What are our goals in analysing data from continuous quantitative variables?
To construct an equation for predicting the DV from values of the IV
To describe the strength of the relationship between variables
The general term for this is regression analysis
What are analyses focusing solely on the strength of relationship known as?
Correlational analyses
These often make no distinction between predictor and response variables
What are the individual distributions of the IV known as?
Conditional distributions
Conditional distributions are distributions of the response variable conditional on a specified value of the predictor variable
What is the overall distribution of the DV known as?
The marginal distribution
What is the population regression line?
The straight line upon which the population means lie
What is the equation for the population regression line?
The mean population of Y values for a given value of X = (the intercept of the population regression line + the slope of the population regression line) x the value of X
What are the values of the intercept and slope of the regression line?
Population values that are needed to uniquely specify a straight line function
The intercept value specifies how far up the Y axis the line is
The slope value (regression coefficient) specifies how steep the line is
What does the slope of population line reflect?
The rate at which values on the Y axis are changing from one unit change in the X axis
What must we do when modelling sample data?
The slope and intercept values that provide the 'best fit' for data must be found
What is the basic equation for sample data
Score = model fit + residual
What is a best fitting line?
One which minimises the sum of squares of residuals
What is the residual?
The vertical line between data and regression line
Observation-predicted value
What is the equation for the least squares estimate of the slope of the regression line?
Sum of products over sum of squares
What is covariance?
The sum of products divided by the degrees of freedom
What does variance reveal?
The similarity of the structure of the expressions of variance and covariance
What points do regression lines always pass through?