Visualising Regression & Hierarchical Regression (W10) ✅

Question 1

What are the coefficients for multiple regression?

Answer 1

Zero-order2: total variance explained by all predictors, as a proportion of the total variance in y

Part2: unique variance explained by each predictor (no shared variance between each preditor) expressed as a proportion of the total
variance in y

Partial2: unique variance explained by one variable as a proportion of the variance
in y minus other predictors’ explained variance

Question 2

What is meant by hierarchical regression, how does it compare to simple/multiple. regression?

Answer 2

• Assesses whether adding predictor variables allows you to explain additional variance in the outcome variable
• Hierarchical regression: predictor variables are entered in a specified order of ‘steps’
  -> The relative contribution of each ‘step’ can be evaluated in terms of what it adds to the prediction of the outcome variable
• WHILE multiple regression adds all the predictor variables in at the same time
  -> Only tell you the overall explained variance and separate variance

Question 3

Why use Hierarchical Regression?

Answer 3

To examine the influence of predictor variables(s) on an outcome variable, after ‘controlling for’ (rule out) the influence of other variables

Question 4

How to read the change in statistics? (hierarchical regression)

Answer 4

• Compares Model 1 (e.g. x1 variable controlled) and Model 2 (x1 and x2 controlled)
• ΔR2: how much overall variance in y is explained by x2 after the effects of x1 is controlled for
  -> e.g. what additional percentage did [x2] explain in variance of y after the effects of [x1] are controlled for
• ΔF: Provides a measure of how much the model has improved the prediction of y (MSM), relative to the level of inaccuracy of the model (MSR) after the predictive power of Step 1 variables have been partialled out

IMPORTANT! change from simplest model to Model 1 is literally just Model 1 values

Question 5

How to read statistics of each model from SPSS (hierarchical regression)

Answer 5

1. Model Summary:
   Assess the change in variance (including R, Adjusted R2, change in R2, and change in F) for each model
2. ANOVA: evaluating each model -> Assesses whether the overall regression model (with all predictors included at that step) accounts for significantly more variance than the simplest model
   (b = 0)
3. Coefficients: evaluating each predictor within each model
   * The intercept (a)
   * The slopes (b) for each predictor variable
   * Beta: the slopes converted to standardised slopes
   * t-test
   => Assesses whether the model (the slope) for that individual predictor accounts for significantly more variance than the simplest model (b = 0)