# Lecture 14 - Correlation and Multiple Regression Theory Flashcards

1
Q

What are the three types of multiple regression?

A

simultaneous

stepwise

hierarchical

2
Q

what does regression allow us to do?

A

to predict Y based on knowledge of X

3
Q

What does the criterion mean?

A

It can be used to refer to the dependent variable

4
Q

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

A

Pearsons

5
Q

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

A

Spearman’s Rho
OR
Kendall’s Tau

6
Q

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

A

Phi

7
Q

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

A

Point-Biserial

8
Q

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

A

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

9
Q

What do we use a partial correlation for?

A

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

10
Q

How does a partial correlation work?

A

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

11
Q

What is multiple regression for?

A

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?

12
Q

What is the objective of multiple regression

A

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

13
Q

What happens when there is one predictor in a regression?

A

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

14
Q

In a regression equation, what is B0

A

the intercept (where the line meets the y axis)

15
Q

In a regression equation, what is B1

A

the slope of the regression line

16
Q

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

A

multiple correlation coefficient

coefficient of determination (R squared)

F-ratio

17
Q

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

A

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

18
Q

what does Y refer to in a linear regression

A

the criterion

19
Q

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

A

if its a good model:

large MSm
small MSr
large F-ratio

20
Q

What is a simultaneous multiple regression?

A

also called standard

there is no a priori model

enter all IVs at once

21
Q

What is a stepwise multiple regression?

A

no a priori model

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

22
Q

What is a hierarichal multiple regression?

A

also called sequential

there is an priori model

23
Q

name 6 things which affect correlation

A

outliers

homo/heteroscedasticity

singularity/multicollinearity

number of predictors

range

distribution

24
Q

How do we know something is an outlier?

A

there is a ‘cooks difference of 1 or more’

25
Q

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

A

canonical correlation

26
Q

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

A

multiple regression

27
Q

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

A

multiple correlation

28
Q

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

A

partial correlation