1. Statistical Modelling
Relationships
Distributions

2. Modelling Process IDENTIFICATION     ESTIMATION    ITERATION
 
ESTIMATION  
 ITERATION
VALIDATION  
APPLICATION  

3. Relationships Simple Regression Models Multiple Regression Models
Logistic Regression Models
Other functional Models
Lagged Models

4. Simple Regression Assumes one variable (x) relates to another (y)
Assumes errors cancel out
Assumes errors have constant variance
Assumes errors are independent of each other
Assumes errors are normally distributed
(for testing theories)

5. Multiple Regression
Assumes several variables (xi) relates to another (y)
Assumes errors cancel out
Assumes errors have constant variance
Assumes errors are independent of each other
Assumes xi are independent of one another
Assumes errors are normally distributed
(for testing theories)

6. Logistic Regression
Like multiple regression but variable to be predicted (y) is binary.
Estimates odds and log odds rather than direct effects.

7. Other Models Could be almost anything, common ones are:
Log of (some) variables
Polynomials
Trignometric
Power functions

8. Lagged Models Usually associated with time series data
Assume carry-over effects
Carry-over of variable
Carry-over of error
Tend to use simple forms

9. Distribution Models
Discrete
Continuous

10. Discrete Distributions
UNIFORM
Equal chance of each and every outcome
Often a starting hypothesis

11. Discrete Distributions
BINOMIAL
n trials
Equal chance of success in each trial (p)
Gives probability of r successes in n trials

12. Discrete Distributions
POISSON
Random events
Fixed average (mean) rate
Gives probability that r events will occur in a fixed time, distance, space etc

13. Discrete Distributions
GEOMETRIC
Constant probability of success (p)
Gives probability of r trials before first success

14. Continuous Distributions
UNIFORM
Constant density of probability for all measurement values
Limited range of possible values

15. Continuous Distributions
NORMAL
Commonest distribution assumption
Intuitive
Characterised by two parameters, mean and standard deviation
Arises from a number of theoretical perspectives

16. Continuous Distributions
EXPONENTIAL
Complementary to Poisson
Assumes events occur randomly, at fixed mean rate
Gives probability density for time, distance, space etc until event occurs

17. Continuous Distributions
EXTREME VALUE DISTRIBUTIONS
Weibull
Double exponential
Gumbel (or Extreme Value)