Correlations and Regressions

Question 1

What is a correlation?

Answer 1

• Measure of relation between two variable, often continuous
• Association
• Linear, cant estimate other types of relations
• No causality
• Gives us a bivariate association

Question 2

What is the coefficent used for correlation?

Answer 2

• Pearson (most commonly used) r
• Values greater than 1.00 is an error
• 0.00 = no relation
• Positive and negative direction

Question 3

What can the magnitude of r tell us?

Answer 3

• How to infer the association
• .10 small
• .30 moderate
• .50 large

Question 4

Covariation

Answer 4

How much one variable increase or decrease is dependent on the second variable
- No covariation= r should be zero

Question 5

Variation

Answer 5

Variation between each variable
Example: variation in depression scores

Question 6

Correlation - APA style

Answer 6

• r(N-groups)=, p
• Positive or negative association

Question 7

What are other types of correlations?

Answer 7

• Spearman Rank-Order Correlation
  One or both variables are measured on a ordinal scale
• Point-biserial Correlation
  One continuous and one is dichotomous
• Phi-coefficient
  Both are dichotomous

Question 8

What is a partial correlation?

Answer 8

• Looking at an association while controlling some other factors
  Example; looking at shyness and social anxiety, controlling for gender

Question 9

What can a regression analysis give us?

Answer 9

• Being able to make a prediction
  Often a predetermine direction on DV
• Unique effect of predictors on the outcome variable
  Still a linear association
  Which predictor is stronger?
• A correlation

Question 10

How do you decide the direction of the prediction?

Answer 10

• Based on theories and/or conceptual arguments

Question 11

What equation is commonly used with regression analysis?

Answer 11

Y=a + bX + e
- Y = outcome variable
- X = predictor
- a = intercept
- b = the slope, how many points Y changes for one unit change in X
- e = error, refers to variation not explained by X

Question 12

What is the relation between the slope and explained variance?

Answer 12

“In summary, while both models may have positive correlation coefficients, Model A would likely have a higher coefficient and explain more of the variation in the dependent variable compared to Model B, due to the tighter clustering of data points around the line.”
- A has a stronger linear correlation

Question 13

What are the types of regressions?

Answer 13

• Simple regression model
• Multiple regression model

Question 14

Simple Regression

Answer 14

• One predictor
• One outcome variable

Question 15

Simple Regression - SPSS output

Answer 15

Table 1
- List predictors
Table 2
- R square = what portion of variance that explains outcome
Table 3
- Is the explained variance significant
Table 4
- R first lvl=intercept , level of outcome variable when predictor variable is 0
- R second lvl = slope, relation between predictor and outcome variable
- Beta = relation between outcome and predictor, is it significant? Standardised slope (compared to other studies)

Question 16

Simple Regression - APA style

Answer 16

• Variance %
• F value
• Beta

Question 17

Multiple Regression

Answer 17

• 2 or more predictors
• One outcome variable
  Continuous variable

Question 18

Multiple Regression - SPSS output

Answer 18

Table 1
- Descriptives
Table 2
- Correlations
Table 3
- List of all predictors
Table 4
- R square, all predictors
Table 5
- Significant or not?
Table 6
- Beta, unique effect of predictor on outcome

Question 19

Multiple Regression - APA style

Answer 19

• % variance on outcome
• F value
• Beta, each predictor
• Positive or negative prediction?

Question 20

What are some assumptions and restrictions with regression models?

Answer 20

Outliers
- Extreme data?
- Distribution of data and histogram; skewness(2 okay) and kurtosis(7 okay)
- Boxplots
Residual outliers
- Is it +/- 3.00? Inspect those over it
- Difference between predicted and observed outcome values
Linearity
- Test to see if the association is linear
- Multicollinearity

Question 21

What is multicollinearity?

Answer 21

• When the predictor variables are too similar to each other
• Inspecting bivariate associations among predictors
• Raised association gives a biased result

Question 22

How can you see if there is multicollinearity?

Answer 22

Collinearity diagnostics
- Tolerance, under .25
- VIF Variance Inflation Factor, not above 5

Question 23

What can we do if the predictors are highly correlated?

Answer 23

• Remove one of the predictors
• Combine the predictors, composite score

Question 24

What is standardized regression coefficient?

Answer 24

• Beta value
• How big the change in standard deviation of the independent variable to the dependent variable
• Can be bigger than 1, the higher the number the greater the impact

Question 25

Residual

Answer 25

The differences between observed and predicted values of dependent variable

Question 26

What is the residual are independent assumption?

Answer 26

• That residual are not related to each other
• Sample randomly selected
• Durbin-Watson close to 2, i.e they are independent

Question 27

How can you tell if the regression analysis is reasonably linear?

Answer 27

A pearson r between .30 - .80-90.