W8&9 - Multiple Linear Regression

Question 1

What does simple linear regression do?

Answer 1

Quantifies the variance (R^2) in the DV that can be explained by the variance in the IV.

Question 2

What does multiple linear regression test?

Answer 2

What combination from several IV explains the variance in the DV.

Question 3

Can IV overlap in multiple linear regression?

Answer 3

YES

They can correlated with one another to explain the variance in the DV

Question 4

What is unexplained variance known as especially when looking at a graph?

Answer 4

Residuals

Question 5

How many people should you have per variable in the final model for multiple linear regression and why?

Answer 5

At least 10 per variable

Otherwise the variable coefficient can become unreliable.

Question 6

What is the forced entry approach on SPSS in regards to multiple linear regression?

Answer 6

Means variables can still be in the model even if they’re not significant.

Question 7

List the types of multiple regression model building processes

Answer 7

Stepwise/forward

Hierarchical

Forced entry

Question 8

Define stepwise

Answer 8

Data driven + SPSS selects which variables are entered

Question 9

Define hierarchical

Answer 9

Researcher decides the order in which variables are entered

Question 10

Define forced entry

Answer 10

All predictors are entered into 1 model simultaneously

Question 11

Which out of the types of multiple regression model building processes doesn’t determine the unique variance that each IV adds to the model?

Answer 11

Forced entry

Question 12

What does the stepwise identify?

Answer 12

IV that explains the most variance in the DV + puts it in step 1 of the model.

Question 13

What does the stepwise do once it has identified the IV that explains most the variance in the DV?

Answer 13

Looks for the IV that explains the most of the remaining unexplained variance + is included in the model provided it explains a SIG amount of the remaining variance.

This is repeated until there are no IVs left that explain further variance w/ a p<0.05.

Question 14

When is stepwise used?

Answer 14

When data driven

Not a theory drive

And if there are too many variables that you couldn’t possible know which ones are most predictive.

Question 15

Define partial correlation

Answer 15

How strongly each of the variables correlate with the remaining information once we have explained or removed the variation one can explain.

Question 16

What does a higher partial correlation do to the p value?

Answer 16

Makes it smaller

Question 17

Hierarchical regression analysis

Answer 17

Researcher decided order in which variables are enter

• Order should be based on previous research or a plausible theory.

Question 18

What is normally entered in step 1 of the hierarchical regression analysis?

Answer 18

Known confounders

i.e age, gender + ethnicity

Question 19

What is normally entered in step 2 of the hierarchical regression analysis?

Answer 19

Known predictors

Question 20

What is normally entered in step 3 of the hierarchical regression analysis?

Answer 20

Test variables

Question 21

When would a hierarchical regression analysis be used over stepwise or forced entry?

Answer 21

When a ‘new’ variable of interest needs to be tested as for whether it explains further variation in a DV

Question 22

List the assumptions for multiple regression analysis

Answer 22

No multi-collinearity between predictors

Homoscedasticity of residuals

Linearity of residuals

Normality of residuals

Question 23

When does multi-collinearity occur?

Answer 23

When at least 2 predictors are highly correlated w/ each other in the final model.

Question 24

What can multi-collinearity lead to?

Answer 24

Unreliable regression b-coefficients for the predictors.

Question 25

What does the VIF (variance inflation factor) tell us?

Answer 25

How much the SE of the b-coefficient have been inflated.

Don’t want this as it widens the CI meaning you have less chance of showing that coefficient to be stat sig from 0.

Question 26

VIF>5 (r>0.90)

Answer 26

Maybe re-run regression after removing 1 of the ‘highly correlated’ variables (the least sig)

Question 27

VIF = 3.33

Answer 27

Assume there is no or low multi-collinearity