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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.
Theory & Expectations
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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.”
Theory & Expectations
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.
Theory & Expectations
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.
Theory & Expectations
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.
18
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
Variable Coefficient Std. Error t-Statistic Prob.
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
R-squared 0.476161 Mean dependent var 20.80368Adjusted R-squared 0.459478 S.D. dependent var 4.581038S.E. of regression 3.367987 Akaike info criterion 5.302623Sum squared resid 1780.904 Schwarz criterion 5.416503Log likelihood -426.1638 Hannan-Quinn criter. 5.348857F-statistic 28.54210 Durbin-Watson stat 1.205237Prob(F-statistic) 0.000000
Dependent Variable: ECSTASYMethod: Least SquaresDate: 11/21/14 Time: 15:09Sample: 1 163Included observations: 163
Variable Coefficient Std. Error t-Statistic Prob.
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
Variable Coefficient Std. Error t-Statistic Prob.
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
Variable Coefficient Std. Error t-Statistic Prob.
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
R-squared 0.034842 Mean dependent var 0.552147Adjusted R-squared 0.004104 S.D. dependent var 0.498806S.E. of regression 0.497781 Akaike info criterion 1.478802Sum squared resid 38.90238 Schwarz criterion 1.592682Log likelihood -114.5224 Hannan-Quinn criter. 1.525036F-statistic 1.133530 Durbin-Watson stat 0.087072Prob(F-statistic) 0.344904
Dependent Variable: SMOKINGMethod: Least SquaresDate: 11/21/14 Time: 15:10Sample: 1 163
25
Included observations: 163
Variable Coefficient Std. Error t-Statistic Prob.
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
R-squared 0.214295 Mean dependent var 13.93252Adjusted R-squared 0.189273 S.D. dependent var 3.073440S.E. of regression 2.767337 Akaike info criterion 4.909763Sum squared resid 1202.330 Schwarz criterion 5.023644Log likelihood -394.1457 Hannan-Quinn criter. 4.955998F-statistic 8.564133 Durbin-Watson stat 1.915286Prob(F-statistic) 0.000000
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
Variable Coefficient Std. Error t-Statistic Prob.
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
R-squared 0.118411 Mean dependent var 7.791068Adjusted R-squared 0.008213 S.D. dependent var 31.62157S.E. of regression 31.49146 Akaike info criterion 9.846502Sum squared resid 142806.5 Schwarz criterion 10.20712Log likelihood -783.4899 Hannan-Quinn criter. 9.992910F-statistic 1.074526 Durbin-Watson stat 2.051141Prob(F-statistic) 0.383564
BREUSCH-PAGAN-GODFREY
F-statistic 2.393809 Prob. F(5,157) 0.0400Obs*R-squared 11.54623 Prob. Chi-Square(5) 0.0416Scaled explained SS 87.68685 Prob. Chi-Square(5) 0.0000
Test Equation:Dependent Variable: RESID^2Method: Least SquaresDate: 11/24/14 Time: 08:59Sample: 1 163Included observations: 163
Variable Coefficient Std. Error t-Statistic Prob.
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
R-squared 0.070836 Mean dependent var 7.791068Adjusted R-squared 0.041245 S.D. dependent var 31.62157S.E. of regression 30.96260 Akaike info criterion 9.739552Sum squared resid 150513.2 Schwarz criterion 9.853433Log likelihood -787.7735 Hannan-Quinn criter. 9.785786F-statistic 2.393809 Durbin-Watson stat 2.010825Prob(F-statistic) 0.040007
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HARVEY TEST
F-statistic 7.337882 Prob. F(5,157) 0.0000Obs*R-squared 30.87610 Prob. Chi-Square(5) 0.0000Scaled explained SS 36.77783 Prob. Chi-Square(5) 0.0000
Test Equation:Dependent Variable: LRESID2Method: Least SquaresDate: 11/24/14 Time: 09:01Sample: 1 163Included observations: 163
Variable Coefficient Std. Error t-Statistic Prob.
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
F-statistic 8.837166 Prob. F(5,157) 0.0000Obs*R-squared 35.79919 Prob. Chi-Square(5) 0.0000Scaled explained SS 57.73805 Prob. Chi-Square(5) 0.0000
Test Equation:Dependent Variable: ARESIDMethod: Least SquaresDate: 11/24/14 Time: 09:01Sample: 1 163Included observations: 163
Variable Coefficient Std. Error t-Statistic Prob.
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
R-squared 0.219627 Mean dependent var 1.746553Adjusted R-squared 0.194774 S.D. dependent var 2.184006S.E. of regression 1.959804 Akaike info criterion 4.219681Sum squared resid 603.0106 Schwarz criterion 4.333562Log likelihood -337.9040 Hannan-Quinn criter. 4.265915F-statistic 8.837166 Durbin-Watson stat 1.907011Prob(F-statistic) 0.000000
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
Variable Coefficient Std. Error t-Statistic Prob.
C 3.595370 1.431794 2.511095 0.0130COCAINE 0.326929 0.083183 3.930240 0.0001ECSTASY -0.027487 0.033232 -0.827109 0.4094MARITAL 0.444973 0.447963 0.993325 0.3221
SEX 0.610369 0.459957 1.327014 0.1864SMOKING 0.386872 0.079527 4.864666 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
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
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Date: 11/24/14 Time: 09:04Sample: 1 163Included observations: 163Presample missing value lagged residuals set to zero.
Variable Coefficient Std. Error t-Statistic Prob.
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.
Variable Coefficient Std. Error t-Statistic Prob.
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
Variable Coefficient Std. Error t-Statistic Prob.
C 3.878613 1.270803 3.052096 0.0027COCAINE 0.282932 0.070061 4.038375 0.0001ECSTASY -0.007529 0.031003 -0.242855 0.8084MARITAL 0.490768 0.446146 1.100017 0.2731
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
R-squared 0.397921 Mean dependent var 15.77848Adjusted R-squared 0.369824 S.D. dependent var 3.527189S.E. of regression 2.800010 Akaike info criterion 4.946429Sum squared resid 1176.008 Schwarz criterion 5.101497Log likelihood -382.7679 Hannan-Quinn criter. 5.009404F-statistic 14.16241 Durbin-Watson stat 2.005480Prob(F-statistic) 0.000000
Inverted AR Roots .62 .30-.64i .30+.64i -.61+.50i-.61-.50i
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