Multiple Regression

Question 1

Describe what multiple regression is and when it is used

Answer 1

Used when you want to predict the value of a variable based on the value of 2 or more variables.

Need at least 2 predictors.

MR informs you of the relationship between each predictor and the DV, after controlling for the effect of all other predictors in the model

Question 2

What is the equation for multiple regression and does it differ from the simple regression equation?

Answer 2

y = a+b1x1 + b2x2

Only one intercept, but many slopes for the number of predictors

X = Predictor variable

Question 3

What are the different forms of multiple regression?

Answer 3

Standard multiple regression - Predictors are entered simultaneously

Hierarchical multiple regression - Predictors are entered in steps.

Question 4

When conducting multiple regression, which part of the SPSS output do you look at to find out about the goodness-of-fit of the overall model?

Answer 4

ANOVA table

Same as simple regression

Question 5

When carrying out multiple regression, which SPSS output do you refer to to estimate the overall effects of the predictor on the outcome

Answer 5

Model summary. Shows you the relationship between the predictor variables and the DV

Question 6

In a model summary table, what does R refer to?

Answer 6

Multiple correlation coefficient

Refers to the correlation between the observed values of Y and the values of y predicted by the multiple regression model.

Large values represent a large correlation between the predicted and observed values of the outcome.

R of 1 = model perfectly predicts the observed data

Question 7

In the model summary table, what does R square refer to?

Answer 7

Proportion of variance in Y that is explained by the model.

All predictors together.

Question 8

In the model summary table, what does Adjusted R Square refer to?

Answer 8

Adjustment. Reduced value for R squared attempting to make an estimate of the value of R squared in the population.

Adjusted down to compensate for increase in R square.

Question 9

Which type of information about effects does the coefficients table provide in a multiple regression?

Answer 9

The unique effects of the predictor (excluding effects shared with other predictors) on the outcome.

Question 10

In a multiple regression coefficients table, what does B refer to?

Answer 10

Value of the slope for each predictor

Non-standardised.

Two values (1 for each predictor) which are both measured using different values which is why beta is used to standardise them.

Question 11

In a multiple regression coefficients table, what does std.error refer to?

Answer 11

The standard deviation of the distribution of sample b-values for each predictor

Question 12

In a multiple regression coefficients table, what does Beta refer to?

Answer 12

Standardised regression coefficients.

This tells us the number of standard deviations that the outcome will change as a result of one standard deviation change in the predictor.

Differs from simple regression as it concerns the unique contribution of the predictor, excluding any overlap with other predictors.

Question 13

When is a hierarchical multiple regression used?

Answer 13

If you already know the effects of one variable and want to look at another as believe have not been accounted for.

Question 14

Explain the steps of a hierarchical multiple regression

Answer 14

1. Assess a model (model 1) including only one variable as predictor and other as outcome.
2. Assess model 2 including both variables and an outcome to see if it explains more variance than the first model.

Enter the predictors in steps with the known predictor added first.

Question 15

In a hierarchical multiple regression, what does the ANOVA table tell you?

Answer 15

Explain the goodness-of-fit of the regression model.

Each model is tested.

Question 16

What does the r-square change value in the model summary of a multiple regression table refer to?

Answer 16

• Additional variance explained by a specific model
• Effects of a specific model that are not accounted for in previous blocks
• Degree to which a specific model improves the ability to predict an outcome when compared with a model entered in the previous block

Question 17

What is the model summary table used for in a hierarchical multiple regression?

Answer 17

Looking at the overall effects of the predictors on the outcome

Contains info on differences between models in terms of variance in Y that models account for.

Question 18

What does F Change refer to in the model summary table of a hierarchical multiple regression?

Answer 18

The relative improvement in the explained variance that takes place after the new predictor is added to the new model

Question 19

What does Sig F. Change refer to in the model summary table of a hierarchical multiple regression?

Answer 19

Allows you to see if the R square change value is statistically significant.

Question 20

What does the the coefficients table tell you in a hierarchical multiple regression?

Answer 20

Unique effects of each individual predictor on the outcome.

Different to simple regression as specific information offered for each model tested.

Question 21

How does beta relate to b?

Answer 21

Beta is the standardised version of b