L5 - Regression Analysis II Flashcards
What is a spurious correlation?
Relationship between income and height, but gender is the
responsible factor
What is a masked relationship?
Example: Positive relationship between happiness and debt, but
relationship reverses when controlling for income (both happiness and debt are positively related to income)
How can spurious correlations and masked relationships be detected?
By doing multiple linear regression
partial correlation
interpretation of the ß
Interpretation of the ß = standardized regression coefficient: A one unit increase in X so a 1 SD increase in X leads to an e.g. .546 units SD in Y.
F-test
The F-test of overall significance indicates whether your linear regression model provides a better fit to the data than a model that contains no independent variables.
How can you evaluate if the value of the regression coefficients b are significantly different from 0?
t-test
How much variance in the outcome variable
is accounted for by the predictor? Which test?
R-squared
What can you do if there is a nonlinear relationship between DV and IV?
add a quadratic component.
What is a lack of multicollinearity?
Overlap among predictors should not be too large (i.e., there should be no perfect linear relationship between two or more predictors)
What happens under multicollinearity?
Under multicollinearity, the regression coefficients may be unstable (i.e., it will be difficult to assess the individual importance of a predictor) and their standard errors large
What is a problematic pearson correlatino for multicollinearity?
r > .8
What is the tolerance in multicollinearity?
What tolerance is a serious problem?
A small tolerance is problematic like .1 (.02 is a potential problem)
What is the VIF
Variance Inflation Factor = 1/ Tolerance
- largest VIF should not be greater than 10
- average should not be much greater than 1
What can you do if there is an indication for multicollinearity?
Consider dropping redundant predictors.
In MLR how many observations per predictor?
min 10
What should be observations N exceed the # of predictors by
at least 50
Does the recommended sample size depend on purpose of analysis?
Yes.
- if goal is to test model overall: 50 + 8* # predictors
- if goal is to test individual predictors: 104 + # predictors
How to determine correct sample size
power analysis in the program
What is the forward regression method in exploratory analysis?
Stat with predictor that correlates most strongly with outcome variable, then add predictors that yield largest improvement
Are there standardized coefficients ß for dummy-coded predictors?
no. Only for continous predictors
3 conditions in mediation analysis
1) Is there a significant relationship between independent variable and mediator (a)?
2) Is there a significant relationship between mediator and dependent variable (b)?
3) Is there a significant relationship between independent and dependent variable (c)?
Key analysis in mediation analysis
Key analysis: Is regression weight c reduced when mediator and independent variable are used simultaneously to predict the dependent variable (c*)?
