Week 9: Multiple regression analysis

Question 1

What variables do we have when doing multiple linear regression?

Answer 1

More than one predictor variable

One response variable

Question 2

What happens if the data is non-linear?

Answer 2

Trying to fit a straight line through curvy data produces a smaller fit to the data - leading to an underestimate of the relationship

Question 3

How do we check for non-linearity of data?

Answer 3

Regression - correlation matrix and look at the plots

Question 4

What things may make it hard to identify trends in the data?

Answer 4

Attenuated range or under dispersion of scores (clustered)

Question 5

What is homoscedacity?

Answer 5

Means that the error variance should be the same at each level of the predictor variable

Question 6

Heteroskedasticity tests?

Answer 6

You can ask for normality tests under assumptions

Tests the null of homoscedacity - if they are significant this means that it is violated

Question 7

What are the assumptions of linear regression (6)?

Answer 7

Use correct variables (interval data)
Independence of data 
Sample size 
Normality 
Linearity
Homoscedacity

Question 8

How is the linear regression line calculated?

Answer 8

By minimizing the sum of squared differences between observed and predicted values

Question 9

How do you test for outliers (2 ways)?

Answer 9

1. Basic approach (any residual >3 SDs away from the mean)

2. Cooks distance (a measure of the influence of one case on the model as a whole) - under assumption checks

Question 10

What cooks value is concerning?

Answer 10

> 1 may be a concern

Question 11

Multiple regression techniques are more sensitive to…

Answer 11

violations of these assumptions than single regression

Question 12

Why should we use a correlation matrix to check the data?

Answer 12

Correlations are important, they tell us which IVs are related to the DV but also that some of the IVs are related to each other

Question 13

What is it called when IVs are correlated with each other?

Answer 13

Colinearity

Question 14

What does colinearity mean in terms of data?

Answer 14

Means that some of the predictors provide little unique information

Question 15

How do you run a multiple regression in jamovi?

Answer 15

Regression - linear regression

Question 16

How do you set up jamovi to run a simultaneous multiple regression?

Answer 16

Under model builder:

Put all IVs in a single box

Question 17

What are the colinearity statistics?

Answer 17

Tolerance

Variance inflation factor (VIF)

Question 18

What tolerance values are a problem?

Answer 18

<0.1 are a clear problem

Question 19

What variance inflation factors are a problem?

Answer 19

The inverse of tolerance >10 are a problem

Question 20

Simultaneous multiple regression is…

Answer 20

Theory free

Question 21

What kind of multiple regression is driven by theory?

Answer 21

Hierarchical multiple regression

E.g. you want to know what a certain predictor can add to the prediction of an outcome variable beyond the amount that is already explained by a particular predictor

Question 22

How do you set up jamovi for a hierarchical multiple regression?

Answer 22

Using model builder - put most important predictors in block one and then the subsequent predictors or those you want to know how much they add to the model in block 2

Question 23

What does the output from a hierarchical multiple regression tell us?

Answer 23

Will create a change in R2 scores to tell us how much more variation in the outcome is explained by adding the subsequent predictor
As well as a model comparisons box that gives you a delta F equation telling you if the newer model is statistically significant or not

Question 24

What type of linear regression would we use to determine the simplest possible model?

Answer 24

Stepwise multiple regression

Question 25

How do we do a stepwise multiple regression analysis?

Answer 25

Look at the output from simultaneous multiple regression (order them according to statistical significance)

Forward stepwise: put the best predictors into the model first and then only entering more predictors if they improve the quality of the model by significantly increases R2

Backward stepwise removal: Start with all predictors in the model and remove the worst predictors until this has a negative impact on the quality of the predictive model - significantly reducing the R2

Question 26

What are the two kinds of stepwise multiple regression?

Answer 26

Forward stepwise

Backwards stepwise

Question 27

What do you need to be careful of with stepwise multiple regression?

Answer 27

It is data-driven rather than theory-driven so you need to make sure that the outcome still makes sense