SD9: Hierarchical Regression

What does R2 represent?

the variance that is explained

What is the equation for the variance that is not explained?

1 - R2

What is zero-order2 (squared)?

variance explained by xi, expressed as a proportion of the total variance in y

What is part2 (squared)?

unique variance explained by xi, expressed as a proportion of the total variance in y

What is total explained variance?

variance explained all predictors combined (their unique and shared variance) expressed as a proportion of the total variance in y

What is the equation of total explained variance?

Σ(part correlations2 ) + shared variance

What is partial2?

unique variance explained by xi, expressed as a proportion of the variance in y that remains after the variance explained by other predictors has been removed

What is 'standard' multiple regression?

all predictor variables are entered at the same time - obtain a measure of overall variance explained (R2) and of the influence of each separate predictor (coefficients)

What is hierarchical regression?

predictor variables are entered in a specific order of 'steps', based on theoretical grounds - the relative contribution of each step (set of predictor variables) can be evaluated in terms of what it adds to the prediction of the outcome variable (i.e. the additional variance it explains)

Why use hierarchical regression?

to examine the influence of predictor variables on an outcome variable, after 'controlling for' the influence of other variables

What does the t test test for in hierarchical regression?

assesses whether the model (the slope) for that individual predictor accounts for significantly more variance than the simplest models

What does the change statistic show us on model 2?

compares model 1 and model 2 and tells us about the explanatory power of the variable after one variable is controlled for.