Statistics for Decision Making

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Statistics for Decision Making
QM 2113 -- Spring 2003

• Wrapping Up Descriptive Statistics

Instructor John Seydel, Ph.D.
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Student Objectives

• Determine and apply correlation measures
• Avoid modeling errors in regression analysis
• Use regression appropriately with categorical
  variables
• Perform basic multiple regression modeling and
  analysis
• Use Excels Data Analysis tool for regression
• Interpret histograms
• Apply the standard deviation
• Define sampling error and use estimates to
  determine population averages

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Comments/Questions Homework Other Stuff

• Technical reports using nontechnical language!
• Questions about mechanics?
• Crosstabs
• PivotTables
• Interpretations for crosstabs?
• Joint relative frequencies
• Contingent frequencies
• Collect homework
• Report
• Crosstabs (WA and KIVZ)
• How does this all fit together?

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Now, Briefly Back to Regression Analysis

• Often youll see a single statistic used to
  summarize a bivariate relationship
• Correlation coefficient (r)
• Summarizes the estimated strength of the
  relationship
• Square root of R2
• Same sign as b1
• -1 lt r lt 1
• What not to do
• Typical modeling errors
• Reverse Y and X
• Treat categorical variables as numeric
• Use Excel shortcuts to create inflexible
  worksheets
• Data analysis tool (demo)
• Plot trend line (demo)

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That Said, Lets Try Something

• Some interesting scatterplots for GNI data
• Salary versus Race (demo)
• Salary versus Gender (demo)
• Does this present any problems?
• Yes!
• That is, were using the wrong technique to
  incorporate categorical variables
• Thus, these analyses are useless, or are they?

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Treating Categorical Variables as Explanatory
Factors

• Scatterplots
• We can get a sense of how Y differs across
  different categories
• Example (Salary vs Race)
• It appears that salaries are about the same for
  all races
• We can estimate/describe (by inspection)
• Averages
• Variation
• Need to use ANOVA to get better understanding
• Binary variables (i.e., only two possible
  categories)
• Scatterplots and regression might have some value
• Regression remember what the statistics
  represent
• Slope estimated average change in Y as X
  changes by 1 unit
• Intercept estimated average Y when X is 0

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Consider Analysis of Salary versus Gender

• Independent variable is binary
• Lets do some univariate analyses
• Average salary for males
• Average salary for females
• Average salary difference between males and
  females
• Now, look at the regression statistics
• Intercept Average salary for males
• Slope Average salary difference between males
  and females
• Hence, there is some value to using binary
  variables as independent variables in regression
  analysis
• This must, nevertheless, be done with caution

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Regression One Last Thing (for Now)

• Consider Salary vs Performance
• R2 81
• What does this mean?
• Yes, we estimate that 81 of all the variation in
  Salary is explained by Performance
• Now, what about the other 19?
• Lets expand our bivariate analysis into a
  multivariate one

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Multiple Regression

• Just as bivariate analyses consider two variables
  simultaneously, multivariate analyses consider
  many variables at the same time
• Allows us to identify interaction among the
  explanatory variables
• Easily accomplished with Excels Data Analysis
  tool
• But look at all that output
• Compare it to the same output for a bivariate
  analysis
• Our models
• Simple regression y-hat b0 b1x
• Multiple regression y-hat b0 b1x1 b1x2
  b1x3 . . .
• Interpretation of the bi values marginal
  effect, holding other factors constant (i.e.,
  ceteris paribus)
• Now, were really getting beyond the scope of
  this course
• More study/application of this in the next course
  (?)

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Now, Lets Take Another Look at Histograms

• Concepts to consider
• Symmetry, skew, and modality
• Estimating descriptive statistics by inspection
• Skew direction of the long, skinny part
• If on right, then average gt median
• Lets look at some histograms and identify the
  skew
• What does this tell us?
• Now, lets estimate
• Median (remember, its the 50th percentile)
• Mode the most likely data value (or range of
  values)
• Average hint the balance point
• Standard deviation hint R/6 lt s lt R/4
• So, whats the big deal?

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Finally, Lets Revisit the Average and Standard
Deviation

• A couple of rules
• Tchebycheffs rule (100 100/h2)
• The empirical rule
• Now, how well does x-bar estimate m?
• Consider the standard deviation
• Use the observed average to estimate the
  population/process average
• Related to, but different than the empirical rule
• Consider the concept of sampling error
• Difference between observed and population
  measure
• Average sampling error for x-bar is s/vn
• We can be 95 confident that m x-bar s/vn
• Application GNI salary data

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Summary of Objectives

• Determine and apply correlation
• Avoid modeling errors in regression analysis
• Use regression appropriately with categorical
  variables
• Perform basic multiple regression modeling and
  use Excel for calculations
• Interpret histograms
• Apply the standard deviation
• Define sampling error and use estimates to
  determine population averages

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Next Time . . .

• Probability concepts and notation
• Homework
• Read probability material from text
• Perform crosstab analysis of GNI data
• Create PivotTables
• Report on relationship
• Look at last years midterm exam
• Review notation (prepare for quiz)

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Appendix
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Populations and Samples
Population
Sample
Statistic
Parameter
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Schematic View
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Nontechnical . . . ?