LECTURE 3 AND 4 multiple regression

Question 1

what is multiple regression

Answer 1

using linear regression model to predict the value on one variable from several predictor variables - hypothetical relationship between several variables

Question 2

what equation does the multiple regression use

Answer 2

expansion of straight line equation

y = b0X1 + b2X2 ….+error

Question 3

forced entry

Answer 3

all predictors entered simultaneously

Question 4

hierachial

Answer 4

experimenter decides input of variables based on theoretical background

aloows to observe unique predictive influence of a new variable on the outcome as known predictors held constant

Question 5

stepwise

Answer 5

predictors selected using semi partial correlation with outcome

Question 6

r value

Answer 6

correlation between observed value and predicted value

Question 7

r square

Answer 7

proportion of variance accounted for by the model

Question 8

adjusted r square

Answer 8

estimate of r square in popualtion (shrinkage) - estimates the change in r square when generalise from sample to the population

Question 9

beta values

Answer 9

chnage in outcome associated with unit change in the predictor - also has SD value (as increase value by 1SD have a ___ SD effect on second variable)

Question 10

t test in ANOVA

Answer 10

tells whether each IV make a significant contribution to predicting the DV (coeff sig diff from 0) (t= p=)

Question 11

how to interpret SD beta values

Answer 11

when predictor value increase by 1SD, predicted value increase by ___ (beta) of a SD

Question 12

r square change (hierachial)

Answer 12

hows how the second variable has accounted for more of the models variance
ie.e r square of model 1 is how much variance accounted for by 1st vairable
r square of model 2 is how much variance accounted for by both vairable - r square change is the specific variance accounted for by the addition of the second variable

Question 13

how to report anova

Answer 13

F (df, residual df)=__, p= __)

Question 14

how can you assess accuracy of the multiple regression model

Answer 14

standardised residuals and influential cases (cookes distance)

Question 15

describe standardised residuals for accuracy of the multiple regression model

Answer 15

average sample - 95% STDresiduals between +- 2
99% between +- 2.5

outliers of >3

Question 16

describe cookes distance for accuracy of the multiple regression model

Answer 16

measures influence of a single case on the whole model

concern = absolute values > 1

Question 17

‘variable type’ regression assumption

Answer 17

outcome must be a continuous variables

predictors can be continuous or dichotomous

Question 18

‘non zero variance’ regression assumption

Answer 18

predictors cannot have 0 variance

Question 19

‘linearity’ regression assumption

Answer 19

relationship must be linear

Question 20

‘independence’ regression assumption

Answer 20

all values come from different person

Question 21

‘No Multicollinearity’ regression assumption

Answer 21

predictors must not be highly correlated
check with collinearity diagnostics - values should be:
TOLERANCE = > 0.2
VIF =

Question 22

‘Homoscedasticity’ regression assumption

Answer 22

for each value of predictor - variance of error should be constant
check by plot of ZRESID against ZPRED to get normality of errors probability plot

Question 23

‘independent errors’ regression assumption

Answer 23

for any observation, error terms should be uncorrelated

Question 24

‘normality distributed errors’ regression assumption

Answer 24

histogram and normal probability plot of standardised residuals