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## Steps in Writing an Academic Article

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### Steps in Writing an Academic Article. Introduction (tell cute story) Literature Review ... NOTE: We rarely have data for the population. ... – PowerPoint PPT presentation

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Title: Steps in Writing an Academic Article

1
Steps in Writing an Academic Article
• Introduction (tell cute story)
• Literature Review
• Describe Data
• Create model
• Identify dependent variable
• Identify independent variables
• State hypothesis
• Estimate model

2
Data Summary and Description
• Population Parameters Summary and descriptive
measures for the population.
• Sample Statistics Summary and descriptive
measures for a sample.
• NOTE We rarely have data for the population.
Hence we need to be able to draw inferences from
a sample.

3
Measures of Central Tendency
• Mean The average
• Issue You must note the distribution of the
sample. If it is unbalanced the mean may be
• Median Middle observation

4
Symmetrical vs. Skewness
• Symmetrical A balanced distribution. Median
Mean
• Skewness A lack of balance.
• Skewed to the left Median Mean
• Skewed to the right Median
• Again, if the data is skewed, the average will be

5
Measures of Dispersion
• Range Difference between the largest (maximum)
and smallest (minimum) sample observations.
• Only considers the extremes of the sample
• Variance and Standard Deviation
• Sample Variance Average squared deviation from
the sample mean.
• Sample Standard Deviation Squared root of the
sample variance.
• NOTE These are used when we discuss competitive
balance in sports.

6
Hypothesis Testing
• Hypothesis Testing Statistical experiment used
to measure the reasonableness of a given theory
or premise
• NOTE WE DO NOT PROVE A THEORY
• Type I Error Incorrect rejection of a true
hypothesis.
• Type II Error Failure to reject a false
hypothesis.

7
Regression AnalysisDefinitions
• Regression analysis statistical method for
describing the relationship between a dependent
variable Y and independent variable(s) X.
• Deterministic Relation An identity
• A relationship that is known with certainty.
• Statistical Relation An inexact relation
• We use regression analysis for statistical
relations, not deterministic.

8
Regression AnalysisTypes of Data
• Time series A daily, weekly, monthly, or annual
sequence of data. i.e. Attendance data for the
49ers from 1970 to 2007.
• Cross-section Data from a common point in time.
i.e. Attendance data for each team in the NFL for
the 2007 season.
• Panel data Data that combines both
cross-section and time-series data. i.e.
Attendance data for each team in the NFL from
1970 to 2006.

9
The Least Squares Model
• Ordinary Least Squares a statistical method that
chooses the regression line by minimizing the
squared distance between the data points and the
regression line.
• Why not sum the errors? Generally equals zero.

10
The Error Term
• Error term (e) random, included because we do
not expect a perfect relationship.
• Sources of error
• Omitted variables
• Measurement error
• Incorrect functional form

11
Univariate Analysis
• Y a bX Where
• Y The Dependent Variable, or what you are
trying to explain (or predict).
• X The Independent Variable, or what you believe
explains Y.
• a the y-intercept or constant term.
• b the slope or coefficient

12
The t-statistic
• To evaluate the quality of our slope coefficient
we refer to the
• t-statistic.
• T-statistic slope coefficient / standard error
• Standard error - estimated standard deviation of
the coefficient
• Rule of thumb T-stat 2
• This is in absolute terms.
• In other words, the coefficient should be more
than double the standard error.
• Why is this important? We want to know whether or
not the coefficient is statistically different
from zero.

13
Statistical vs. Economic Significance
• Just because we find a statistically significant
relationship, that does not mean we have found
something important.
• You should understand the difference between
statistical significance and economic
significance.

14
The slope coefficient
• How do we interpret the slope coefficient?
• Example
• WINS -82.5 1.3(Points per game)
• Each additional one point per game results in a
1.3 more wins.
• Is this the truth? We never know the truth, we
are simply attempting to derive estimates.
• Is this a good estimate? Clearly points alone
do not explain wins (and consequently, this is a

15
The constant term
• How do we interpret the constant term?
• The constant term must be included in the
regression, or else we are forcing the regression
line through zero.
• The constant term is used captures all the
factors not explicitly utilized in the equation.
• The constant term is theoretically the value of Y
when X is zero. Frequently this is outside the
range of possibility, and therefore the constant
term should not be interpreted.

16
Multivariate Analysis
• Introducing the idea of ceteris paribus.
• Ceteris paribus holding all else constant
• One cannot impose ceteris paribus unless all
relevant variables are included in the model.

17
Wins and ORB
18
Wins and Missed Shots
19
Offensive Rebounds and Missed Shots
20
Wins, ORB, and Missed Shots
• Wins -57.8 - 1.3ORB
• As illustrated earlier, the estimated impact of
offensive rebounds (ORB) on wins is negative.
• Wins 149.4 - 2.4(Missed Shots)
• ORB -5.1 0.4(Missed Shots)
• In words, missed shots and offensive rebounds are
positively related. So when we estimate wins as
a function of offensive rebounds, we are simply
picking up the relationship between wins and
missed shots.

21
R-squared
• How do we know how accurate our equation is?
• R-squared How much variation your model
explained divided by how much variation there was
to explain.
• Or, how much variation did our model explain.
• In more technical terms.
• R-squared Explained Sum of Squares / Total Sum
of Squares

22
• Total Sum of Squares TSS How much variation
there is to explain.
• Explained Sum of Squares ESS How much
variation you explained.
• Residual Sum of Squares RSS How much
variation you did not explain.

23
• Total sum of squares Sum of the squared
difference between the actual Y and the mean of
Y, or,
• TSS ?(Yi - mean of Y)2
• Explained sum of squares Sum of the squared
differences between the predicted Y and the mean
of Y, or,
• ESS ?(Y - mean of Y)2
• Residual sum of squares Sum of the squared
differences between the actual Y and the
predicted Y, or,

24
• Adding any independent variable will increase R2.
• To combat this problem, we often report the

25
Model Evaluation
• It is important to note that R-squared tells us
something, but it is not everything.
• Low R-squared does not necessarily mean the model
is bad, high R-squared does not necessarily mean
the model is good.
• Models must be theoretically sound. In other
words, we do not play with data until we get a
model with the highest r-squared. You have to
have a reason why your model is constructed as
you suggest.

26
Multicollinearity
• Multicollinearity - more than two independent
variables exhibit a linear correlation.
• Example Including total rebounds and defensive
rebounds in the same model.
• Consequences
• Standard errors will rise, t-stats will fall
• What does that mean? You will think variables are
insignificant when they are not.

27
Other Issues
• Omitted Variable Bias You cannot impose ceteris
paribus if relevant independent variables are not
included in the model.
• Small Sample Bias You cannot adequately assess a