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
.