Lecture 14 - Correlation and Multiple Regression Theory

Question 1

What are the three types of multiple regression?

Answer 1

simultaneous

stepwise

hierarchical

Question 2

what does regression allow us to do?

Answer 2

to predict Y based on knowledge of X

Question 3

What does the criterion mean?

Answer 3

It can be used to refer to the dependent variable

Question 4

What measure of association do we use when variable 1 and 2 are both interval or ratio level data (e.g. height and agE)

Answer 4

Pearsons

Question 5

what measure of association do we use when variable one and 2 are both ordinal (ranked)

Answer 5

Spearman’s Rho
OR
Kendall’s Tau

Question 6

What measure of association do we use when both variables are a ‘true dichotomy’ (only two options), e.g. gender and pass/fail

Answer 6

Phi

Question 7

What measure of association do we use when one variable is a true dichotomy (e.g. gender) and one variable is interval/ratio level data (e.g. weight

Answer 7

Point-Biserial

Question 8

In a venn diagram what does the size of the circle represent?

Answer 8

The variance of that variable. So the bigger the more variable that data is.

Question 9

What do we use a partial correlation for?

Answer 9

To tell us about the relationship between 2 variables, once all other variables have been removed

Question 10

How does a partial correlation work?

Answer 10

it measures the strength of dependence between two variables, which is not accounted for by the way in which they both change in response to variations in a selected subset of other variables

Question 11

What is multiple regression for?

Answer 11

It lets us learn about the relationship between several IV’s (predictors) and one dependent variable (the crierion)

such as, how does size, number of bedrooms, income of area relate to the selling price of a house?

how does age, gender, stress etc relate to depression?

Question 12

What is the objective of multiple regression

Answer 12

to find the model that best fits the data whilst minimising overall prediction error

Question 13

What happens when there is one predictor in a regression?

Answer 13

that’s when its linear regression - the line must be a straight line since there is only the one IV and the DV

Question 14

In a regression equation, what is B0

Answer 14

the intercept (where the line meets the y axis)

Question 15

In a regression equation, what is B1

Answer 15

the slope of the regression line

Question 16

What are the three ways in which we can assess the goodness of fit of a regression model?

Answer 16

multiple correlation coefficient

coefficient of determination (R squared)

F-ratio

Question 17

How do we use multiple correlation coefficient to assess the goodness of fit of a linear regression model?

Answer 17

we correlate the criterion (Y) and the best linear combination of the predictors

Question 18

what does Y refer to in a linear regression

Answer 18

the criterion

Question 19

What do we find, when we do a coefficient of determination (R squared) on a regression and find it to be a good model?

Answer 19

if its a good model:

large MSm
small MSr
large F-ratio

Question 20

What is a simultaneous multiple regression?

Answer 20

also called standard

there is no a priori model

enter all IVs at once

Question 21

What is a stepwise multiple regression?

Answer 21

no a priori model

computer chooses statistically an a posteriori model using the best subset of IVs

Question 22

What is a hierarichal multiple regression?

Answer 22

also called sequential

there is an priori model

Question 23

name 6 things which affect correlation

Answer 23

outliers

homo/heteroscedasticity

singularity/multicollinearity

number of predictors

range

distribution

Question 24

How do we know something is an outlier?

Answer 24

there is a ‘cooks difference of 1 or more’

Question 25

what do we use when we have two sets of IVs and we want to work out what is common between these IVs?

Answer 25

canonical correlation

Question 26

what do we use when we have one dependent variable (criterion) and many IV’s (predictors) and we want to predict the IVs from the DV

Answer 26

multiple regression

Question 27

what do we use when we have one dependent variable (criterion) and many IV’s (predictors) and we want to study the relationship between IVs and DV

Answer 27

multiple correlation

Question 28

what do we use when we have one dependent variable (criterion) and many IV’s (predictors) when we want to study the relationship between two or more variables once the effect of the others has been removed

Answer 28

partial correlation