Business Statistics: Exam 3
    Tuesday March 19, 2013
1:30 pm

The final exam will be comprehensive.  You should review the material we covered for exam 1 and exam 2 .  You will need a calculator for this exam.  I will provide normal and "t" tables and a list of formulas.


I. Regression

A. Dependent (y) and independent (x) variables
    1. Y = a + bX + . . .

B. Ordinary Least Squares
    1. best, linear, unbiased estimate
    2. computer estimation
C. Hypothesis testing
    1. typical test is there a statistically significant relation between Y and X ?
    2. null hypothesis b = 0
    3. use standard error of the coefficient to construct critical region
    4. reject if b is outside critical region
    5. t-stat = b/s.e. can be a fast method to check significance

D. Variations on OLS
    1. dummy variables
    2. transforming non-linear relations to use OLS
        a. quadratic terms
        b. natural logs

E. R-squared
    1. coefficient of determination
    2. low R-squared-- lots of unexplained variation in Y

II. Regression Problems

A. regression does not show causality

B. statistical significance is not the same as real-world importance
    a. differences may be non-random (statistical significance)
    b. but, size may be very small (unimportant)

C. Data collection must be methodologically sound
    1. random sample, representative of population
    2. avoid bias in survey questions
    3. results are sensitive to extreme values (outliers)

D. Statistical Issues

    1. model must be correctly specified
        a. missing variables
        b. spurious relations
    2. multicollinearity
       a. correlation between X variables
    3. heteroscedasticity
    4. autocorrelation
       a. time series problem
       b. trends, cycles

E. Graphs can be powerful analytic tools
    1. data
    2. residuals

III. Uncertainty and Probability

A. Knowledge, risk, and decision making
    1. lack of information vs. random outcomes
    2. classical, relative frequency, subjective probabilities
 
B. Expected value
    1. decision making under uncertainty
    2. fair bet
    3. calculating expected value
    
C. Risk
    1. measuring risk
        a. variance
        b. standard deviation
    2. Risk aversion
          a. no uncompensated risk
          b. risk premium

D. Portfolios
    1. combinations of random variables
       a. E(X+Y) = E(X) + E(Y)
       b. VAR(X+Y) = VAR(X) + VAR(Y) + 2 COV(XY) [not covered this term]
    2. diversification

E. Financial markets and risk
    1. Beta
       a. compares asset to overall market
       b. volatility and correlation
       c. regression coefficient
    2. Capital Asset Pricing Model (CAPM)
       a. risk premium
       b. calculations

IV. Direct Observation

A. Data from studying subjects
            1. direct measurement (as opposed to a survey)
            2. without treatment (which would be an experiment)
            3. important for business
                        a. quality control
                        b. sales figures
                        c. market research
                        d. traffic counts

B. Design
            1. random sample
            2. measuring device
                        a. accuracy
                        b. miscounts

V. Experiments

A. Experiments can show cause and effect
            1. medical studies
            2. test marketing
            3. policy

B. Experimental design
            1. control group and study group
            2. random assignment to each group
            3. blind
            4. double-blind
            5. many variations on design are possible
                    a. multiple treatments
                    b. multiple variables
                    c. block design

C. Without good design, experimental results are suspect

D. Matched pairs
            1. not always feasible
            2. compare treatments on same subject
            3. reduces variability by controlling for subject specific variation

 

VI. Closing

A. Read statistics critically
            1. Methodology
                        a. random sample
                        b. control group for experiment
                        c. other sources of bias
            2. Significance
                        a. standard error & margin of error
                        b. real-world meaning
            3. Interpretation
                        a. correlation does not imply causation
                        b. conclusions may not match results
                        c. how far can conclusions be generalized?
            4. Sponsorship
                        a. money can bias results
                        b. what conclusion would please the sponsor?
                        c. displeasing results may be suppressed

B. Statistical methods are used widely
            1. data collection
                        a. surveys
                        b. direct observation
                        c. experiments
            2. descriptive and inferential statistics
            3. many possible extensions
                        a. econometrics
                        b. mathematical statistics
                        c. graduate classes
                        d. forecasting
            3. All built on these basic components


 

 



Review sheets for exam 1 and exam 2 .

Business Statistics class page

Chuck Stull's homepage

Department of economics

Kalamazoo College Homepage