Lecture 7 - Multiple Regression

Question 1

Define a plane

Answer 1

A flat surface

Question 2

What is the equation of a plane?

Answer 2

Y = b0 + b1x1 + b2x2

Question 3

Why do we use a residuals plot when working with 3D planes?

Answer 3

It’s much easier to visualise the residuals.

Question 4

If our histogram of residuals is more or less normally distributed, what does this qualify us to do?

Answer 4

Run a regression analysis.

Question 5

What is multicollinearity?

Answer 5

Inter correlations between different predictors, meaning that the amount of unique information explained by each predictor is reduced.

Question 6

Overlapping predictors that explain some of the variance can be counted how many times towards the overall prediction of the DV?

Answer 6

Only once - this is why you don’t simply add up all the different R^2s, as it will add up to a percentage greater than 100.

Question 7

What is a part correlation?

Answer 7

The amount of unique variance explained by the predictor (IV) as a proportion of the total variance in the criterion (DV).

Question 8

What is a partial correlation?

Answer 8

The proportion of variance once other relationships are accounted for/partialled out (controlled for).

Question 9

What does R Square tell us?

Answer 9

the amount of variance that the model accounts for overall

Question 10

What does R Square Adjusted tell us?

Answer 10

The amount of variance the model accounts for in a population with the same parameters as your sample.

Question 11

When looking at the co-efficients of the predictors on SPSS, when should standardised be used and when should unstandardized be used?

Answer 11

Unstandardised co-efficients should be used if you want to form a regression equation.

Standardised co-efficients should be used when reporting, as they are comparable.

Question 12

Which predictors must be included if you are to form a regression equation for your model?

Answer 12

All, not just the significant ones.

Question 13

What are the assumptions of multiple regressions?

Answer 13

• Parametric assumptions must be met

- Regression surface needs to be linear (flat). Way to check is if the residuals plot is also linear.

Question 14

What are the restrictions of multiple regressions?

Answer 14

• Outliers can be difficult to identify (a value looking like an outlier on one variable may not look like an outlier on the other)
• Best equation from the model may not be the most sensible in psychological terms (suppressor effect/variables).

Question 15

Comparing 2 or more models allows you to….?

Answer 15

• Evaluate individual predictors

- Isolates impact of one particular predictor on a model of data.

Question 16

In a hierarchical multiple regression, does the order of variables entered affect the outcome?

Answer 16

Yes, in a way. The first variable entered will be analysed according to how much of the variance it can explain on it’s own. Following this, each further variable added will be analysed according to how much unique variance it can account for.

Question 17

How many degrees of freedom do you get in a hierarchical multiple regression?

Answer 17

2 - one for the number of predictors and one for the number of participants.

Question 18

What does the first degrees of freedom value (df1) refer to in a hierarchical multiple regression?

Answer 18

The number of predictors

Question 19

What does the second degrees of freedom value (df2) refer to in a hierarchical multiple regression?

Answer 19

The number of participants.

Question 20

What are zero-order correlations?

Answer 20

Correlation between criterion and predictor, without any corrections or partials out.