Griffiths, W. E., & Lim, G. (2011). Principles of Econometrics. USA: John Wiley & Sons, Inc.

Kaestner, R. (1997). The effects of cocaine & cannabis use on marriage & marital stability. Journal of Family Issues, 18, 145-173. doi: 10.3386/w5038

Morral, A. R., McCaffrey, D. F., & Paddock, S. M. (2002). Reassessing the cannabis gateway effect. Society for the Study of Addiction to Alcohol and Other Drugs, 97, p.1493-1504. doi: 10.1046/j.1360-0443.2002.00280.x

Tarter, R. E., Vanyukou, M., Levent, K., Reynolds, M., & Clark, D. B. (2006). Predictors of cannabis use in adolescents before & after licit drug use: examination of the gateway hypothesis. The American Journal of Psychiatry, 183, p.2134-2140. Retrieved Fromhttp://ajp.psychiatryonline.org/doi/full/10.1176/ajp.2006.163.12.2134

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APPENDICES

INITIAL REGRESSION

Dependent Variable: CANNABISMethod: Least SquaresDate: 11/21/14 Time: 15:02Sample: 1 163Included observations: 163

Variable Coefficient Std. Error t-Statistic Prob.

C 3.595370 1.319606 2.724578 0.0072COCAINE 0.326929 0.062138 5.261295 0.0000ECSTASY -0.027487 0.037004 -0.742812 0.4587MARITAL 0.444973 0.447183 0.995058 0.3212

SEX 0.610369 0.453380 1.346264 0.1802SMOKING 0.386872 0.075989 5.091164 0.0000

R-squared 0.360374 Mean dependent var 15.71166Adjusted R-squared 0.340004 S.D. dependent var 3.500836S.E. of regression 2.844084 Akaike info criterion 4.964475Sum squared resid 1269.944 Schwarz criterion 5.078355Log likelihood -398.6047 Hannan-Quinn criter. 5.010709F-statistic 17.69118 Durbin-Watson stat 2.085080Prob(F-statistic) 0.000000

DESCRIPTIVE STATISTICS

CANNABIS C COCAINE ECSTASY MARITAL SEX SMOKING Mean 15.71 1.00 20.80 22.84 0.48 0.55 13.93 Median 15.00 1.00 20.00 20.00 0.00 1.00 14.00 Maximum 35.00 1.00 40.00 48.00 1.00 1.00 24.00 Minimum 9.00 1.00 12.00 12.00 0.00 0.00 5.00 Std. Dev. 3.50 0.00 4.58 7.56 0.50 0.50 3.07 Skewness 2.04 NA 1.39 1.51 0.06 -0.21 0.37 Kurtosis 9.54 NA 6.04 4.69 1.00 1.04 5.22

Jarque-Bera 403.36 NA 115.07 81.01 27.17 27.18 37.37 Probability 0.00 NA 0.00 0.00 0.00 0.00 0.00

Sum 2,561.00 163.00 3,391.00 3,723.00 79.00 90.00 2,271.00 Sum Sq. Dev. 1,985.45 0.00 3,399.72 9,269.85 40.71 40.31 1,530.26

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MULTICOLLINEARITY

CORRELATION MATRIX

CANNABIS COCAINE ECSTASY MARITAL SEX SMOKINGCANNABIS 1.000000 0.486428 0.264448 0.066052 0.102340 0.455997COCAINE 0.486428 1.000000 0.591380 -0.028199 0.009911 0.278769ECSTASY 0.264448 0.591380 1.000000 -0.041344 0.116736 0.186453MARITAL 0.066052 -0.028199 -0.041344 1.000000 -0.039982 0.045398

SEX 0.102340 0.009911 0.116736 -0.039982 1.000000 0.060694SMOKING 0.455997 0.278769 0.186453 0.045398 0.060694 1.000000

R2

Dependent Variable: COCAINEMethod: Least SquaresDate: 11/21/14 Time: 15:08Sample: 1 163Included observations: 163


C 6.593343 1.510154 4.366008 0.0000CANNABIS 0.458468 0.087140 5.261295 0.0000ECSTASY 0.303685 0.036599 8.297565 0.0000MARITAL -0.325275 0.530590 -0.613045 0.5407

SEX -0.807063 0.536131 -1.505349 0.1342SMOKING 0.048375 0.097054 0.498434 0.6189


Dependent Variable: ECSTASYMethod: Least SquaresDate: 11/21/14 Time: 15:09Sample: 1 163Included observations: 163


C 1.839420 2.903803 0.633452 0.5274CANNABIS -0.127413 0.171527 -0.742812 0.4587COCAINE 1.003826 0.120978 8.297565 0.0000MARITAL -0.263666 0.965589 -0.273062 0.7852

SEX 1.725115 0.972045 1.774727 0.0779SMOKING 0.092943 0.176438 0.526777 0.5991

R-squared 0.364958 Mean dependent var 22.84049Adjusted R-squared 0.344734 S.D. dependent var 7.564477S.E. of regression 6.123331 Akaike info criterion 6.498205

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Sum squared resid 5886.743 Schwarz criterion 6.612085Log likelihood -523.6037 Hannan-Quinn criter. 6.544439F-statistic 18.04557 Durbin-Watson stat 1.754944Prob(F-statistic) 0.000000

Dependent Variable: MARITALMethod: Least SquaresDate: 11/21/14 Time: 15:09Sample: 1 163Included observations: 163


C 0.421932 0.237886 1.773675 0.0781CANNABIS 0.014084 0.014154 0.995058 0.3212COCAINE -0.007342 0.011976 -0.613045 0.5407ECSTASY -0.001800 0.006593 -0.273062 0.7852

SEX -0.048104 0.081034 -0.593624 0.5536SMOKING 0.004440 0.014588 0.304352 0.7613

R-squared 0.012661 Mean dependent var 0.484663Adjusted R-squared -0.018783 S.D. dependent var 0.501305S.E. of regression 0.505991 Akaike info criterion 1.511519Sum squared resid 40.19620 Schwarz criterion 1.625399Log likelihood -117.1888 Hannan-Quinn criter. 1.557753F-statistic 0.402660 Durbin-Watson stat 0.091857Prob(F-statistic) 0.846437

Dependent Variable: SEXMethod: Least SquaresDate: 11/21/14 Time: 15:10Sample: 1 163Included observations: 163


C 0.351408 0.234689 1.497333 0.1363CANNABIS 0.018698 0.013888 1.346264 0.1802COCAINE -0.017630 0.011711 -1.505349 0.1342ECSTASY 0.011400 0.006424 1.774727 0.0779MARITAL -0.046555 0.078426 -0.593624 0.5536SMOKING 0.002577 0.014354 0.179535 0.8577


Dependent Variable: SMOKINGMethod: Least SquaresDate: 11/21/14 Time: 15:10Sample: 1 163

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Included observations: 163


C 6.956383 1.190955 5.841010 0.0000CANNABIS 0.366274 0.071943 5.091164 0.0000COCAINE 0.032659 0.065524 0.498434 0.6189ECSTASY 0.018983 0.036036 0.526777 0.5991MARITAL 0.132806 0.436357 0.304352 0.7613

SEX 0.079648 0.443639 0.179535 0.8577


VARIANCE INFLATION FACTORS (1/(1-R2)

X1 on others (smoking) – (1/.7857) = 1.273

X2 on others (cocaine) - (1/.5238) = 1.909

X3 on others (ecstasy) – (1/.6350) = 1.575

X4 on others (sex) – (1/.9652) = 1.036

X5 on others (marital) – (1/.9873) = 1.013

HETEROSKEDASTICITY

WHITE TEST

F-statistic 1.074526 Prob. F(18,144) 0.3836Obs*R-squared 19.30103 Prob. Chi-Square(18) 0.3735Scaled explained SS 146.5801 Prob. Chi-Square(18) 0.0000

Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 11/24/14 Time: 08:58Sample: 1 163Included observations: 163Collinear test regressors dropped from specification


C -62.07058 63.86145 -0.971957 0.3327COCAINE 5.345927 5.256802 1.016954 0.3109

COCAINE^2 -0.001120 0.149091 -0.007511 0.9940COCAINE*ECSTASY 0.079068 0.144679 0.546507 0.5856

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COCAINE*MARITAL 2.368875 1.642295 1.442417 0.1514COCAINE*SEX -1.753528 1.563200 -1.121755 0.2638

COCAINE*SMOKING -0.420575 0.314205 -1.338540 0.1828ECSTASY 0.472660 3.185058 0.148399 0.8822

ECSTASY^2 -0.056536 0.063565 -0.889410 0.3753ECSTASY*MARITAL -0.110857 0.967446 -0.114588 0.9089

ECSTASY*SEX 0.108453 1.056237 0.102679 0.9184ECSTASY*SMOKING 0.085808 0.130597 0.657039 0.5122

MARITAL -25.54998 32.47278 -0.786812 0.4327MARITAL*SEX -9.069146 10.54850 -0.859757 0.3914

MARITAL*SMOKING -0.880043 1.819581 -0.483651 0.6294SEX -0.340432 34.32916 -0.009917 0.9921

SEX*SMOKING 2.509268 2.115412 1.186184 0.2375SMOKING 0.575136 4.658782 0.123452 0.9019

SMOKING^2 0.134455 0.200036 0.672150 0.5026


BREUSCH-PAGAN-GODFREY


Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 11/24/14 Time: 08:59Sample: 1 163Included observations: 163


C -15.85495 14.36611 -1.103635 0.2714COCAINE 1.681990 0.676481 2.486381 0.0140ECSTASY 0.116808 0.402845 0.289956 0.7722MARITAL 4.573097 4.868327 0.939357 0.3490

SEX -3.747926 4.935792 -0.759336 0.4488SMOKING -1.016364 0.827265 -1.228583 0.2211


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HARVEY TEST


Test Equation:Dependent Variable: LRESID2Method: Least SquaresDate: 11/24/14 Time: 09:01Sample: 1 163Included observations: 163


C -4.119528 1.031952 -3.991978 0.0001COCAINE 0.248659 0.048593 5.117158 0.0000ECSTASY -0.022637 0.028937 -0.782266 0.4352MARITAL 0.150393 0.349703 0.430058 0.6677

SEX 0.697810 0.354550 1.968160 0.0508SMOKING -0.076986 0.059424 -1.295528 0.1970

R-squared 0.189424 Mean dependent var -0.077959Adjusted R-squared 0.163609 S.D. dependent var 2.431941S.E. of regression 2.224117 Akaike info criterion 4.472712Sum squared resid 776.6310 Schwarz criterion 4.586592Log likelihood -358.5260 Hannan-Quinn criter. 4.518946F-statistic 7.337882 Durbin-Watson stat 2.070699Prob(F-statistic) 0.000003

GLEJSER TEST


Test Equation:Dependent Variable: ARESIDMethod: Least SquaresDate: 11/24/14 Time: 09:01Sample: 1 163Included observations: 163


C -2.029591 0.909315 -2.231999 0.0270COCAINE 0.232141 0.042818 5.421522 0.0000ECSTASY -0.000557 0.025498 -0.021851 0.9826MARITAL 0.262155 0.308145 0.850752 0.3962

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SEX 0.130787 0.312415 0.418631 0.6761SMOKING -0.088985 0.052362 -1.699411 0.0912


SERIAL (AUTO) CORRELATION

DURBIN-WATSON TEST

Dependent Variable: CANNABISMethod: Least SquaresDate: 11/24/14 Time: 09:03Sample: 1 163Included observations: 163White heteroskedasticity-consistent standard errors & covariance



SEX 0.610369 0.459957 1.327014 0.1864SMOKING 0.386872 0.079527 4.864666 0.0000


5% Significance level, using critical values where n=150 as it was the closest to 163

1.665 1.802 2.198 2.335

1 2 3 4 5

dl du 4-du 4-dl

CORRELOGRAM

29

Date: 11/21/14 Time: 16:04Sample: 1 163Included observations: 163

Autocorrelation Partial Correlation AC PAC Q-Stat Prob

.|. | .|. | 1 -0.055 -0.055 0.4936 0.482 .|. | .|. | 2 0.019 0.016 0.5514 0.759 .|. | .|. | 3 -0.007 -0.005 0.5600 0.906 *|. | *|. | 4 -0.162 -0.163 4.9925 0.288 .|* | .|* | 5 0.189 0.177 11.094 0.050 *|. | *|. | 6 -0.114 -0.099 13.309 0.038 .|. | .|. | 7 -0.008 -0.024 13.320 0.065 .|. | .|. | 8 -0.013 -0.033 13.350 0.100 .|. | .|. | 9 0.004 0.062 13.352 0.147 .|. | *|. | 10 -0.007 -0.078 13.360 0.204 .|. | .|* | 11 0.039 0.078 13.631 0.254 .|. | .|. | 12 -0.026 -0.041 13.749 0.317 .|. | .|. | 13 -0.019 -0.005 13.814 0.387 .|. | .|. | 14 0.013 -0.019 13.844 0.461 .|. | .|. | 15 -0.007 0.038 13.853 0.537 .|. | .|. | 16 0.054 0.011 14.394 0.569 *|. | .|. | 17 -0.080 -0.062 15.569 0.555 .|. | .|. | 18 -0.000 -0.004 15.569 0.623 .|. | .|. | 19 0.034 0.044 15.782 0.672 .|. | .|. | 20 -0.050 -0.057 16.261 0.700 *|. | *|. | 21 -0.067 -0.106 17.104 0.705 .|. | .|. | 22 -0.002 0.035 17.105 0.758 .|. | .|. | 23 -0.038 -0.045 17.380 0.790 .|. | .|. | 24 0.068 0.040 18.275 0.789 *|. | *|. | 25 -0.090 -0.110 19.842 0.755 *|. | .|. | 26 -0.078 -0.047 21.037 0.740 .|* | .|. | 27 0.114 0.074 23.607 0.652 .|. | .|. | 28 -0.013 0.032 23.640 0.700 .|. | .|. | 29 0.041 -0.032 23.982 0.730 .|. | .|. | 30 -0.028 -0.002 24.137 0.766 .|. | .|. | 31 -0.042 -0.012 24.491 0.790 .|. | .|. | 32 0.022 -0.013 24.593 0.822 .|. | .|. | 33 0.020 0.033 24.675 0.851 .|. | .|. | 34 0.058 0.057 25.378 0.857 *|. | *|. | 35 -0.096 -0.119 27.319 0.820 .|. | .|. | 36 -0.044 -0.033 27.732 0.837

LM TEST

Breusch-Godfrey Serial Correlation LM Test:

F-statistic 2.115609 Prob. F(6,151) 0.0546Obs*R-squared 12.63986 Prob. Chi-Square(6) 0.0491

Test Equation:Dependent Variable: RESIDMethod: Least Squares

30

Date: 11/24/14 Time: 09:04Sample: 1 163Included observations: 163Presample missing value lagged residuals set to zero.


C 0.664505 1.335086 0.497724 0.6194COCAINE -0.056785 0.063440 -0.895105 0.3722ECSTASY 0.024379 0.037147 0.656291 0.5126MARITAL -0.045396 0.441995 -0.102708 0.9183

SEX -0.093273 0.450581 -0.207005 0.8363SMOKING 0.003922 0.074815 0.052418 0.9583RESID(-1) -0.015496 0.082000 -0.188973 0.8504RESID(-2) -0.007411 0.082323 -0.090019 0.9284RESID(-3) -0.039389 0.086168 -0.457123 0.6482RESID(-4) -0.176263 0.086180 -2.045287 0.0426RESID(-5) 0.180059 0.086912 2.071734 0.0400RESID(-6) -0.122534 0.088122 -1.390502 0.1664

R-squared 0.077545 Mean dependent var -1.89E-15Adjusted R-squared 0.010346 S.D. dependent var 2.799850S.E. of regression 2.785328 Akaike info criterion 4.957377Sum squared resid 1171.466 Schwarz criterion 5.185138Log likelihood -392.0263 Hannan-Quinn criter. 5.049846F-statistic 1.153968 Durbin-Watson stat 1.981748Prob(F-statistic) 0.323995

LM TEST – CORRECTED EQUATION AR(4) AR(5)

F-statistic 0.682484 Prob. F(6,144) 0.6640Obs*R-squared 4.368783 Prob. Chi-Square(6) 0.6269

Test Equation:Dependent Variable: RESIDMethod: Least SquaresDate: 11/24/14 Time: 12:33Sample: 6 163Included observations: 158Presample missing value lagged residuals set to zero.


C 0.449810 1.346309 0.334106 0.7388COCAINE -0.022208 0.065574 -0.338663 0.7354ECSTASY 0.008675 0.038630 0.224575 0.8226MARITAL -0.024243 0.465396 -0.052092 0.9585

SEX -0.095942 0.478310 -0.200586 0.8413SMOKING -0.006301 0.075809 -0.083121 0.9339

AR(4) 0.164229 0.325689 0.504251 0.6149AR(5) -0.063165 0.324671 -0.194551 0.8460

RESID(-1) -0.013368 0.083556 -0.159992 0.8731RESID(-2) -0.010349 0.084541 -0.122412 0.9027

31

RESID(-3) -0.037412 0.089528 -0.417882 0.6767RESID(-4) -0.200253 0.332540 -0.602192 0.5480RESID(-5) 0.059223 0.336232 0.176136 0.8604RESID(-6) -0.162794 0.088908 -1.831031 0.0692

R-squared 0.027651 Mean dependent var -6.66E-14Adjusted R-squared -0.060131 S.D. dependent var 2.736878S.E. of regression 2.817962 Akaike info criterion 4.994338Sum squared resid 1143.491 Schwarz criterion 5.265708Log likelihood -380.5527 Hannan-Quinn criter. 5.104545F-statistic 0.314992 Durbin-Watson stat 1.981112Prob(F-statistic) 0.988993

FINAL EQUATION

Dependent Variable: CANNABISMethod: Least SquaresDate: 11/24/14 Time: 09:05Sample (adjusted): 6 163Included observations: 158 after adjustmentsConvergence achieved after 6 iterationsWhite heteroskedasticity-consistent standard errors & covariance



SEX 0.645398 0.482672 1.337136 0.1832SMOKING 0.398341 0.072947 5.460704 0.0000

AR(4) -0.162218 0.085385 -1.899853 0.0594AR(5) 0.196611 0.089271 2.202398 0.0292


Inverted AR Roots .62 .30-.64i .30+.64i -.61+.50i-.61-.50i

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can the usage and experimentation with illicit drugs and...

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