Hierarchical Multiple Regression

Question 1

rules for hierarchical MR/when to use

Answer 1

provides best prediction of criterion variable from predictors

predicted values are plotted on regression line passing through scatterplot

regression line attempts to minimise residuals

Question 2

what does the regression model do?

Answer 2

statistically predicts outcome based on correlations on predictors

Question 3

regression model is a combination of…

Answer 3

correlation coefficients that maximise variance explained by predictors

Question 4

regression equation

Answer 4

Ŷ = b0 + b1x1 + b2x2… +error

Y is the criterion/outcome
B0 is intercept
B1 is coefficient associated with predictor
X1 is name of predictor

Question 5

What does multicollinearity do to beta errors and R and what does this mean?

Answer 5

increases beta errors, limits size of R and makes determining predictor importance difficult

Question 6

addressing issues with multicollinearity

Answer 6

check errors in data entry and coding

reduce the number of predictor variables

delete predictors highly related to other predictors

Question 7

what is an outlier

Answer 7

substantially different value

Question 8

impact of outliers

Answer 8

large impact on results of regression analysis

Question 9

how are outliers detected?

Answer 9

scatterplot and residual plots

Question 10

identifying outliers on SPSS tables

Answer 10

residual statistics table (standardised residuals, Cooks distance)

Question 11

what is a standardised residual

Answer 11

rescaling residual by residual/std. deviation

Question 12

what do standardised residuals do?

Answer 12

help identify where predicted score is quite different to actual score

Question 13

identifying standardised residuals

Answer 13

fall outside +/- 3.3
Tabachnick and Fidell (2007)

Question 14

what does Cooks distance show

Answer 14

influence of deleting a case

Question 15

value for Cooks distance and meaning

Answer 15

> 1 are large values

Question 16

brief explanation of how hierarchical MR is done in SPSS

Answer 16

sequential
predictors entered in equation in specified order (blocks)
blocks assessed on what it adds to prediction

Question 17

steps in analysing hierarchical MR

Answer 17

check assumptions are met
assess model overall
evaluate predictor variables

formally report results

Question 18

check assumptions are met step

Answer 18

sample size - N>50+8M
multicollinearity - tolerance>.5, VIF<10
normality - histogram
linearity - p-plot
homoscedasticity - equal variances

outliers - residual stats, std. residual +/-3.3, cooks D <1

Question 19

assess model overall step

Answer 19

variables entered/removed - see whats included
model summary - adj. R2 = % variance
R2 change - effects after variable removed
ANOVA table - F( , ) = ,p<0.001
decimal found in F column (brackets found for between and within subjects figures)

Question 20

evaluating predictors step

Answer 20

coefficients table
regression equations

Question 21

formally reporting the results of hierarchical MR

Answer 21

A hierarchical MR was used to assess the ability of the predictor (name) on the criterion (name) after controlling for (other predictor variables)

Preliminary analyses were conducted to ensure no violation of the assumptions of normality, linearity, multicollinearity, homoscedasticity and sample size (state whether assumptions were met or not).

(name predictor variables) were entered into model 1, explaining (adj. R2)% of the variation in (criterion variable) (adj. R2 = ), F( , ) = ,p<0.001 (state which variables were/were not significant predictors of the criterion variable) (P<0.001).

After entry of (name another predictor variable) in model 2, the model explained (more/less) variance,
F( , ) = ,p<0.001
The total variance in (criterion) explained by the model as a whole was (adj. R2)% (adj. R2 = ). (state significant/non-significant predictors in model 2) (p<0.001)

Then interpret the results - explain what they mean in words.