Basic%20Review%20of%20Statistics

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Basic Review of Statistics

• By this point in your college career, the BB
  students should have taken STAT 171 and perhaps
  DS 303/ ECON 387 (core requirements for the BB
  degree).
• For the BA students, deficiency MA students, and
  those of you that havent completed your
  statistics requirements we will overview the key
  topics necessary for applications directly
  related to Econ 330.

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Population Parameters vs. Sample Statistics

• Population Parameters descriptive measures of
  the entire population that youre interested in
  examining
• Ex All US households
•  
• Ex All Illinois households with m gt 25,000
• In the absence of complete and detailed
  information on every household you are interested
  in you must estimate the population parameters.
  Most common way is using sample statistics.
• Sample Statistics descriptive measures of a
  representative sample, or subset, of the
  population.
• Ex instead of surveying every US household we
  send out surveys to a subset of the population
  and use that basic information to estimate what
  the values would be for the overall population.

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Measures of Central Tendency

• Mean (or arithmetic mean or average) the sum
  of numbers included in the sample divided by the
  number of observations, n.
• Ex calculate the average cost per unit (AC)
  across different firms given cost data 20.6,
  40.3, 15.8, 23.7
•  
• Typically written as
• Limitation of the Mean because it is only an
  average, you can expect that actual data will
  rarely coincide exactly with your estimate. If
  there is high variation in your data the average
  may not be very useful in estimation.

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Measures of Central Tendency continued

• 2. Median is the middle observation in your
  data.
• Indicates that half of your observations are
  above this value and half of your observations
  are below this value
• to find the value of the median, rank in
  ascending or descending order your observations
  by value. The observation in the middle is the
  median.
• Ex 40, 80, 18, 32, 50

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Measures of Central Tendency continued

• 3. Mode the most frequent value in the sample.
• useful when there is little variation in the data
  (values tend to be continuous and close to one
  another e.g. sales)
• ex sales data of ice cream in gallons over 8
  weeks
•   100, 99, 100, 102, 97, 110, 100, 103
• Aids in identifying the most common value for
  marketing purposes such as color or size of an
  item
•  

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Measures of Dispersion

• 1. Range difference between the largest and the
  smallest sample observation value
• Our firms highest profit this year was 20
  million, and the lowest profit this year was 12
  million ___________
• ________________________________
• The larger the range, the more variation or
  dispersion.
•  
• Often used for best case and worst case
  scenario projections.
• Limitation only focuses on the extreme values
  and may not be really representative of the
  entire sample.

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• 2. Variance and Standard Deviation
• Variance (s2 or s2) arithmetic mean of the
  squared deviation of each observation from the
  overall mean
• How far observation values are from the average
  or how far they deviate from the average value
  whether they are above or below doesnt matter
  squaring the deviations makes sure positive and
  negative deviations dont cancel out each other.
•  
• Where x is the value in your sample µ is the
  population average or mean so (x- µ) is how far
  your value deviates from the average n is the
  number of observations. 
• Standard Deviation (s or s) is the square root
  of the variance
•  
• Often used as a measure of potential risk when
  there is uncertainty.
•  

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• 3. Coefficient of Variation (V) compares the
  standard deviation to the mean.
• Used often by managers because the value is
  unaffected by the size or the unit of measure
  (such as thousands of dollars vs. millions of
  dollars).
• For example a manager is comparing two projects
  one that costs thousands of dollars and one that
  costs millions of dollars and projecting profits
  for each. Looking at standard deviations and
  comparing them doesnt allow you to compare
  apples to apples. Need a measure that isnt
  affected by the measurement unit. Coefficient of
  Variation is such a measure.
•  
• V s/ µ or
•  
• Numerator is a measure of risk denominator is a
  central tendency measureaverage outcome.
• Hence, in capital budgeting it is used to compare
  risk-reward ratios for different projects that
  differ widely in profitability or investment
  requirements.

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Measure of Goodness of Fit

• R2 or coefficient of determination measures
  how much variation in the dependent variable is
  explained by our independent variables.
• Higher numbers mean greater explanation and that
  deviations from the equation will be smaller
• Coefficient of determination numbers are bounded
  between 0 and 1

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Variable Significance

• t-statistics and p-values are commonly used to
  measure significance (the influence of an
  independent variable on the dependent variable)
• Excel which provides both. However, p-values
  are more commonly used so this is the measure we
  will use.
• You define your research question Is there a
  difference in blood pressures between those in
  group A (receiving a drug) and those in group B
  (receiving a sugar pillno drug).
• The null hypothesis is usually an hypothesis of
  "no difference"
• For example no difference between blood
  pressures in group A and group B.
• You then test this hypothesis with data including
  blood pressures of member of group A and group B.

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• The p- value or sometimes called the
  calculated probability is the estimated
  probability of rejecting the null hypothesis (H0)
  of a study question when that hypothesis is true.
• The probability of saying there is a difference
  in blood pressures (rejecting the null) when in
  fact there is not (there are no differences in
  blood pressure)
• Standard practice in the field defines
  statistically significant if _______________
  (smaller number such as 0.01 means greater
  significance)

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Regression Analysis (OLS)

• Regression Analysis uses data to describe how
  variables are related to one another.
• In markets, many variables change simultaneously
  and regression analysis accounts for multiple
  changes
• Example Qf( P, Psub, ADV, m, POP, time)
• Where Qsales of Brand Name icecream (dependent
  variable)
• Pprice of brand name ice cream
• Psub price of a substitute, competing, brand
• ADVadverstsing dollars
• mIncome
• POPpopulation
• ttime (sales quarter, to show trends or
  seasonality)
• The right-hand side variables are called
  independent variables
•  
• Using data gathered on all variables, regression
  analysis allows us to see the relative importance
  of each independent variable (Price, income, etc)
  on the dependent variable, sales or quantity.

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Excel Summary Stats and Regression Analysis

• Show in excel how to create summary statistics
  (mean, median, mode, range, etc)
• Show in excel how to run the regression
• Copy data into excel
• Under Data Tab use Data Analysis
• select regression from drop down list
• select y range of data (dependent variable
  Qselect only data not title)
• select x range of data (all independent variable
  data)
• click OK
• results pop into another window showing
  coefficients for our variables 

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SUMMARY STATS (1ST 3 VARIABLES)
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REGRESSION OUTPUT

• Regression equation (using coefficients above)
• Q647071 -127436P 5.35ADV 29339Pcomp 0.3403m
  0.02POP 4407t

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Statistically significant variables

• This means changes in price have a statistically
  significant impact on sales (same with
  competitors price and advertising)
• Note each coefficient is ?Q/?variable
• Example if the firm increased price by 1.00
  then estimated impact on sales is
  ____________________________________
• If asked for a 0.50 change it would be
  _______________________
• Income has no discernible effect in this model so
  predictions about changes in income would result
  in zero impact on quantity.