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Statistical Modelling: Relationships & Distributions Exploration

Explore various relationship models such as Simple, Multiple, Logistic Regression, and other functional models. Dive into discrete and continuous distribution models like Uniform, Binomial, Poisson, Normal, and more.

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Statistical Modelling: Relationships & Distributions Exploration

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  1. Statistical Modelling Relationships Distributions

  2. Modelling Process IDENTIFICATION     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)

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