Correlation and regression

• Define correlation

  This is used when there is a strong relationship between two variables
• Types of correlation

  Linear and curvilinear
• What is the correlation coefficient

  The strength of correlation
• What is p (rho)

  Population coefficient
• Waht is r (rho)

  Sample coefficient
• What is rho

  Pearsons correlation coefficient
• What values does rho take

  -1 to 1
• Waht does rho = + or - 1 mean

  Perfect correlation
• What does rho = 0 mean

  No correlation
• Equation for rho


  The sum of (X - X bar) * (Y - Y bar) / The square root of the sum of (X - X bar) squared * (Y - Y bar) squared.
• What are the limitations of correlation

  It does not tell you about the cause of the correlation or the significance.

  Correlation is used for linear relationships.
• Define a model

  It is a simplification of reality.

  It focuses on the important details and removes the complexity of systems.
• Give an example of an exploraty data analysis technique

  Empirical modelling
• Waht is empirical modelling

  Describing what the data looks like
• What are the explanatory variables

  These are those that you measure. Also called independent variables.
• What axis are explanatory variables on

  The X
• What axis are response variables on

  Y
• What is a bivariate regression

  This is a linear relationship with two variables
• What is a response variable

  The change caused by the change of the explanatory variable. Also known as the dependent variable.
• What is the ordinary least squares model

  This is a line of best fit that minimises the deviations from the mean.
• Equation for the ordinary least sqaures model 


  Y = alpha + Beta * X.

  Where Y is the response variable.

  Alpha is the population Y intercept.

  Beta is the population slope coefficient.

  X is the explanatory variable.
• What is the ordinary least sqaures equation meaing

  This is the linear regression equation
• Where are alpha and Beta derived from in the linear regression equation

  The population
• What do the accents on alpha and beta in the lienar equation mean

  They are estimates calculated from the equation or graph
• Why would a linear regression equation predict a negative value for a discrete variable

  This is due to extrapolation
• What is regression analysis

  It quantifies the relationship between the response and explanatory variables
• What is caluclated from linear regression

  R squared, which is a goodness of fit measure.
• Eqaurion for R squared

  Average variance using model / Total variance in sample or population
• What does R sqaured = 1 mean

  The model is perfect and explains all the variability in the population or sample.
• What is R sqaured = 0

  The model does not explain the variability within the sample or population
• What is multivariate data

  This has multiple variables