Multiple Regression

Question 1

When is multiple regression used?

Answer 1

When there are multiple continuous predictors

Question 2

What does B1X1 mean in the model?

Answer 2

The slope of variable 1

Question 3

What does B1X1i mean in the model?

Answer 3

The expected value for person i on variable 1

Question 4

What additional assumptions are in multiple regression?

Answer 4

Multicollinearity- There mustn’t be too high linear relation between predictor variables (measuring same thing)
Linearity- the predictor must have a linear relation with the outcome variable

Question 5

How can multicollinearity be assessed? (4)

Answer 5

Correlations
Matrix scatterplot
VIF: max <10 mean <1
Tolerance > 0.2

Question 6

How can linearity be checked? (2)

Answer 6

correlations

Matrix scatterplot

Question 7

How do you check if a further variable adds anything to your model on spss?

Answer 7

Add them in block two on spss

Question 8

What save options do you add?

Answer 8

All the distances, you can add unstandardised predicted values to see what the predicted values are for each participant

Question 9

How do you check for Homoscedasticity?

Answer 9

plots > zpred and zresid

both z ones

Question 10

How do you know which model explains the variance more?

Answer 10

The second model will have a sig. correlation under model summary, first model will always be sig.

Question 11

In a 3D scatter plot, where is the explained variance and the unexplained variance?

Answer 11

Explained- distance between the average score and “green” plane, unexplained - difference between red dots and green plane

Question 12

How do we get the expected values for person i based on a model?

Answer 12

Fill in the slopes for b1 b2 etc in the regression equation, add in there scores and add the intercept at b0 and calculate the equation for person i

Question 13

What does the R represent under model summary?

Answer 13

The correlation between the model (predicted values) and the actual values

Question 14

What happens if you square this r?

Answer 14

Explained variance

Question 15

What is meant by the assumption of normality

Answer 15

the residuals of the model are normally distributed, or the sampling distribution of the parameter is. This assumption doesn’t refer to the data themselves being normally distributed.

Question 16

What is meant by the assumption of additivity and linearity?

Answer 16

the relationship between the dependent variable and the independent variable(s) is linear. This is the most important assumption.

Question 17

How can you test normality in spss?

Answer 17

Probability-probability plot (P-P plot) = analyze>descriptive statistics>P-P plots. Drag the dependent variable to variables.
Shapiro-Wilk and Kolmogorov-Smirnov test = analyze>descriptive statistics>explore. There you click on plots and select normality plots with tests to produce the K-S and S-W test.

Question 18

What does the Probability- probability plot do?

Answer 18

a plot of the cumulative probability of a variable against the cumulative probability of a particular distribution (normal distribution in this case). If the data are normally distributed you’ll get a straight diagonal line.

Question 19

When do you use the Shapiro-Wilk test and when do you use the Kolgmorov -Smirnov test?

Answer 19

The S-W is used for samples smaller than 2000, otherwise the K-S is used. The test should be non- significant: then the distribution of the sample is not significantly different from a normal distribution.

Question 20

How do you test for linearity and homoscedasticity?

Answer 20

Scatterplot- Both can be tested at the same time using a scatterplot plotting the values of the residuals (ZRESID) against the corresponding values of the outcome predicted by our model (ZPRED). There should be no systematic relationship between the errors and the predicted values (just a straight horizontal line).

Question 21

How can independence be tested?

Answer 21

Durbin-Watson test- a test that looks for serial correlations between errors. It varies between 0 and 4, with a value of 2 meaning the residuals are uncorrelated. Values less than 1 or more than 3 are cause for concern.
Access the test with analyse> regression> linear> statistics> Durbin-Watson.

Question 22

How can you reduce bias?

Answer 22

TWAT
Trimming- deleting a quantity of data from the extremes. It could be deleting the data from the person who contributed the outlier.
Winsorzing- substituting outliers with the highest value that isn’t an outlier.
Applying robust methods- A commonly used robust method is bootstrapping. This can be done using SPSS.
Transforming- applying a mathematical function to all scores. There are various transformations that you basically try out until one helps.

Question 23

When should trimming be done?

Answer 23

this should only be done if there is a good reason to believe this case is not from the population you intended to sample.

Question 24

What rules may trimming abide by? (2)

Answer 24

(1) a percentage based rule (deleting the 10% of highest and lowest scores), or;
(2) a standard deviation based rule: calculating the mean and standard deviation of a set of scores, and
then removing values that are a certain number of standard deviations greater than the mean.