Multiple Regression

Question 1

What is the difference between univariate analysis and multivariate analysis?

Answer 1

Multivariate analysis looks at determining the effect of multiple x variables upon the variance of Y whereas univariate just looks at one

Question 2

What is the ‘model’?

Answer 2

The name given to the structure of different predictors that all together go in to predicting the variance in Y.

Question 3

What does the linear ‘line of best fit’ become when you are looking at multivariate analysis?

Answer 3

‘plane of best fit’

Question 4

What statistic do we look to in multiple regression for the ‘coefficient of explanation’?

Answer 4

Adjusted R squared

Question 5

What is the process of standardisation in multiple regression and why do we do it?

Answer 5

Because the different predictors that go in to a model may be measured with different units, we are unable to compare their relative influence upon the variance of Y. This warrants us to standardise them so that they are comparable and we can determine the most influential factor.

Question 6

In SPSS, what symbols denote the unstandardised and standardised coefficients for the different predictors??

Answer 6

Unstandardised = alpha
Standardised = beta

Question 7

What is the F statistic?

Answer 7

this denotes the regression model’s level of significance in explaining the y variance

Question 8

What is multicollinearity?

Answer 8

When different predictors correlate with each other

Question 9

What is multicollinearity and an why is it a problem?

Answer 9

Multicollinearity is when two or more predictors are related/correlated with each other. Problem because if we are conducting multiple regression analysis then we are aiming to determine the impact of each individual predictor upon the y variance and so if two predictors correlate with each other then it distorts our interpretation of that result as there may be an unidentified relationship

Question 10

What test do we use ot test for multicollinearity?

Answer 10

Variance Inflation Factor (VIF)

Question 11

If multicollinearity is not present between the predictors then what value would the VIF take?

Answer 11

VIF < 5

Question 12

What can we do to remove multicollinearity?

Answer 12

1) remove predictor and re-run the test
2) create an interaction term where there is logical observable relationship
3) conduct a factor analysis

Question 13

What is the F-test?

Answer 13

this test identifies the effect taking a specific predictor out of the model has upon the model’s ability to explain variance in Y.

Question 14

What would be the result of the F-test if the predictor taken out of the model was really important?

Answer 14

There would be a big change in value relative to the initial value

Question 15

What is the p-value of the p-test?

Answer 15

this value denotes the associated level of significance of the change to the F-test

Question 16

What are the 3 methods for constructing a multiple regression model?

Answer 16

1. hierarchical
2. step-wise
3. simultaneous

Question 17

What is the hierarchical method for constructing a multiple regression model?

Answer 17

Tell SPSS to input different predictors based on their presumed coefficient of explanation (r squared).

Question 18

What is required in order to validly construct a multiple regression model using the hierarchical construction method?

Answer 18

Prior knowledge about which predictors will highly likely be the most influential

Question 19

What is the step-wise method for constructing a multiple regression model?

Answer 19

SPSS would determine the statistical significance of the different predictors then add them in based off that information.

Question 20

What is the simultaneous method for constructing a multiple regression model?

Answer 20

Inputting all predictors at the same time via a ‘cauldron’ approach

Question 21

What are 3 top tips for constructing a multiple regression model?

Answer 21

1. do not ‘scattergun’
2. use multiple statistics to inform judgement of different predictors
3. do not overcomplicate model construction

Question 22

What is the tolerance statistic in SPSS?

Answer 22

This outlines whether or not a given factor is classed as providing enough explanation to the overall y variance

Question 23

What value does the tolerance need to be for each factor in order to be classed as a factor that contributes enough to the variance of Y?

Answer 23

They need to have a value above 0.2. This means they need to explain at least 20% of the variance in Y.